Journal articles on the topic 'Hydrodynamic nonlinearities'
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Giorgi, Giuseppe, and John V. Ringwood. "Articulating Parametric Nonlinearities in Computationally Efficient Hydrodynamic Models." IFAC-PapersOnLine 51, no. 29 (2018): 56–61. http://dx.doi.org/10.1016/j.ifacol.2018.09.469.
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Mockutė, Agota, Enzo Marino, Claudio Lugni, and Claudio Borri. "Comparison of Nonlinear Wave-Loading Models on Rigid Cylinders in Regular Waves." Energies 12, no. 21 (October 23, 2019): 4022. http://dx.doi.org/10.3390/en12214022.
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Monopiles able to support very large offshore wind turbines are slender structures susceptible to nonlinear resonant phenomena. With the aim to better understand and model the wave-loading on these structures in very steep waves where ringing occurs and the numerical wave-loading models tend to lose validity, this study investigates the distinct influences of nonlinearities in the wave kinematics and in the hydrodynamic loading models. Six wave kinematics from linear to fully nonlinear are modelled in combination with four hydrodynamic loading models from three theories, assessing the effects of both types of nonlinearities and the wave conditions where each type has stronger influence. The main findings include that the nonlinearities in the wave kinematics have stronger influence in the intermediate water depth, while the choice of the hydrodynamic loading model has larger influence in deep water. Moreover, finite-depth FNV theory captures the loading in the widest range of wave and cylinder conditions. The areas of worst prediction by the numerical models were found to be the largest steepness and wave numbers for second harmonic, as well as the vicinity of the wave-breaking limit, especially for the third harmonic. The main cause is the non-monotonic growth of the experimental loading with increasing steepness due to flow separation, which leads to increasing numerical overpredictions since the numerical wave-loading models increase monotonically.
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Viana, Carlos Alberto Alves, Diogo Stuani Alves, and Tiago Henrique Machado. "Linear and Nonlinear Performance Analysis of Hydrodynamic Journal Bearings with Different Geometries." Applied Sciences 12, no. 7 (March 22, 2022): 3215. http://dx.doi.org/10.3390/app12073215.
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In rotor dynamics, a traditional way of representing the dynamics of hydrodynamic bearings is using stiffness/damping coefficients. It is thus necessary to carry out a linearization of hydrodynamic forces around the shaft’s equilibrium position. However, hydrodynamic bearings have highly nonlinear nature, depending on operating conditions. Therefore, this paper discusses the applicability of these linear/nonlinear approaches using a computational model of the rotating system, where the finite element method is used for rotor modelling and the finite volume method for bearing calculation. The main goal is to investigate the boundaries for linear approximation of the hydrodynamic forces present in lobed hydrodynamic bearings, with the system operating under high loading conditions. Several numerical simulations were performed varying preload parameter and rotating speed. A comparison of the system’s responses, in time domain (shaft orbits) and frequency domain (full spectrum), is made for linear and nonlinear models. Results showed that trilobed bearings are more susceptible to nonlinearities, even in situations of smaller vibration amplitudes, while elliptical bearings are sensitive only under larger vibration amplitudes. These analyses are of great importance for mapping the influence of nonlinearities in different types of lobed hydrodynamic bearings with fixed geometry, varying the preload parameter to verify the influence on the system’s dynamic response. This study is important and serves as the basis for cases of monitoring and fault diagnosis (in the field of structural health monitoring) since it is crucial to distinguish what would be a fault signature or a standard nonlinear effect created by the use of hydrodynamic bearings.
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Huang, Yifeng, and Paul D. Sclavounos. "Nonlinear Ship Motions." Journal of Ship Research 42, no. 02 (June 1, 1998): 120–30. http://dx.doi.org/10.5957/jsr.1998.42.2.120.
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A nonlinear numerical method has been developed to compute motion responses for a ship traveling in steep ambient waves. The method is based on an approximate theory and is an extension to a well-established linear time-domain numerical method. The nonlinear solution is found to be greatly improved over the classical linear and quasi-nonlinear solutions, in comparison to experimental measurements for conventional commercial ships. Through this study, it is also demonstrated that the free surface hydrodynamic nonlinearities are at least as important as, if not more than, the hydrostatic and Froude-Krylov nonlinearities. Stability, consistency and convergence for the nonlinear method are also addressed.
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Ande, Raghu, Stefanie Gutschmidt, and Mathieu Sellier. "Non-linear finite-amplitude oscillations of the large beam arrays oscillating in viscous fluids." Journal of Applied Physics 132, no. 17 (November 7, 2022): 174904. http://dx.doi.org/10.1063/5.0106293.
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Over the past decade, several studies have been conducted on a single and multiple oscillating thin cantilever beams in an unbounded viscous fluid. With an increase in the applications of large array oscillators in a fluid environment for fields like medicine, biology, and energy harvesting devices, it is crucial to understand the nature of the surrounding fluid dynamics. In this present study, we perform a two-dimensional computational fluid dynamics (CFD) analysis of an array of beams oscillating in an unbounded viscous fluid. The two-dimensional Navier Stokes and continuity equations are solved to investigate the hydrodynamic forces exerted on the array members from interaction with the fluid environment. A complex hydrodynamic function is proposed here to represent the distributed hydrodynamic loading experienced by the oscillating beams. Results suggest that there is an increase in viscous damping with an increase in the size of the array. In addition, the nonlinearities become dominant when an array of beams is subjected to large amplitude oscillations. The number of beams in an array determines the overall hydrodynamics and the array effect. CFD analysis can predict the non-linearities unlike boundary integral method (BIM) approach, which is limited for low amplitudes. The results from the full Navier–Stokes simulations compared favorably with results using the BIM for the time-harmonic linearized Stokes equations.
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Abroug, Iskander, Nizar Abcha, Fahd Mejri, Emma Imen Turki, and Elena Ojeda. "The Hydrodynamic Behavior of Vortex Shedding behind Circular Cylinder in the Presence of Group Focused Waves." Fluids 7, no. 1 (December 22, 2021): 4. http://dx.doi.org/10.3390/fluids7010004.
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Vortex shedding behind an elastically mounted circular cylinder in the presence of group focused waves propagating upstream was investigated using a classical approach (time series and FFT) and nonclassical approach (complex 2D Morlet wavelets). Wavelet analysis emerged as a novel solution in this regard. Our results include wave trains with different nonlinearities propagating in different water depths and derived from three types of spectra (Pierson–Moskowitz, JONSWAP (γ = 3.3 or γ = 7)). It was found that the generated wave trains could modify regimes of shedding behind the cylinder, and subharmonic frequency lock-in could arise in particular situations. The occurrence of a lock-in regime in the case of wave trains propagating in intermediate water locations was shown experimentally even for small nonlinearities. Moreover, the application of time-localized wavelet analysis was found to be a powerful approach. In fact, the frequency lock-in regime and its duration could be readily identified from the wavelet-based energy and its corresponding ridges.
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Krasavin, Alexey V., Pavel Ginzburg, and Anatoly V. Zayats. "Free-electron Optical Nonlinearities in Plasmonic Nanostructures: A Review of the Hydrodynamic Description." Laser & Photonics Reviews 12, no. 1 (December 13, 2017): 1700082. http://dx.doi.org/10.1002/lpor.201700082.
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DIAZ-GUILERA, ALBERT. "NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONS AND SELF-ORGANIZED CRITICALITY." Fractals 01, no. 04 (December 1993): 963–67. http://dx.doi.org/10.1142/s0218348x93001039.
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Several nonlinear stochastic differential equations have been proposed in connection with self-organized critical phenomena. Due to the threshold condition involved in its dynamic evolution, an infinite number of nonlinearities arise in a hydrodynamic description. We study two models with different noise correlations which make all nonlinear contributions to be equally relevant below the upper critical dimension. The asymptotic values of the critical exponents are estimated from a systematic expansion in the number of coupling constants by means of the dynamic renormalization group.
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Gong, Yihui, Lin Li, Shengbo Qi, Changbin Wang, and Dalei Song. "Enhanced disturbance observer-based robust yaw servo control for ROVs with multi-vector propulsion." Industrial Robot: the international journal of robotics research and application 48, no. 3 (April 6, 2021): 366–77. http://dx.doi.org/10.1108/ir-09-2020-0184.
