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1
Bich, Dao Huy, Nguyen Xuan Nguyen, and Hoang Van Tung. "Postbuckling of functionally graded cylindrical shells based on improved Donnell equations." Vietnam Journal of Mechanics 35, no. 1 (April 10, 2013): 1–15. http://dx.doi.org/10.15625/0866-7136/35/1/2894.
Повний текст джерелаАнотація:
This paper presents an analytical approach to investigate the buckling and postbuckling of functionally graded cylindrical shells subjected to axial and transversemechanical loads incorporating the effects of temperature. Material properties are assumed to be temperature independent, and graded in the thickness direction accordingto a simple power law distribution in terms of the volume fractions of constituents. Equilibrium equations for perfect cylindrical shells are derived by using improved Donnell shell theory taking into account geometrical nonlinearity. One-term approximate solution is assumed to satisfy simply supported boundary conditions and closed-form expressions of buckling loads and load-deflection curves are determined by Galerkin method. Analysis shows the effects of material and the geometric parameters, buckling mode, pre-existent axial compressive and thermal loads on the nonlinear response of the shells.
2
Dung, Dao Van, and Vu Hoai Nam. "An analytical approach to analyze nonlinear dynamic response of eccentrically stiffened functionally graded circular cylindrical shells subjected to time dependent axial compression and external pressure. Part 2: Numerical results and discussion." Vietnam Journal of Mechanics 36, no. 4 (December 2, 2014): 255–65. http://dx.doi.org/10.15625/0866-7136/36/4/3986.
Повний текст джерелаАнотація:
Based on the classical thin shell theory with the geometrical nonlinearity in von Karman-Donnell sense, the smeared stiffener technique, Galerkin method and an approximate three-term solution of deflection taking into account the nonlinear buckling shape is chosen, the governing nonlinear dynamic equations of eccentrically stiffened functionally graded circular cylindrical shells subjected to time dependent axial compression and external pressure is established in part 1. In this study, the nonlinear dynamic responses are obtained by fourth order Runge-Kutta method and the nonlinear dynamic buckling behavior of stiffened functionally graded shells under linear-time loading is determined by according to Budiansky-Roth criterion. Numerical results are investigated to reveal effects of stiffener, input factors on the vibration and nonlinear dynamic buckling loads of stiffened functionally graded circular cylindrical shells.
3
Coulaud, O., P. Morel, and J. P. Caltagirone. "Numerical modelling of nonlinear effects in laminar flow through a porous medium." Journal of Fluid Mechanics 190 (May 1988): 393–407. http://dx.doi.org/10.1017/s0022112088001375.
Повний текст джерелаАнотація:
This paper deals with the introduction of a nonlinear term into Darcy's equation to describe inertial effects in a porous medium. The method chosen is the numerical resolution of flow equations at a pore scale. The medium is modelled by cylinders of either equal or unequal diameters arranged in a regular pattern with a square or triangular base. For a given flow through this medium the pressure drop is evaluated numerically.The Navier-Stokes equations are discretized by the mixed finite-element method. The numerical solution is based on operator-splitting methods whose purpose is to separate the difficulties due to the nonlinear operator in the equation of motion and the necessity of taking into account the continuity equation. The associated Stokes problems are solved by a mixed formulation proposed by Glowinski & Pironneau.For Reynolds numbers lower than 1, the relationship between the global pressure gradient and the filtration velocity is linear as predicted by Darcy's law. For higher values of the Reynolds number the pressure drop is influenced by inertial effects which can be interpreted by the addition of a quadratic term in Darcy's law.On the one hand this study confirms the presence of a nonlinear term in the motion equation as experimentally predicted by several authors, and on the other hand analyses the fluid behaviour in simple media. In addition to the detailed numerical solutions, an estimation of the hydrodynamical constants in the Forchheimer equation is given in terms of porosity and the geometrical characteristics of the models studied.
4
Tho Hung, Vu, Dang Thuy Dong, Nguyen Thi Phuong, Le Ngoc Ly, Tran Quang Minh, Nguyen-Thoi Trung, and Vu Hoai Nam. "Nonlinear Buckling Behavior of Spiral Corrugated Sandwich FGM Cylindrical Shells Surrounded by an Elastic Medium." Materials 13, no. 8 (April 24, 2020): 1984. http://dx.doi.org/10.3390/ma13081984.