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Purpose A novel proportional integral derivative-extended state disturbance observer-based control (PID-ESDOBC) algorithm is proposed to solve the nonlinear hydrodynamics, parameters perturbation and external disturbance in yaw control of remote operated vehicles (ROVs). The effectiveness of PID-ESDOBC is verified through the experiments and the results indicate that the proposed method can effectively track the desired attitude and attenuate the external disturbance. Design/methodology/approach This study fully investigates the hydrodynamic model of ROVs and proposes a control-oriented hydrodynamic state space model of ROVs in yaw direction. Based on this, this study designs the PID-ESDOBC controller, whose stability is also analyzed through Kharitonov theorem and Mikhailov criterion. The conventional proportional-integral-derivative (PID) and active disturbance rejection control (ADRC) are compared with our method in our experiment. Findings In this paper, the authors address the nonlinear hydrodynamics, parameters perturbation and external disturbance problems of ROVs with multi-vector propulsion by using PID-ESDOBC control scheme. The advantage is that the nonlinearities and external disturbance can be estimated accurately and attenuate promptly without requiring the precise model of ROVs. Compared to PID and ADRC, both in overshoot and settling time, the improvement is 2X on average compared to conventional PID and ADRC in the pool experiment. Research limitations/implications The delays occurred in the control process can be solved in the future work. Practical implications The attitude control is a kernel problem for ROVs. A precise kinematic and dynamic model for ROVs and an advanced control system are the key factors to obtain the better maneuverability in attitude control. The PID-ESDOBC method proposed in this paper can effectively attenuate nonlinearities and external disturbance, which leads to a quick response and good tracking performance to baseline controller. Social implications The PID-ESDOBC algorithm proposed in this paper can be ensure the precise and fast maneuverability in attitude control of ROVs or other underwater equipment operating in the complex underwater environment. In this way, the robot can better perform undersea work and tasks. Originality/value The dynamics of the ROV and the nominal control model are investigated. A novel control scheme PID-ESDOBC is proposed to achieve rapidly yaw attitude tracking and effectively reject the external disturbance. The robustness of the controller is also analyzed which provides parameters tuning guidelines. The effectiveness of the proposed controller is experimental verified with a comparison by conventional PID, ADRC.
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Matthaeus, William H., Gary P. Zank, and Sean Oughton. "Phenomenology of hydromagnetic turbulence in a uniformly expanding medium." Journal of Plasma Physics 56, no. 3 (December 1996): 659–75. http://dx.doi.org/10.1017/s0022377800019516.
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A simple phenomenology is developed for the decay and transport of turbulence in a constant-speed, uniformly expanding medium. The fluctuations are assumed to be locally incompressible, and either of the hydrodynamic or non-Alfvénic magnetohydrodynamic (MHD) type. In order to represent local effects of nonlinearities, a simple model of the Kaármá-Dryden type for locally homogeneous turbulent decay is adopted. A detailed discussion of the parameters of this familiar one-point hydrodynamic closure is given, which has been shown recently to be applicable to non-Alfvénic MHD as well. The effects of the large-scale flow and expansion are incorporated using a two-scale approach, in which assumptions of particular turbulence symmetries provide simplifications. The derived model is tractable and provides a basis for understanding turbulence in the outer heliosphere, as well as in other astrophysical applications.
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ANDREEV, P. A. "FIRST PRINCIPLES DERIVATION OF NLS EQUATION FOR BEC WITH CUBIC AND QUINTIC NONLINEARITIES AT NONZERO TEMPERATURE: DISPERSION OF LINEAR WAVES." International Journal of Modern Physics B 27, no. 06 (February 5, 2013): 1350017. http://dx.doi.org/10.1142/s0217979213500173.
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We present a derivation of the quantum hydrodynamic (QHD) equations for neutral bosons. We consider the short-range interaction between particles. This interaction consist of a binary interaction U( ri, rj) and a three-particle interaction (TPI) U( ri, rj, rk) and the last one does not include binary interaction between particles. From QHD equations for Bose–Einstein condensate we derive a nonlinear Schrödinger equation. This equation was derived for zero temperature and contains the nonlinearities of the third and the fifth degree. Explicit form of the constant of the TPI is obtained. First of all, developed method we used for studying of dispersion of the linear waves. Dispersion characteristics of the linear waves are compared for different particular cases. We make comparison of the two-particle interaction in the third order by the interaction radius (TOIR) and TPI at the zero temperature. We consider influence of the temperature on the dispersion of the elementary excitations. For this aim we derive a system of the QHD equations at nonzero temperature. Obtained system of equation is an analog of the well-known two-fluid hydrodynamics. Moreover, it is generalization of the two-fluid hydrodynamics equations due to TPI. Explicit expressions of the velocities for the first and the second sound via the concentration of superfluid and noncondensate components is calculated.
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Akhtar, Imran, and Mohammad Elyyan. "Higher-Order Spectral Analysis to Identify Quadratic Nonlinearities in Fluid-Structure Interaction." Mathematical Problems in Engineering 2018 (2018): 1–14. http://dx.doi.org/10.1155/2018/2394124.
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Hydrodynamic forces on a structure are the manifestation of fluid-structure interaction. Since this interaction is nonlinear, these forces consist of various frequencies: fundamental, harmonics, excitation, sum, and difference of these frequencies. To analyze this phenomenon, we perform numerical simulations of the flow past stationary and oscillating cylinders at low Reynolds numbers. We compute the pressure, integrate it over the surface, and obtain the lift and drag coefficients for the two configurations: stationary and transversely oscillating cylinders. Higher-order spectral analysis is performed to investigate the nonlinear interaction between the forces. We confirmed and investigated the quadratic coupling between the lift and drag coefficients and their phase relationship. We identify additional frequencies and their corresponding energy present in the flow field that appear as the manifestation of quadratic nonlinear interaction.
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Hirdaris, S. E., Y. Lee, G. Mortola, A. Incecik, O. Turan, S. Y. Hong, B. W. Kim, et al. "The influence of nonlinearities on the symmetric hydrodynamic response of a 10,000 TEU Container ship." Ocean Engineering 111 (January 2016): 166–78. http://dx.doi.org/10.1016/j.oceaneng.2015.10.049.
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De Luca, Federico, Michele Ortolani, and Cristian Ciracì. "Free electron harmonic generation in heavily doped semiconductors: the role of the materials properties." EPJ Applied Metamaterials 9 (2022): 13. http://dx.doi.org/10.1051/epjam/2022011.
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Heavily doped semiconductors have emerged as low-loss and tunable materials for plasmonics at mid-infrared frequencies. We analyze the nonlinear optical response of free electrons and show how nonlinear optical phenomena associated with high electron concentration are influenced by the intrinsic properties of semiconductors, namely background permittivity and effective mass. We apply our recently developed hydrodynamic description that takes into account nonlinear contributions up to the third order, usually negligible for noble metals, to compare third-harmonic generation from InP, Ge, GaAs, Si, ITO and InSb. We show how free electron nonlinearities may be enhanced with a proper choice of the semiconductor.
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Kumar, Punit, and Nisha Singh Rathore. "Laser beam guiding in partially stripped magnetized quantum plasma." Laser Physics 32, no. 1 (December 14, 2021): 016002. http://dx.doi.org/10.1088/1555-6611/ac3ee7.
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Abstract Relativistic and ponderomotive nonlinearities arising by the passage of a linearly polarized laser beam through a partially stripped magnetized quantum plasma are analyzed. The interaction formalism has been developed using the recently developed quantum hydrodynamic model. The effects associated with the Fermi pressure, quantum Bohm potential and electron spin have been incorporated. A nonparaxial, non-linear wave equation has been obtained by the use of source dependent expansion technique and spot size has been evaluated. The nonlinear relativistic self-focusing tends to focus the beam while the ponderomotive nonlinearity tends to defocus. The effect of magnetization and quantum effects on the spot size and the beam power have been studied.
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Reid, R. E., and J. Y. Zheng. "Time Domain Simulation of Ship Steering Gear Control Systems." Journal of Energy Resources Technology 108, no. 1 (March 1, 1986): 84–90. http://dx.doi.org/10.1115/1.3231246.
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Considering the effects of oil compressibility, leakage, hydrodynamic damping and friction, in addition to other nonlinearities, such as bang-bang relay, pump saturation and limiters of oil pressure and pump flow, the performance of five different types of ship steering gear control systems are examined using digital computer simulation techniques. Three of the controllers examined are “bang-bang” controllers, while the remaining two are “analog”. The behavior and performance of the various systems on three ship configurations are compared. It is shown that the analog steering gear controllers can be expected to demonstrate superior performance of the ship/steering system in calm water operations.
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Hicks, J. D., A. W. Troesch, and C. Jiang. "Simulation and Nonlinear Dynamics Analysis of Planing Hulls." Journal of Offshore Mechanics and Arctic Engineering 117, no. 1 (February 1, 1995): 38–45. http://dx.doi.org/10.1115/1.2826989.
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The high speeds, small trim angles, and shallow drafts of planing hulls produce large changes in vessel wetted surface which, in turn, lead to significant hydrodynamic and dynamic nonlinearities. Due to the complex nonlinearities of this type of craft, naval architects and planing boat designers tend to rely upon experimental tests or simulation for guidance. In order for simulation to be an effective design tool, a fundamental understanding of the system’s dynamic characteristics is required. This paper describes a developing methodology by which the necessary insight may be obtained. A demonstration of the combined use of modern methods of dynamical system analysis with simulation is given in the evaluation of the vertical motions of a typical planing hull. Extending the work of Troesch and Hicks (1992) and Troesch and Falzarano (1993), the complete nonlinear hydrodynamic force and moment equations of Zarnick (1978) are expanded in a multi-variable Taylor series. As a result, the nonlinear integro-differential equations of motion are replaced by a set of highly coupled, ordinary differential equations with constant coefficients, valid through third order. Closed-form, analytic expressions are available for the coefficients (Hicks, 1993). Numerical examples for all first-order and some second-order terms are presented. Once completely determined, the coefficient matrices will serve as input to path following or continuation methods (e.g., Seydel, 1988) where heave and pitch magnification curves can be generated, allowing the entire system response to be viewed. The branching behavior of the solutions resulting from a variation of the center of gravity is examined in detail. These studies of the second-order accurate model show the potential of the method to identify areas of critical dynamic response, which in turn can be verified and explored further through the use of the simulator.
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Giorgi, Giuseppe, Josh Davidson, Giuseppe Habib, Giovanni Bracco, Giuliana Mattiazzo, and Tamás Kalmár-Nagy. "Nonlinear Dynamic and Kinematic Model of a Spar-Buoy: Parametric Resonance and Yaw Numerical Instability." Journal of Marine Science and Engineering 8, no. 7 (July 9, 2020): 504. http://dx.doi.org/10.3390/jmse8070504.
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Mathematical models are essential for the design and control of offshore systems, to simulate the fluid–structure interactions and predict the motions and the structural loads. In the development and derivation of the models, simplifying assumptions are normally required, usually implying linear kinematics and hydrodynamics. However, while the assumption of linear, small amplitude motion fits traditional offshore problems, in normal operational conditions (it is desirable to stabilize ships, boats, and offshore platforms), large motion and potential dynamic instability may arise (e.g., harsh sea conditions). Furthermore, such nonlinearities are particularly evident in wave energy converters, as large motions are expected (and desired) to enhance power extraction. The inadequacy of linear models has led to an increasing number of publications and codes implementing nonlinear hydrodynamics. However, nonlinear kinematics has received very little attention, as few models yet consider six degrees of freedom and large rotations. This paper implements a nonlinear hydrodynamic and kinematic model for an archetypal floating structure, commonplace in offshore applications: an axisymmetric spar-buoy. The influence of nonlinear dynamics and kinematics causing coupling between modes of motion are demonstrated. The nonlinear dynamics are shown to cause parametric resonance in the roll and pitch degrees of freedom, while the nonlinear kinematics are shown to potentially cause numerical instability in the yaw degree of freedom. A case study example is presented to highlight the nonlinear dynamic and kinematic effects, and the importance of including a nominal restoring term in the yaw DoF presented.
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Liut, Daniel A., Kenneth M. Weems, and Tin-Guen Yen. "A Quasi-three-dimensional Finite-volume Shallow Water Model for Green Water on Deck." Journal of Ship Research 57, no. 03 (September 1, 2013): 125–40. http://dx.doi.org/10.5957/jsr.2013.57.3.125.
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A quasi-three-dimensional hydrodynamic model is presented to simulate shallow water phenomena. The method is based on a finite-volume approach designed to solve shallow water equations in the time domain. The nonlinearities of the governing equations are considered. The methodology can be used to compute green water effects on a variety of platforms with six-degrees-of-freedom motions. Different boundary and initial conditions can be applied for multiple types of moving platforms, like a ship's deck, tanks, etc. Comparisons with experimental data are discussed. The shallow water model has been integrated with the Large Amplitude Motions Program to compute the effects of green water flow over decks within a time-domain simulation of ship motions in waves. Results associated to this implementation are presented.
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Tomera, Mirosław. "Nonlinear controller design of a ship autopilot." International Journal of Applied Mathematics and Computer Science 20, no. 2 (June 1, 2010): 271–80. http://dx.doi.org/10.2478/v10006-010-0020-8.
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Nonlinear controller design of a ship autopilotThe main goal here is to design a proper and efficient controller for a ship autopilot based on the sliding mode control method. A hydrodynamic numerical model of CyberShip II including wave effects is applied to simulate the ship autopilot system by using time domain analysis. To compare the results similar research was conducted with the PD controller, which was adapted to the autopilot system. The differences in simulation results between two controllers are analyzed by a cost function composed of a heading angle error and rudder deflection either in calm water or in waves. Simulation results show the effectiveness of the method in the presence of nonlinearities and disturbances, and high performance of the proposed controller.
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Ismail, Zool H., and Matthew W. Dunnigan. "NonlinearH∞Optimal Control Scheme for an Underwater Vehicle with Regional Function Formulation." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/732738.
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A conventional region control technique cannot meet the demands for an accurate tracking performance in view of its inability to accommodate highly nonlinear system dynamics, imprecise hydrodynamic coefficients, and external disturbances. In this paper, a robust technique is presented for an Autonomous Underwater Vehicle (AUV) with region tracking function. Within this control scheme, nonlinearH∞and region based control schemes are used. A Lyapunov-like function is presented for stability analysis of the proposed control law. Numerical simulations are presented to demonstrate the performance of the proposed tracking control of the AUV. It is shown that the proposed control law is robust against parameter uncertainties, external disturbances, and nonlinearities and it leads to uniform ultimate boundedness of the region tracking error.
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Sawicki, Jerzy T., and T. V. V. L. N. Rao. "A Nonlinear Model for Prediction of Dynamic Coefficients in a Hydrodynamic Journal Bearing." International Journal of Rotating Machinery 10, no. 6 (2004): 507–13. http://dx.doi.org/10.1155/s1023621x04000508.
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This paper investigates the variation of nonlinear stiffness and damping coefficients in a journal orbit with respect to equilibrium position. The journal orbit is obtained by the combined solution of equations of motion and Reynolds equation. In the linearized dynamic analysis, dynamic pressure is written as a perturbation of static pressure and pressure gradients at equilibrium position. However, in order to obtain nonlinear dynamic coefficients about equilibrium position, the dynamic pressure gradients in the orbit are also written as the first order perturbation of static pressure gradients and higher order pressure gradients for displacement and velocity perturbations. The dynamic coefficients are functions of bearing displacement and velocity perturbations. The higher order pressure gradients at equilibrium position are evaluated at various eccentricity ratios and L/D ratios of 0.5 and 1.0. The variation of nonlinear dynamic coefficients is analyzed for three Sommerfeld numbers of a two-axial groove journal bearing under the action of an external synchronous load along and perpendicular to the radial journal load. Results indicate that the oil film nonlinearities affect the journal motion at lower eccentricity ratios (higher Sommerfeld numbers) with wide variation in stiffness and damping coefficients.
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RUDIN, SERGEY. "NON-LINEAR PLASMA OSCILLATIONS IN SEMICONDUCTOR AND GRAPHENE CHANNELS AND APPLICATION TO THE DETECTION OF TERAHERTZ SIGNALS." International Journal of High Speed Electronics and Systems 20, no. 03 (September 2011): 567–82. http://dx.doi.org/10.1142/s0129156411006866.