Повний текст джерелаАнотація:
This paper presents a semi-analytical approach for investigating the nonlinear buckling and postbuckling of spiral corrugated sandwich functionally graded (FGM) cylindrical shells under external pressure and surrounded by a two-parameter elastic foundation based on Donnell shell theory. The improved homogenization theory for the spiral corrugated FGM structure is applied and the geometrical nonlinearity in a von Karman sense is taken into account. The nonlinear equilibrium equation system can be solved by using the Galerkin method with the three-term solution form of deflection. An explicit solution form for the nonlinear buckling behavior of shells is obtained. The critical buckling pressure and the postbuckling strength of shells are numerically investigated. Additionally, the effects of spiral corrugation in enhancing the nonlinear buckling behavior of spiral corrugated sandwich FGM cylindrical shells are validated and discussed.
5
Dehghani, M., and B. Pourhassan. "Quantum corrected thermodynamics of nonlinearly charged BTZ black holes in massive gravity’s rainbow." Modern Physics Letters A 36, no. 22 (July 19, 2021): 2150158. http://dx.doi.org/10.1142/s0217732321501583.
Повний текст джерелаАнотація:
In this paper, we consider three-dimensional massive gravity’s rainbow and obtain black hole solutions in three different cases of Born–Infeld, logarithmic, and exponential theories of nonlinear electrodynamics. We discuss the horizon structure and geometrical properties. Then, we study thermodynamics of these models by considering the first-order quantum correction effects, which appear as a logarithmic term in the black hole entropy. We discuss such effects on the black hole stability and phase transitions. We find that due to the quantum corrections, the second-order phase transition happens in Born–Infeld and logarithmic models. We obtain the modified first law of black hole thermodynamics in the presence of logarithmic corrections.
6
Hieu, Pham Thanh, and Hoang Van Tung. "Thermomechanical nonlinear buckling of pressure-loaded carbon nanotube reinforced composite toroidal shell segment surrounded by an elastic medium with tangentially restrained edges." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 9 (September 30, 2018): 3193–207. http://dx.doi.org/10.1177/0954406218802942.
Повний текст джерелаАнотація:
Buckling and postbuckling behaviors of toroidal shell segment reinforced by single-walled carbon nanotubes, surrounded by an elastic medium, exposed to a thermal environment and subjected to uniform external pressure are investigated in this paper. Carbon nanotubes are reinforced into matrix phase by uniform distribution or functionally graded distribution along the thickness direction. Material properties of constituents are assumed to be temperature dependent, and the effective properties of carbon nanotube reinforced composite are estimated by extended mixture rule through a micromechanical model. Governing equations for toroidal shell segments are based on the classical thin shell theory taking into account geometrical nonlinearity, surrounding elastic medium, and varying degree of tangential constraints of edges. Three-term solution of deflection and stress function are assumed to satisfy simply supported boundary condition, and Galerkin method is applied to derive nonlinear load–deflection relation from which buckling loads and postbuckling equilibrium paths are determined. Analysis shows that tangential edge restraints have significant effects on nonlinear buckling of carbon nanotube reinforced composite toroidal shell segments. In addition, the effects of carbon nanotube volume fraction, distribution types, geometrical ratios, elastic foundation, and thermal environments on the buckling and postbuckling behaviors of carbon nanotube reinforced composite toroidal shell segments are analyzed and discussed.
7
Tung, Hoang Van, and Pham Thanh Hieu. "Nonlinear buckling of CNT-reinforced composite toroidal shell segment surrounded by an elastic medium and subjected to uniform external pressure." Vietnam Journal of Mechanics 40, no. 3 (September 24, 2018): 285–301. http://dx.doi.org/10.15625/0866-7136/12397.
Повний текст джерелаАнотація:
Buckling and postbuckling behaviors of Toroidal Shell Segment (TSS) reinforced by single-walled carbon nanotubes (SWCNT), surrounded by an elastic medium and subjected to uniform external pressure are investigated in this paper. Carbon nanotubes (CNTs) are reinforced into matrix phase by uniform distribution (UD) or functionally graded (FG) distribution along the thickness direction. Effective properties of carbon nanotube reinforced composite (CNTRC) are estimated by an extended rule of mixture through a micromechanical model. Governing equations for TSSs are based on the classical thin shell theory taking into account geometrical nonlinearity and surrounding elastic medium. Three-term solution of deflection and stress function are assumed to satisfy simply supported boundary condition, and Galerkin method is applied to obtain nonlinear load-deflection relation from which buckling loads and postbuckling equilibrium paths are determined. The effects of CNT volume fraction, distribution types, geometrical ratios and elastic foundation on the buckling and postbuckling behaviors of CNTRC TSSs are analyzed and discussed.
8
Ceylan, Zekai, and Mohamed B. Trabia. "Optimization of the Closure-Weld Region of Cylindrical Containers for Long-Term Corrosion Resistance Using the Successive Heuristic Quadratic Approximation Technique*." Journal of Mechanical Design 125, no. 3 (September 1, 2003): 533–39. http://dx.doi.org/10.1115/1.1565082.
Повний текст джерелаАнотація:
Welded cylindrical containers are susceptible to stress corrosion cracking (SCC) in the closure-weld area. An induction coil heating technique may be used to relieve the residual stresses in the closure-weld. This technique involves localized heating of the material by the surrounding coils. The material is then cooled to room temperature by quenching. A two-dimensional axisymmetric finite element model is developed to study the effects of induction coil heating and subsequent quenching. The finite element results are validated through an experimental test. The container design is tuned to maximize the compressive stress from the outer surface to a depth that is equal to the long-term general corrosion rate of the container material multiplied by the desired container lifetime. The problem is subject to several geometrical and stress constraints. Two different solution methods are implemented for this purpose. First, an off-the-shelf optimization software is used. The results however were unsatisfactory because of the highly nonlinear nature of the problem. The paper proposes a novel alternative: the Successive Heuristic Quadratic Approximation (SHQA) technique. This algorithm combines successive quadratic approximation with an adaptive random search within varying search space. SHQA promises to be a suitable search method for computationally intensive, highly nonlinear problems.
9
Howard, A. Q., and W. C. Chew. "Electromagnetic borehole fields in a layered, dipping‐bed environment with invasion." GEOPHYSICS 57, no. 3 (March 1992): 451–65. http://dx.doi.org/10.1190/1.1443259.
Повний текст джерелаАнотація:
Electromagnetic modeling of an induction sonde (1–100 kHz) in a dipping‐bed environment is a 3-D problem. The capability for such an analysis is necessary for interpretation of oil‐well logs in offshore environments where most holes are deviated. 3-D geometrical effects require vector field analysis. The method accounts for transverse magnetic mode (TM) coupling arising from surface charges deposited by eddy currents passing through bed boundaries. If borehole and invasion effects are included, the only available rigorous analytical methods are finite elements or finite‐difference techniques. These approaches require large‐scale computing. In contrast, our method is approximate and is an extension of the geometrical‐factor theory and Born approximation. The variational method does not require matrices and is numerically simpler than the more rigorous finite element method. The method uses a new electric field vector integral equation developed by Chew. The formulation accounts for low‐frequency behavior at bed boundaries where current channeling and surface charge phenomena dominate the interactions. The receiver voltage has two parts, a volumetric term [Formula: see text] and a surface term [Formula: see text]. The term [Formula: see text] reduces to the Born result when the dip angle goes to zero; [Formula: see text] accounts for the surface charge effect and is only significant when the receivers are in close proximity to a bed boundary. The local nature of the charge interaction results from double scattering events, which are necessary to produce this effect. The charge term is second order as explained intuitively in terms of polarization. The bed boundary interaction is proportional to the factor [Formula: see text], where [Formula: see text] is the dip angle, and [Formula: see text] and [Formula: see text] are the conductivities of the adjacent beds. Since the charge interaction is strongly nonlinear in conductivity, common induction log interpretation, which assumes linearity, is expected to fail near bed boundaries. Results for dip angles up to 60 degrees for variational results and eigenfunction solutions for the case of no borehole or invasion show good agreement. A few 3-D results are computed with simultaneous layering, dip, and invasion.
10
Vecchio, F. J., and S. Balopoulou. "On the nonlinear behaviour of reinforced concrete frames." Canadian Journal of Civil Engineering 17, no. 5 (October 1, 1990): 698–704. http://dx.doi.org/10.1139/l90-083.
Повний текст джерелаАнотація:
An experimental investigation is described in which a large-scale reinforced concrete plane frame is tested to study factors contributing to its nonlinear behaviour under short-term loading conditions. The test results indicate that frame behaviour can be significantly affected by second-order influences such as material nonlinearities, geometric nonlinearities, concrete shrinkage, tension stiffening effects, shear deformations, and membrane action. A nonlinear frame analysis procedure, previously developed taking these mechanisms into account, is shown to accurately predict most aspects of behaviour, including deflection response, ultimate load capacity, and failure mechansim. Aspects of the theoretical modelling which are in need of further improvement are also identified. Key words: analysis, behaviour, deformation, frame, large scale, nonlinear, reinforced concrete, strength, test.