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The conduction channel of a semiconductor Field Effect Transistor (FET) or a heterostructure High Electron Mobility Transistor (HEMT) can act as a plasma wave resonator for density oscillations in electron gas, at frequencies significantly higher than the transistor cut-off frequency in a short channel device. The hydrodynamic model predicts a resonance response to electromagnetic radiation at the plasma oscillation frequency. In particular, the hydrodynamic nonlinearities produce a constant source-to-drain voltage when gate-to-channel voltage has a time-harmonic component. In the Dyakonov-Shur detector a short channel HEMT is used for the resonant tunable detection of terahertz radiation. Starting with the quasi-classical Boltzmann equation for a semiconductor and graphene channels, we derived the viscous hydrodynamic model with temperature dependent transport coefficients in both cases. We evaluated the detector response function and in the case of semiconductor channel we also obtained the temperature dependence of the quality factor of the plasma resonance. The present treatment extends the theory of Dyakonov-Shur plasma resonator and detector to account for the temperature dependence of viscosity. In the case of semiconductor channels the treatment here also includes the energy balance equation into the analysis. The numerical results are given in cases of GaAs and GaN channels. We showed that in high mobility semiconductor channels at low temperature the quality of the resonance is strongly limited by the viscosity of the electron fluid. In the case of graphene channel the hydrodynamic model derived here accounts both for electrons and holes, and includes the related diffusion currents. When the gate voltage is a few volts, the Fermi temperature of the electron-hole liquid is considerably higher than the room temperature. In such cases the diffusion currents can be ignored, and from the simplified hydrodynamic equations we evaluated the non-linear response of the plasma in graphene channel to the external perturbation. The results are of interest in potential application to graphene based detectors due to potential of obtaining a channel with the room temperature mobility considerably higher than the mobility in semiconductor channels.
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Troesch, Armin W., and Jeffrey M. Falzarano. "Modern Nonlinear Dynamical Analysis of Vertical Plane Motion of Planing Hulls." Journal of Ship Research 37, no. 03 (September 1, 1993): 189–99. http://dx.doi.org/10.5957/jsr.1993.37.3.189.
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When operating in a seaway, high-speed planing hulls exhibit strong nonlinearities. This paper investigates the vertical plane dynamic stability and response associated with such craft. Explicit expressions for the hydrodynamic forces are developed and modern methods of dynamical systems analysis are applied. An illustrative example is given in which the forced and unforced motions are examined. Parameter studies relating to the following topics are made: the onset of porpoising, the magnitude of motions while porpoising, and forced motions due to regular waves. It is found that while nonlinear effects can reduce the response over that predicted by linear theory, these same effects can also be responsible for sudden extreme behavior. The method described here is another tool that designers and operators can use to provide a more comfortable and safer vessel performance.
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Fox, Rodney O. "On multiphase turbulence models for collisional fluid–particle flows." Journal of Fluid Mechanics 742 (February 21, 2014): 368–424. http://dx.doi.org/10.1017/jfm.2014.21.
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AbstractStarting from a kinetic theory (KT) model for monodisperse granular flow, the exact Reynolds-averaged (RA) equations are derived for the particle phase in a collisional fluid–particle flow. The corresponding equations for a constant-density fluid phase are derived from a model that includes drag and buoyancy coupling with the particle phase. The fully coupled macroscale/hydrodynamic model, rigorously derived from a kinetic equation for the particles, is written in terms of the particle-phase volume fraction, the particle-phase velocity and the granular temperature (or total granular energy). As derived from the hydrodynamic model, the RA turbulence model solves for the RA particle-phase volume fraction, the phase-averaged (PA) particle-phase velocity, the PA granular temperature and the PA turbulent kinetic energy of the particle phase. Thus, unlike in most previous derivations of macroscale turbulence models for moderately dense granular flows, a clear distinction is made between the PA granular temperature $\Theta _\textit {p}$, which appears in the KT constitutive relations, and the particle-phase turbulent kinetic energy $k_\textit {p}$, which appears in the turbulent transport coefficients. The exact RA equations contain unclosed terms due to nonlinearities in the hydrodynamic model and we briefly discuss the available closures for these terms. Finally, we demonstrate by comparing model predictions with direct numerical simulation results that even for non-collisional fluid–particle flows it is necessary to provide separate models for $\Theta _\textit {p}$ and $k_\textit {p}$ in order to correctly account for the effect of the particle Stokes number and mass loading.
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Müller, Maximilian, Malte Woidt, Matthias Haupt, and Peter Horst. "Challenges of fully-coupled high-fidelity ditching simulations." MATEC Web of Conferences 233 (2018): 00020. http://dx.doi.org/10.1051/matecconf/201823300020.
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An important element of the process of aircraft certification is the demonstration of the crashworthiness of the structure in the event of an emergency landing on water, also referred to as ditching. Novel numerical simulation methods that incorporate the interaction between fluid and structure open up a promising way to model ditching in full scale. This study presents a numerical framework for the simulation of ditching on a high–fidelity level. A partitioned approach that combines a finite volume hydrodynamic fluid solver as well as an finite element structural solver is implemented using a Python-based distributed coupling environment [1]. High demands are placed both on the fluid and the structural solver. The fluid solver needs to account for hydrodynamic effects such as cavitation in order to correctly compute the ditching loads acting on the aircraft structure. In the structural model, the highly localized damage induces nonlinearities and large differences in model scale. In order to reduce the computational effort a reduced order model is used to model the failure of fuselage frames. The fluid-structure coupling requires an explicit coupling scheme. It is shown that the standard Dirichlet-Neumann approach exhibits unstable behaviour if a strong added-mass effect is present, as is the case in aircraft ditching. This indicates a need for methods other than the standard Dirichlet-Neumann approach [2].
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Zhao, Yong. "Finite Element Modeling and Analysis of Nonlinear Impact and Frictional Motion Responses Including Fluid—Structure Coupling Effects." Shock and Vibration 4, no. 5-6 (1997): 311–25. http://dx.doi.org/10.1155/1997/496945.
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A nonlinear three dimensional (3D) single rack model and a nonlinear 3D whole pool multi-rack model are developed for the spent fuel storage racks of a nuclear power plant (NPP) to determine impacts and frictional motion responses when subjected to 3D excitations from the supporting building floor. The submerged free standing rack system and surrounding water are coupled due to hydrodynamic fluid-structure interaction (FSI) using potential theory. The models developed have features that allow consideration of geometric and material nonlinearities including (1) the impacts of fuel assemblies to rack cells, a rack to adjacent racks or pool walls, and rack support legs to the pool floor; (2) the hydrodynamic coupling of fuel assemblies with their storing racks, and of a rack with adjacent racks, pool walls, and the pool floor; and (3) the dynamic motion behavior of rocking, twisting, and frictional sliding of rack modules. Using these models 3D nonlinear time history dynamic analyses are performed per the U.S. Nuclear Regulatory Commission (USNRC) criteria. Since few such modeling, analyses, and results using both the 3D single and whole pool multiple rack models are available in the literature, this paper emphasizes description of modeling and analysis techniques using the SOLVIA general purpose nonlinear finite element code. Typical response results with different Coulomb friction coefficients are presented and discussed.
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Shi, Chun Xia, Marco Domaneschi, and Luca Martinelli. "Nonlinear Behaviors of Submerged Floating Tunnels under Seismic Excitation." Applied Mechanics and Materials 226-228 (November 2012): 1124–27. http://dx.doi.org/10.4028/www.scientific.net/amm.226-228.1124.
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The Submerged Floating Tunnels are one new type of infrastructure, representing a challenge in structural engineering, both on the theoretical and operational fields. In this paper, a 3D finite element analysis procedure is developed accounting for material and geometrical nonlinearities, soil-structure interaction and multiple-support seismic excitation. A comparison between dynamic response in case of elastic and inelastic material behavior of the anchor bars is given, which shows the beneficial effect of this source of energy dissipation. Furthermore, the effects of introducing dissipation devices for restraining the tunnel axial motion have been investigated as well. Besides this, the earthquake transmission through water (seaquake) is here introduced as an additional hydrodynamic loading on the tunnel. The ensuing increase of loading in the tunnel indicates that a significant role is played by this loading source and highlights the need of further investigations on seaquake effects.
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Jiao, Jialong, Yong Jiang, Hao Zhang, Chengjun Li, and Chaohe Chen. "Predictions of Ship Extreme Hydroelastic Load Responses in Harsh Irregular Waves and Hull Girder Ultimate Strength Assessment." Applied Sciences 9, no. 2 (January 10, 2019): 240. http://dx.doi.org/10.3390/app9020240.
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In this paper, the hydroelastic motion and load responses of a large flexible ship sailing in irregular seaways are predicted and the hull girder ultimate strength is subsequently evaluated. A three-dimensional time-domain nonlinear hydroelasticity theory is developed where the included nonlinearities are those arising from incident wave force, hydrostatic restoring force and slamming loads. The hull girder structure is simplified as a slender Timoshenko beam and fully coupled with the hydrodynamic model in a time domain. Segmented model towing-tank tests are then conducted to validate the proposed hydroelasticity theory. In addition, short-term and long-term predictions of ship responses in irregular seaways are conducted with the help of the developed hydroelastic code in order to determine the extreme design loads. Finally, a simplified strength-check equation is proposed, which will provide significant reference and convenience for ship design and evaluation. The hull girder ultimate strength is assessed by both the improved Rule approach and direct calculation.
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Lin, Ray-Qing, and Weijia Kuang. "A fully nonlinear, dynamically consistent numerical model for solid-body ship motion. I. Ship motion with fixed heading." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2128 (August 25, 2010): 911–27. http://dx.doi.org/10.1098/rspa.2010.0310.
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In this paper, we describe the details of our numerical model for simulating ship solid-body motion in a given environment. In this model, the fully nonlinear dynamical equations governing the time-varying solid-body ship motion under the forces arising from ship–wave interactions are solved with given initial conditions. The net force and moment (torque) on the ship body are directly calculated via integration of the hydrodynamic pressure over the wetted surface and the buoyancy effect from the underwater volume of the actual ship hull with a hybrid finite-difference/finite-element method. Neither empirical nor free parametrization is introduced in this model, i.e. no a priori experimental data are needed for modelling. This model is benchmarked with many experiments of various ship hulls for heave, roll and pitch motion. In addition to the benchmark cases, numerical experiments are also carried out for strongly nonlinear ship motion with a fixed heading. These new cases demonstrate clearly the importance of nonlinearities in ship motion modelling.
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Suzuki, H., and K. Yoshida. "Three-Dimensional Nonlinear Dynamic Analysis Method of Underwater Line Structure and Its Validation." Journal of Offshore Mechanics and Arctic Engineering 114, no. 3 (August 1, 1992): 139–45. http://dx.doi.org/10.1115/1.2919965.
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A 3-dimensional nonlinear method for analysis of underwater line structures is presented. This analysis method is formulated by the finite element method, and dynamic behavior of the structures is solved in time domain. The motion equations are solved by Newmark time integration scheme. The method can handle all nonlinearities relating to the dynamic motion of the line structures such as hydrodynamic nonlinearity, geometrical nonlinearity, nonlinear boundary condition, and so on. The Newton method is employed to improve stability of the iteration solution when a dynamic equilibrium condition is obtained. The computational method has been verified through comparison with model tests conducted by the authors. These tests required the development of a general-purpose ultrasonic ranging system, which is described briefly. Usually high accuracy is required for the ranging system because of the small size of models used in the basin test, and high frequency is employed. By this system, coordinates of maximum 16 points can be determined at an accuracy of 1 mm.
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Elmoselhy, Salah A. M., Waleed F. Faris, and Hesham A. Rakha. "Validated Analytical Modeling of Eccentricity and Dynamic Displacement in Diesel Engines with Flexible Crankshaft." Energies 15, no. 16 (August 22, 2022): 6083. http://dx.doi.org/10.3390/en15166083.
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In spite of the fact that the flexibility of the crankshaft of diesel engines exhibits notable nonlinearities, analytical modeling of such nonlinearities is not yet realized. The present study thus analytically models the effect of eccentricity on flexible crankshaft and piston secondary motion. The eccentricity of the crankshaft is modeled as the summation of the hydrodynamic eccentricity and the dynamic mass eccentricity of the crankshaft. The study also models the absolute value of the vibrational dynamic displacement of the center of the crankshaft. The paper proves that such dynamic displacement of the center of the crankshaft is sensitive to the changes in its independent variables. It was found that the most influential parameters on the dynamic displacement of the center of the crankshaft due to vibration are the natural frequency and the eccentricity of the crankshaft. The modeling of the dynamic displacement in a flexible crankshaft was validated using a case study based on the eccentricity of the crankshaft showing a relative error of 4%, which is less than the relative error in the CMEM and GT-Power. Furthermore, the analytical modeling of the dynamic displacement in the flexible crankshaft was validated using another case study based on fatigue analysis of the crankshaft showing a relative error of 9%, which is less than that the relative error in Newman’s model of diesel engine fuel consumption and Lansky’s model of diesel engine cylinders. The paper also presents a proposed approach of fatigue failure analysis for vehicular dynamic components and presents a proposed nanostructure of crankshafts for improving such fatigue performance. The developed models would help develop efficient diesel engines and help prolong their service life.
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Choy, F. K., M. J. Braun, and Y. Hu. "Nonlinear Effects in a Plain Journal Bearing: Part 1—Analytical Study." Journal of Tribology 113, no. 3 (July 1, 1991): 555–61. http://dx.doi.org/10.1115/1.2920659.
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Hydrodynamic/hydrostatic journal bearings have been widely used in various types of high speed rotating machinery. For space applications, the issue of using cryogenic fluids as working lubricants has steadily gained in significance. The primary goal of this paper is to model the nonlinearities that occur in a hydrodynamic journal bearing with both cryogenic and oil lubricants. Results will be examined through bearing fluid film pressure distribution and bearing linear and nonlinear stiffness characteristics. The numerical model that couples a variable property Reynolds equation with the dynamics of the rotor is solved by means of a finite difference solution technique. The procedure for the fluid film pressure solution involves an iterative scheme that solves the Reynolds equation coupled with the equations of state for liquid oxygen (LO2). The pressure curve is then integrated to calculate bearing supporting forces. A two-dimensional Newton-Raphson iteration method is used to locate the journal equilibrium position from which both linear and nonlinear bearing stiffness are evaluated by means of the small perturbation technique. The effects of load on the linear/nonlinear plain journal bearing characteristics are analyzed and presented in a parametric form. The relationship between the accuracy of the linear solution and the various orders (3rd, 5th, and 7th power for ΔX) of the nonlinear approximation are also discussed. The validity of both linear and nonlinear solutions at various distances from the journal equilibrium position is also examined. A complete parametric study on the effects of load, temperature, operating speed, and shaft misalignment will be given in Part 2 of this paper.
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Behbahani-Nejad, M., and N. C. Perkins. "Numerical Analysis of Nonlinear Wave Propagation in Elastic Submerged Cables." Journal of Offshore Mechanics and Arctic Engineering 121, no. 2 (May 1, 1999): 116–25. http://dx.doi.org/10.1115/1.2830075.
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This paper analyzes the coupled nonlinear tangential-normal waves that propagate along underwater cable suspensions. Taken with the recently developed linear theory governing the in-plane structural waves (Behbahani-Nejad and Perkins, 1996) and an analysis of nonlinear out-of-plane waves for submerged cables (Behbahani-Nejad and Perkins, 1997), this investigation contributes further understanding toward a nonlinear three-dimensional theory for wave propagation along fluid-loaded cables. The nonlinearities present in the in-plane model render the cable/fluid model intractable by exact analytical methods. A numerical solution is pursued in this study using finite difference algorithms. To this end, an infinite cable domain is divided to two subdomains, namely an interior (finite computational) domain and exterior (infinite far-field) domain. Closed-form solutions for the approximate linear theory are employed for the far field in constructing nonreflecting boundary conditions for the computational domain. Numerical results highlight the governing role of nonlinear hydrodynamic drag for underwater cable suspensions. The numerical results further demonstrate that most analyses of cables in air are not useful for underwater cable applications.
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Tu, C. Y., and E. Marsch. "Transfer equations for spectral densities of inhomogeneous MHD turbulence." Journal of Plasma Physics 44, no. 1 (August 1990): 103–22. http://dx.doi.org/10.1017/s002237780001504x.