11
Jafarzade, Khadije, Mahdi Kord Zangeneh, and Francisco S. N. Lobo. "Optical Features of AdS Black Holes in the Novel 4D Einstein-Gauss-Bonnet Gravity Coupled to Nonlinear Electrodynamics." Universe 8, no. 3 (March 14, 2022): 182. http://dx.doi.org/10.3390/universe8030182.
Повний текст джерелаАнотація:
An alternative theory of gravity that has attracted much attention recently is the novel four-dimensional Einstein-Gauss-Bonnet (4D EGB) gravity. The theory is rescaled by the Gauss-Bonnet (GB) coupling constant α→α/(D−4) in D dimensions and redefined as four-dimensional gravity in the limit D→4. Thus, in this manner, the GB term yields a non-trivial contribution to the gravitational dynamics. In fact, regularized black hole solutions and applications in the novel 4D EGB gravity have also been extensively explored. In this work, motivated by recent astrophysical observations, we present an in-depth study of the optical features of AdS black holes in the novel 4D EGB gravity coupled to exponential nonlinear electrodynamics (NED), such as the shadow geometrical shape, the energy emission rate, the deflection angle and quasinormal modes. Taking into account these dynamic quantities, we investigate the effects on the black hole solution by varying the parameters of the models. More specifically, we show that the variation of the GB and NED parameters, and of the cosmological constant, imprints specific signatures on the optical features of AdS black holes in the novel 4D EGB gravity coupled to nonlinear electrodynamics, thus leading to the possibility of directly testing these black hole models by using astrophysical observations.
12
Chang, Xue Ping, Xiao Dong Zhang, and Qing You Liu. "Geometrically Nonlinear Analysis of Cross-Ply Laminated Composite Beams Subjected to Uniform Temperature Rise." Advanced Materials Research 335-336 (September 2011): 527–30. http://dx.doi.org/10.4028/www.scientific.net/amr.335-336.527.
Повний текст джерелаАнотація:
Abstract: On the basis of Reddy’s higher order shear deformation plate theory and the von Kármán’s geometry nonlinear theory, governing equations for nonlinear thermal buckling and post-buckling of cross-ply laminated composite beam subjected to a temperature rise are derived, in which the stretching-bending coupling terms produced by the non-homogenous distribution of the material properties are included. By using the shooting method to solve the corresponding nonlinear boundary value problem, numerical solutions for thermal post-buckling of cross-ply shear deformation laminated composite beam with its both ends immovably simply supported under uniform temperature rise are obtained. As an example, equilibrium paths and configurations for laminated composite beam paved in term of 0/90/0 are presented and characteristic curves of the nonlinear deformation changing with the thermal load were plotted. The effects of the geometric and physical parameters on the deformation of the beam are also examined. The theoretical analysis and numerical results show that different thermal expansion coefficient ratio, elastic moduli ratio, shear stiffness ratio will influence of the non-dimension critical buckling temperature.
13
Krommer, Michael, and Hans Irschik. "Post-Buckling of Piezoelectric Thin Plates." International Journal of Structural Stability and Dynamics 15, no. 07 (August 31, 2015): 1540020. http://dx.doi.org/10.1142/s0219455415400209.
Повний текст джерелаАнотація:
In the present paper, the geometrically nonlinear behavior of piezoelastic thin plates is studied. First, the governing equations for the electromechanically coupled problem are derived based on the von Karman–Tsien kinematic assumption. Here, the Berger approximation is extended to the coupled piezoelastic problem. The general equations are then reduced to a single nonlinear partial differential equation for the special case of simply supported polygonal edges. The nonlinear equations are approximated by using a problem-oriented Ritz Ansatz in combination with a Galerkin procedure. Based on the resulting equations the buckling and post-buckling behavior of a polygonal simply supported plate is studied in a nondimensional form, where the special geometry of the polygonal plate enters via the eigenvalues of a Helmholtz problem with Dirichlet boundary conditions. Single term as well as multi-term solutions are discussed including the effects of piezoelectric actuation and transverse force loadings upon the solution. Novel results concerning the buckling, snap through and snap buckling behavior are presented.
14
Schäfer, Dominik. "Influence of Fluid Viscosity and Compressibility on Nonlinearities in Generalized Aerodynamic Forces for T-Tail Flutter." Aerospace 9, no. 5 (May 9, 2022): 256. http://dx.doi.org/10.3390/aerospace9050256.