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On the basis of the dynamic equations governing the evolution of magneto-hydrodynamic fluctuations expressed in terms of Elsässer variables and of their correlation functions derived by Marsch and Tu, a new set of equations is presented here describing the evolutions of the energy spectrum e± and of the residual energy spectra eR and es of MHD turbulence in an inhomogeneous magnetofluid. The nonlinearities associated with triple correlations in these equations are analysed in detail and evaluated approximately. The resulting energy-transfer functions across wavenumber space are discussed. For e± they are shown to be approximately energy-conserving if the gradients of the flow speed and density are weak. New cascading functions are heuristically determined by an appropriate dimensional analysis and plausible physical arguments, following the standard phenomenology of fluid turbulence. However, for eR the triple correlations do not correspond to an ‘energy’ conserving process, but also represent a nonlinear source term for eR. If this source term can be neglected, the spectrum equations are found to be closed. The problem of dealing with the nonlinear source terms remains to be solved in future investigations.
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Hinch, E. J., and Ludwig C. Nitsche. "Nonlinear drift interactions between fluctuating colloidal particles: oscillatory and stochastic motions." Journal of Fluid Mechanics 256 (November 1993): 343–401. http://dx.doi.org/10.1017/s0022112093002812.
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In this work we consider how nonlinear hydrodynamic effects can lead to a mean force of interaction between two spheres of equal radius a undergoing translational fluctuations parallel or perpendicular to their line of centres. Motivated by amplitudes and Reynolds numbers characteristic of Brownian motion in colloidal systems, nonlinearities due to motion of the boundaries and to inertia throughout the fluid are treated as regular perturbations of the time-dependent Stokes equations. This formulation ultimately leads to a prescription for computing, at leading order, the time-average nonlinear force for the case of pure oscillatory modes – which represents the Fourier decomposition of more general motions. The associated hydrodynamic problems are solved numerically using a least-squares boundary singularity method. Frequency-dependent results over the whole spectrum are presented for a sphere-sphere gap equal to one radius; illustrative calculations are also carried out at other separations. Subsequently we extend the analysis of nonlinear drift to a Langevin equation formulation of the more complex problem of stochastic motion due to thermal fluctuations in the suspending fluid, i.e. Brownian motion. By integrating (numerically) over the spectrum of frequencies, we quantify how the mutual interactions of all translational disturbance modes give rise, on ensemble average, to a stochastic nonlinear force of interaction between the particles. It is particularly interesting that this net interaction – arising from a zero-mean random force – is of O(1) on the Brownian scale kT/a, even though it represents a small O(Re) correction at each frequency of pure oscillations. Finally, we discuss how the presence of stochastic nonlinear drift would lead to non-uniform equilibrium distributions of dilute colloidal suspensions, unless one adds to the random force in the Langevin equation a cancelling non-zero mean component.
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Haritos, N. "Peak Response Statistics of Vertical Cylinders in Two-Dimensional Irregular Waves." Journal of Offshore Mechanics and Arctic Engineering 118, no. 4 (November 1, 1996): 276–83. http://dx.doi.org/10.1115/1.2833916.
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When dealing with the probabilistic estimation of the peak response of an offshore structure dynamically responding under excitation by unidirectional irregular waves, it becomes apparent that nonlinearities introduced by the wave-structure interaction, and principally associated with the drag contribution of the Morison force model that has been traditionally used to describe this forcing, leads to non-Gaussian statistical properties of not only the forcing, but also the response. However, it is also apparent that for lightly damped structures, the response under certain circumstances can be very “narrow-banded,” and hence its statistical description would then approach the Gaussian form irrespective of whether the forcing associated with the response is itself highly non-Gaussian or otherwise. This paper treats both a numerical and experimental investigation of the peak response characteristics of compliant bottom-pivoted surface-piercing cylinders subjected to hydrodynamic excitation by unidirectional Pierson-Moskowitz (P-M) irregular waves and modeled as single-degree-of-freedom (SDOF) oscillators with a fixed “straight line” mode shape (the result of the bottom-pivoted support condition). Conditions under which the response can reasonably be approximated as Gaussian are identified via an upcrossing investigation for the likely peak response in a storm of a nominated period of duration.
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Wendt, Nielsen, Yu, Bingham, Eskilsson, Kramer, Babarit, et al. "Ocean Energy Systems Wave Energy Modelling Task: Modelling, Verification and Validation of Wave Energy Converters." Journal of Marine Science and Engineering 7, no. 11 (October 25, 2019): 379. http://dx.doi.org/10.3390/jmse7110379.
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The International Energy Agency Technology Collaboration Programme for Ocean Energy Systems (OES) initiated the OES Wave Energy Conversion Modelling Task, which focused on the verification and validation of numerical models for simulating wave energy converters (WECs). The long-term goal is to assess the accuracy of and establish confidence in the use of numerical models used in design as well as power performance assessment of WECs. To establish this confidence, the authors used different existing computational modelling tools to simulate given tasks to identify uncertainties related to simulation methodologies: (i) linear potential flow methods; (ii) weakly nonlinear Froude–Krylov methods; and (iii) fully nonlinear methods (fully nonlinear potential flow and Navier–Stokes models). This article summarizes the code-to-code task and code-to-experiment task that have been performed so far in this project, with a focus on investigating the impact of different levels of nonlinearities in the numerical models. Two different WECs were studied and simulated. The first was a heaving semi-submerged sphere, where free-decay tests and both regular and irregular wave cases were investigated in a code-to-code comparison. The second case was a heaving float corresponding to a physical model tested in a wave tank. We considered radiation, diffraction, and regular wave cases and compared quantities, such as the WEC motion, power output and hydrodynamic loading.
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Donadon, Maurício V., and Mariano A. Arbelo. "Bird Strike Modeling in Fiber-Reinforced Polymer Composites." International Journal of Structural Stability and Dynamics 17, no. 06 (August 2017): 1750065. http://dx.doi.org/10.1142/s0219455417500651.
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The present paper describes a numerical modeling approach to predict impact resistance and residual Shear Strength After Impact (SSAI) of fiber reinforced polymer composites subjected to bird strike loading. An improved damage mechanics based on material model, previously developed by the authors, is combined with an equation of state to simulate the progressive failure in composite aerostructures subjected to bird strike loading. A series of bird strike impacts on flat panels fabricated from low cost woven glass composite materials are used to validate the material model for practical composite component applications. A numerical study on the residual SSAI of a typical composite shear web is also presented. The panels are modelled with shell elements only. The proposed material model formulation accounts for the strain rate enhancement to strength and shear nonlinearities observed in composite materials. A hydrodynamic model for the bird, based on 90% water and 10% air, is derived to represent the behavior of the bird for all impact scenarios considered. The bird is heterogeneous in nature. However, a uniform material behavior is assumed with a geometry based on a 2:1 length to diameter ratio with a cylindrical body and spherical end caps using Lagrangian mesh. Appropriate contact definitions are used between the bird and the composite panel. The simulations results are compared to experimental results and conclusions drawn.
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Mo, O., and T. Moan. "Environmental Load Effect Analysis of Guyed Towers." Journal of Energy Resources Technology 107, no. 1 (March 1, 1985): 24–33. http://dx.doi.org/10.1115/1.3231158.
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A general method for dynamic load effect analysis of slender offshore structures subjected to short crested random waves, current and wind, is given. The structure is represented by a three-dimensional space frame model utilizing dash-pots and linear or nonlinear spring elements to represent guy lines and coupling between structure and foundation. The component mode synthesis formulation is adopted for reduction of the number of degrees of freedom. The hydrodynamic forces are computed by Morison’s equation, accounting for finite wave elevation, directionality, and relative fluid-structure motion. Various kinematic models for the fluid field in the splashing zone are compared. To get a reasonable representation of nonlinearities in the loading and the structural model, a Monte Carlo approach is adopted. Starting with simulated samples of the random fluid field and wind forces, time series of structural responses are found by numerical time integration utilizing the Newmark β-family of time integration operators. Numerical results for a guyed tower at 450-m water depth are presented. The statistical uncertainties associated with the stochastic time domain simulations are discussed. A significant discrepancy is found between linearized frequency domain solutions and the present nonlinear time domain formulation. The importance of an adequate representation of superharmonic responses is particularly discussed. The differences in results due to various solution methods are found to vary significantly with sea-state conditions.
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Liu, J. T. C. "Nonlinear instability of developing streamwise vortices with applications to boundary layer heat transfer intensification through an extended Reynolds analogy." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1876 (May 21, 2008): 2699–716. http://dx.doi.org/10.1098/rsta.2008.0057.
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The intent of the present contribution is to explain theoretically the experimentally measured surface heat transfer rates on a slightly concave surface with a thin boundary layer in an otherwise laminar flow. As the flow develops downstream, the measured heat transfer rate deviates from the local laminar value and eventually exceeds the local turbulent value in a non-trivial manner even in the absence of turbulence. While the theory for steady strong nonlinear development of streamwise vortices can bridge the heat transfer from laminar to the local turbulent value, further intensification is attributable to the transport effects of instability of the basic steady streamwise vortex system. The problem of heat transport by steady and fluctuating nonlinear secondary instability is formulated. An extended Reynolds analogy for Prandtl number unity, Pr =1, is developed, showing the similarity between streamwise velocity and the temperature. The role played by the fluctuation-induced heat flux is similar to momentum flux by the Reynolds shear stress. Inferences from the momentum problem indicate that the intensified heat flux developing well beyond the local turbulent value is attributed to the transport effects of the nonlinear secondary instability, which leads to the formation of ‘coherent structures’ of the flow. The basic underlying pinions of the non-linear hydrodynamic stability problem are the analyses of J. T. Stuart, which uncovered physical mechanisms of nonlinearities that are crucial to the present developing boundary layers supporting streamwise vortices and their efficient scalar transporting mechanisms.
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Badshah, Saeed, Ahsan Naeem, Amer Farhan Rafique, Ihsan Ul Haq, and Suheel Abdullah Malik. "Numerical Study on the Critical Frequency Response of Jet Engine Rotors for Blade-Off Conditions against Bird Strike." Applied Sciences 9, no. 24 (December 17, 2019): 5568. http://dx.doi.org/10.3390/app9245568.
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Vibrations are usually induced in aero engines under their normal operating conditions. Therefore, it is necessary to predict the critical frequencies of the rotating components carefully. Blade deformation of a jet engine under its normal operating conditions due to fatigue or bird strike is a realistic possibility. This puts the deformed blade as one of the major safety concerns in commercially operating civil aviation. A bird strike introduces unbalanced forces and non-linearities into the engine rotor system. Such dynamic behavior is a primary cause of catastrophic failures. The introduction of unbalanced forces due to a deformed blade, as a result of a bird strike, can change the critical frequency behavior of engine rotor systems. Therefore, it is necessary to predict their critical frequencies and dynamic behavior carefully. The simplified approach of the one-dimensional and two-dimensional elements can be used to predict critical frequencies and critical mode shapes in many cases, but the use of three-dimensional elements is the best method to achieve the goals of a modal analysis. This research explores the effect of a bird strike on the critical frequencies of an engine rotor. The changes in critical mode shapes and critical frequencies as a result of a bird strike on an engine blade are studied in this research. Commercially available analysis software ANSYS version 18.2 is used in this study. In order to account for the material nonlinearities, a Johnson Cook material model is used for the fan blades and an isotropic–elastic–plastic–hydrodynamic material model is used for modeling the bird. The bird strike event is analyzed using Eularian and smoothed particle hydrodynamics (SPH) techniques. A difference of 0.1% is noted in the results of both techniques. In the modal analysis simulation of the engine rotor before and after the bird strike event, the critical failure modes remain same. However, a change in the critical frequencies of the modes is observed. An increase in the critical frequencies and excitation RPMs (revolution per minute) of each mode are observed. As the mode order is increased, the higher the rise in critical frequency and excitation RPMs. Also, a change in the whirl direction of the different modes is noted.
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Pape, L., and B. G. Ruessink. "Multivariate analysis of nonlinearity in sandbar behavior." Nonlinear Processes in Geophysics 15, no. 1 (February 18, 2008): 145–58. http://dx.doi.org/10.5194/npg-15-145-2008.
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Abstract. Alongshore sandbars are often present in the nearshore zones of storm-dominated micro- to mesotidal coasts. Sandbar migration is the result of a large number of small-scale physical processes that are generated by the incoming waves and the interaction between the wave-generated processes and the morphology. The presence of nonlinearity in a sandbar system is an important factor determining its predictability. However, not all nonlinearities in the underlying system are equally expressed in the time-series of sandbar observations. Detecting the presence of nonlinearity in sandbar data is complicated by the dependence of sandbar migration on the external wave forcings. Here, a method for detecting nonlinearity in multivariate time-series data is introduced that can reveal the nonlinear nature of the dependencies between system state and forcing variables. First, this method is applied to four synthetic datasets to demonstrate its ability to qualify nonlinearity for all possible combinations of linear and nonlinear relations between two variables. Next, the method is applied to three sandbar datasets consisting of daily-observed cross-shore sandbar positions and hydrodynamic forcings, spanning between 5 and 9 years. Our analysis reveals the presence of nonlinearity in the time-series of sandbar and wave data, and the relative importance of nonlinearity for each variable. The relation between the results of each sandbar case and patterns in bar behavior are discussed, together with the effects of noise. The small effect of nonlinearity implies that long-term prediction of sandbar positions based on wave forcings might not require sophisticated nonlinear models.
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STEPCHYN, Yaroslav, Valentyn OTAMANSKYI, and Illia MALYSHEV. "DYNAMIC PROCESSES ANALYSIS IN HIGH-SPEED SPINDLE ASSEMBLIES OF MACHINES TOOL WITH ACCOUNT DIFFERENT TYPES NONLINEARITY." Herald of Khmelnytskyi National University 305, no. 1 (February 23, 2022): 130–35. http://dx.doi.org/10.31891/2307-5732-2022-305-1-130-135.
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The productivity and accuracy machine parts often depend on the dynamic processes during machine and cutting operation. The increase requirements for machining operation and quality machine parts leads to the need to evaluate and take into account all the capabilities of the technological processing system (TS) to ensure the stability of the cutting process and increase speed. One of the features emergence and existence of self-oscillating processes, the least studied and dangerous in terms of the effect on sustainability ТS is the nonlinearity parameters elastic system of the machine tool and the processes occurring during cutting operation. Therefore, to assess the conditions for implementation of the cutting process with a steady limited amplitude of oscillations, it is necessary to analyze and take into account the main nonlinearities dynamics of the TS. The article considers dynamic processes in high-speed processing systems on the example of high-precision spindle assemblies, with analysis and following review of their different types nonlinearity. The machine tool spindle unit for the case of high-speed processing according to the working conditions approaches the scheme of the rotor system which self-oscillations can be caused by the action of non-conservative circulation-type forces that are not associated with external periodic loads or any resonant relationships: internal friction forces, hydrodynamic forces in sliding bearings and seals, electrodynamic and electromagnetic forces in the electrical components of motor-spindles. It is shown that if the nonlinearity is associated only with internal external friction and coefficients of friction forces do not depend on frequency, the amplitude and frequency of self-oscillations (unlike linear system) will depend only on relationship of friction forces.
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BURR, ULRICH, LEOPOLD BARLEON, PAUL JOCHMANN, and ARKADY TSINOBER. "Magnetohydrodynamic convection in a vertical slot with horizontal magnetic field." Journal of Fluid Mechanics 475 (January 25, 2003): 21–40. http://dx.doi.org/10.1017/s0022112002002811.
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This article presents an experimental study of magnetohydrodynamic convection in a tall vertical slot under the influence of a horizontal magnetic field. The test fluid is an eutectic sodium potassium Na22K78 alloy with a small Prandtl number of Pr ≈ 0:02. The experimental setup covers Rayleigh numbers in the range 103 [lsim ] Ra [lsim ] 8×104 and Hartmann numbers 0 < M < 1600. The effect of the magnetic field on the convective heat transport is determined not only by damping as expected from Joule dissipation but also, for magnetic fields not too strong, the convective heat transfer may be considerably enhanced compared to ordinary hydrodynamic (OHD) flow. Estimates of the isotropy properties of the flow by a four-element temperature probe demonstrate that the increase in convective heat transport accompanies the formation of strong local anisotropy of the turbulent eddies in the sense of an alignment of the main direction of vorticity with the magnetic field. The reduced three-dimensional nonlinearities in non-isotropic flow favour the formation of largescale vortex structures compared to OHD flow, which are more effective for convective heat transport. Along with the formation of quasi-two-dimensional vortex structures, temperature fluctuations may be considerably enhanced in a magnetic field that is not too strong. However, above Hartmann numbers M [gsim ] 400 the formerly strongly time-dependent flow suddenly becomes stationary with an extended region of high convective heat transport at stationary flow. Finally, for very high Hartmann numbers the convective motion is strongly suppressed and the heat transport is reduced to a state close to pure heat conduction.