Повний текст джерелаАнотація:
The numerical assessment of T-tail flutter requires a nonlinear description of the structural deformations when the unsteady aerodynamic forces comprise terms from lifting surface roll motion. For linear flutter, a linear deformation description of the vertical tail plane (VTP) out-of-plane bending results in a spurious stiffening proportional to the steady lift forces, which is corrected by incorporating second-order deformation terms in the equations of motion. While the effect of these nonlinear deformation components on the stiffness of the VTP out-of-plane bending mode shape is known from the literature, their impact on the aerodynamic coupling terms involved in T-tail flutter has not been studied so far, especially regarding amplitude-dependent characteristics. This term affects numerical results targeting common flutter analysis, as well as the study of amplitude-dependent dynamic aeroelastic stability phenomena, e.g., Limit Cycle Oscillations (LCOs). As LCOs might occur below the linear flutter boundary, fundamental knowledge about the structural and aerodynamic nonlinearities occurring in the dynamical system is essential. This paper gives an insight into the aerodynamic nonlinearities for representative structural deformations usually encountered in T-tail flutter mechanisms using a CFD approach in the time domain. It further outlines the impact of geometrically nonlinear deformations on the aerodynamic nonlinearities. For this, the horizontal tail plane (HTP) is considered in isolated form to exclude aerodynamic interference effects from the studies and subjected to rigid body roll and yaw motion as an approximation to the structural mode shapes. The complexity of the aerodynamics is increased successively from subsonic inviscid flow to transonic viscous flow. At a subsonic Mach number, a distinct aerodynamic nonlinearity in stiffness and damping in the aerodynamic coupling term HTP roll on yaw is shown. Geometric nonlinearities result in an almost entire cancellation of the stiffness nonlinearity and an increase in damping nonlinearity. The viscous forces result in a stiffness offset with respect to the inviscid results, but do not alter the observed nonlinearities, as well as the impact of geometric nonlinearities. At a transonic Mach number, the aerodynamic stiffness nonlinearity is amplified further and the damping nonlinearity is reduced considerably. Here, the geometrically nonlinear motion description reduces the aerodynamic stiffness nonlinearity as well, but does not cancel it.
15
Koundy, V., T. Forgeron, and F. Le Naour. "Modeling of Multiaxial Creep Behavior for Incoloy 800 Tubes Under Internal Pressure." Journal of Pressure Vessel Technology 119, no. 3 (August 1, 1997): 313–18. http://dx.doi.org/10.1115/1.2842310.
Повний текст джерелаАнотація:
In order to validate the long-term behavior of fast breeder reactor steam generator tubes, a creep test monitoring program has been undertaken. A series of over one hundred tests was performed on small specimen tubes which were cut from the as-received tube material of Incoloy 800, similar to those used in generator applications. In contrast to uniaxial conditions in which constant load conditions usually apply, multiaxial experiments were performed assuming constant stress conditions. Thin walled tube approximation was used to estimate the stresses across the tube wall thickness required for given internal tube pressures. This paper deals with a refined numerical modeling of stresses and strains in the pressurized test specimens, taking into account: internal pressure changes, nonlinear geometrical effects, and creep deformation during all the test procedure cycles. Comparison of the numerical results with the experimental measurements shows a good agreement which validates the multiaxial generalization of the RCC-MR strain creep laws which were used in the calculations. A multiaxial creep rupture criterion is discussed.
16
Azmi, A., and T. R. Marchant. "Circular dispersive shock waves in colloidal media." Journal of Nonlinear Optical Physics & Materials 25, no. 04 (December 2016): 1650044. http://dx.doi.org/10.1142/s0218863516500442.
Повний текст джерелаАнотація:
A dispersive shock wave (DSW), with a circular geometry, is studied in a colloidal medium. The colloidal particle interaction is based on the repulsive theoretical hard sphere model, where a series in the particle density, or packing fraction is used for the compressibility. Experimental results show that the particle interactions are temperature dependent and can be either repulsive or attractive, so the second term in the compressibility series is modified to allow for temperature dependent effects, using a power-law relationship. The governing equation is a focusing nonlinear Schrödinger-type equation with an implicit nonlinearity. The initial jump in electric field amplitude is resolved via a DSW, which forms before the onset of modulational instability. A semi-analytical solution for the amplitude of the solitary waves in a DSW of large radius, is derived based on a combination of conservation laws and geometrical considerations. The effect of temperature and background packing fraction on the evolution of the DSW and the amplitude of the solitary waves is discussed and the semi-analytical solutions are found to be very accurate, when compared with numerical solutions.