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CHANDRASEKARAN, S., A. K. JAIN, and N. R. CHANDAK. "SEISMIC ANALYSIS OF OFFSHORE TRIANGULAR TENSION LEG PLATFORMS." International Journal of Structural Stability and Dynamics 06, no. 01 (March 2006): 97–120. http://dx.doi.org/10.1142/s0219455406001848.
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Oil and gas production from deep-water offshore fields represent a major structural engineering challenge for the industry. The tension leg platform (TLP) is a well-established concept for deep-water oil exploration. It is necessary to design an offshore TLP such that it can respond to moderate environmental loads without damage, and is capable of resisting severe environmental loads without seriously endangering the occupants. Seismic analysis of triangular TLP under moderate regular waves is investigated. The analysis considers nonlinearities due to the change in tether tension and nonlinear hydrodynamic drag forces. The coupled response of TLP under moderate regular sea waves due to change in initial pretension in the tethers caused by seismic forces (vertical direction) is then investigated. Seismic forces are imposed at the bottom of each tether as axial forces. The tether tension becomes unbalanced when the hull is under offset position. The vertical component of seismic force is an important item to take into consideration, because it is directly superposed to pretension of tethers. The change in initial pretension due to the vertical component of the earthquake affects the response of the triangular TLP in degrees-of-freedom experiencing such forces. The tether tension varies nonlinearly when the platform is subjected to seismic forces caused by the El Centro earthquake and artificially generated earthquake using Kanai–Tajimi's power spectrum. The response due to earthquakes varies with the intensity of the input ground motion. The seismic response of the triangular TLP exhibits nonlinear behavior in the presence of waves and it is non-proportionately influenced by the wave period and the wave height.
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Chang, Xueping, Jinming Fan, Wenwu Yang, and Yinghui Li. "In-Line and Cross-Flow Coupling Vibration Response Characteristics of a Marine Viscoelastic Riser Subjected to Two-Phase Internal Flow." Shock and Vibration 2021 (February 16, 2021): 1–27. http://dx.doi.org/10.1155/2021/7866802.
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This paper studies the in-line and cross-flow coupling vibration response characteristics of a marine viscoelastic riser subjected to two-phase internal flow and affected by the combined effects of several parameters including the volume fraction of gas phase, sea water flow velocity, viscoelastic coefficient of the marine riser, axial tension amplitude, and the in-line and cross-flow coupling effect taking into account both the geometric and hydrodynamic nonlinearities. On the base of extended Hamilton’s principle for open systems, the dynamic equations of the marine viscoelastic riser subjected to the axial tension and gas-liquid-structure interaction are established. Two distributed and coupled van der Pol wake oscillators are utilized to model the fluctuating lift and drag coefficients, respectively. The finite element method is adopted to directly solve the highly coupled nonlinear fluid-structure interaction equations. Model validations are firstly performed through comparisons with the published experimental data and numerical simulation results, and the characteristic curves of the in-line and cross-flow vibration pattern, the in-line and cross-flow displacement trajectories, the in-line and cross-flow space-time response of displacement, and the in-line and cross-flow space-time response of stress versus different parameters are obtained, respectively. The results show that the volume fraction of gas phase, sea water flow velocity, viscoelastic coefficient of marine riser, axial tension amplitude, the in-line and cross-flow coupling effect, and multiphase internal flow velocity have significant influences on the dynamic response characteristics of the marine viscoelastic riser. Furthermore, the maximum displacements and stresses of the marine viscoelastic riser can be increased or decreased depending on the internal flow velocity, and the critical internal flow velocities result in the increase of mode order for different cross-flow velocities. It is also demonstrated that appropriate viscoelastic coefficients are very important to effectively suppress the maximum displacements and stresses.
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Isaacson, Michael de St Q. "Recent advances in the computation of nonlinear wave effects on offshore structures." Canadian Journal of Civil Engineering 12, no. 3 (September 1, 1985): 439–53. http://dx.doi.org/10.1139/l85-052.
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The present paper provides a review of recent research on various nonlinearities that arise in ocean wave interactions with offshore structures. These include nonlinearities associated with the incident waves alone, the response of slender structural members to waves, and the nonlinear diffraction problem involving wave interactions with large structures. Emphasis is given to areas of current research into two particular nonlinear problems. One concerns an investigation into alternative approximations to the Morison equation for flexible structures and the other concerns the numerical simulation of nonlinear wave diffraction around large structures. Key words: diffraction, hydrodynamics, nonlinear flow, ocean engineering, offshore structures, waves.
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LANGE, ADRIAN. "THE ADJOINT PROBLEM IN THE PRESENCE OF A DEFORMED SURFACE: THE EXAMPLE OF THE ROSENSWEIG INSTABILITY ON MAGNETIC FLUIDS." International Journal of Modern Physics B 16, no. 08 (March 30, 2002): 1155–70. http://dx.doi.org/10.1142/s0217979202010105.
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The Rosensweig instability is the phenomenon that above a certain threshold of a vertical magnetic field peaks appear on the free surface of a horizontal layer of magnetic fluid. In contrast to almost all classical hydrodynamical systems, the nonlinearities of the Rosensweig instability are entirely triggered by the properties of a deformed and a priori unknown surface. The resulting problems in defining an adjoint operator for such nonlinearities are illustrated. The implications concerning amplitude equations for pattern forming systems with a deformed surface are discussed.
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Shukla, Priyanka, Istafaul H. Ansari, Devaraj van der Meer, Detlef Lohse, and Meheboob Alam. "Nonlinear instability and convection in a vertically vibrated granular bed." Journal of Fluid Mechanics 761 (November 17, 2014): 123–67. http://dx.doi.org/10.1017/jfm.2014.624.
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AbstractThe nonlinear instability of the density-inverted granular Leidenfrost state and the resulting convective motion in strongly shaken granular matter are analysed via a weakly nonlinear analysis of the hydrodynamic equations. The base state is assumed to be quasi-steady and the effect of harmonic shaking is incorporated by specifying a constant granular temperature at the vibrating plate. Under these mean-field assumptions, the base-state temperature decreases with increasing height away from the vibrating plate, but the density profile consists of three distinct regions: (i) a collisional dilute layer at the bottom, (ii) a levitated dense layer at some intermediate height and (iii) a ballistic dilute layer at the top of the granular bed. For the nonlinear stability analysis (Shukla & Alam, J. Fluid Mech., vol. 672, 2011b, pp. 147–195), the nonlinearities up to cubic order in the perturbation amplitude are retained, leading to the Landau equation, and the related adjoint stability problem is formulated taking into account appropriate boundary conditions. The first Landau coefficient and the related modal eigenfunctions (the fundamental mode and its adjoint, the second harmonic and the base-flow distortion, and the third harmonic and the cubic-order distortion to the fundamental mode) are calculated using a spectral-based numerical method. The genesis of granular convection is shown to be tied to a supercritical pitchfork bifurcation from the density-inverted Leidenfrost state. Near the bifurcation point the equilibrium amplitude ($A_{e}$) is found to follow a square-root scaling law, $A_{e}\sim \sqrt{{\it\Delta}}$, with the distance ${\it\Delta}$ from the bifurcation point. We show that the strength of convection (measured in terms of velocity circulation) is maximal at some intermediate value of the shaking strength, with weaker convection at both weaker and stronger shaking. Our theory predicts that at very strong shaking the convective motion remains concentrated only near the top surface, with the bulk of the expanded granular bed resembling the conduction state of a granular gas, dubbed as a floating-convection state. The linear and nonlinear patterns of the density and velocity fields are analysed and compared with experiments qualitatively. Evidence of 2:1 resonance is shown for certain parameter combinations. The influences of bulk viscosity, effective Prandtl number, shear work and free-surface boundary conditions on nonlinear equilibrium states are critically assessed.