17
Flowers, G. T., and B. H. Tongue. "Nonlinear Behavior of a Rotorcraft Model During Air Resonance." Journal of Vibration and Acoustics 113, no. 2 (April 1, 1991): 141–51. http://dx.doi.org/10.1115/1.2930162.
Повний текст джерелаАнотація:
The term “air resonance” refers to an instability associated with helicopters in hover. It is characterized by a coupling between motions of the fuselage and the blades and is of primary concern for helicopters having soft in-plane rotors. This paper presents a study of the effects of nonlinearities on the dynamical behavior of a simplified air resonance model. In order to provide a direct comparison between the behavior of the linearized system and the nonlinear one, a linear analysis of the air resonance model is first performed. Then, the system is analyzed for the effect of selected nonlinearities on its steady state dynamical responses. Geometric nonlinearities and cubic lag damping are considered in these analyses.
18
Guérin, Charles-Antoine, Nicolas Desmars, Stéphan T. Grilli, Guillaume Ducrozet, Yves Perignon, and Pierre Ferrant. "An improved Lagrangian model for the time evolution of nonlinear surface waves." Journal of Fluid Mechanics 876 (August 1, 2019): 527–52. http://dx.doi.org/10.1017/jfm.2019.519.
Повний текст джерелаАнотація:
Accurate real-time simulations and forecasting of phase-revolved ocean surface waves require nonlinear effects, both geometrical and kinematic, to be accurately represented. For this purpose, wave models based on a Lagrangian steepness expansion have proved particularly efficient, as compared to those based on Eulerian expansions, as they feature higher-order nonlinearities at a reduced numerical cost. However, while they can accurately model the instantaneous nonlinear wave shape, Lagrangian models developed to date cannot accurately predict the time evolution of even simple periodic waves. Here, we propose a novel and simple method to perform a Lagrangian expansion of surface waves to second order in wave steepness, based on the dynamical system relating particle locations and the Eulerian velocity field. We show that a simple redefinition of reference particles allows us to correct the time evolution of surface waves, through a modified nonlinear dispersion relationship. The resulting expressions of free surface particle locations can then be made numerically efficient by only retaining the most significant contributions to second-order terms, i.e. Stokes drift and mean vertical level. This results in a hybrid model, referred to as the ‘improved choppy wave model’ (ICWM) (with respect to Nouguier et al.’s J. Geophys. Res., vol. 114, 2009, p. C09012), whose performance is numerically assessed for long-crested waves, both periodic and irregular. To do so, ICWM results are compared to those of models based on a high-order spectral method and classical second-order Lagrangian expansions. For irregular waves, two generic types of narrow- and broad-banded wave spectra are considered, for which ICWM is shown to significantly improve wave forecast accuracy as compared to other Lagrangian models; hence, ICWM is well suited to providing accurate and efficient short-term ocean wave forecast (e.g. over a few peak periods). This aspect will be the object of future work.
19
Huang, Yue, Rui Rao, Yonghui Huang, and Zilin Zhong. "Theoretical Investigation of Nonlinear Time-Dependent Behavior of Two-Way High-Strength Concrete Walls." Mathematical Problems in Engineering 2020 (April 20, 2020): 1–12. http://dx.doi.org/10.1155/2020/4587089.
Повний текст джерелаАнотація:
High-strength concrete (HSC) walls have been increasingly used in the past decades. However, the time-dependent behavior of HSC wall panels in two-way action was not investigated, and the time effect of creep is not included in the design codes in most countries. For this purpose, the nonlinear long-term behavior of two-way HSC wall is investigated in this paper. A theoretical model is developed using time-stepping analysis considering geometric nonlinearity and creep of concrete. A rheological material model that is based on the generalized Maxwell chain is adopted to model the concrete creep. Von Karman plate theory is used to derive the incremental governing equations. The equations are solved numerically at each time step based on a Fourier series expansion of the deformations and loads and numerical multiple shooting method. It shows that the model can effectively predict the time-dependent behavior of two-way HSC panels, where the out-of-plane deflection and internal bending moments increase with time due to the combined effects of creep and geometric nonlinearity, which may ultimately lead to creep buckling failures. A parametric study shows that the long-term behavior of the panel is very sensitive to the in-plane load level and eccentricity, slenderness ratio, aspect ratio, and edge support conditions.
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Chang, Xue Ping, Zheng Liang, and Qing You Liu. "Buckling and Post-Buckling Analysis of Symmetrically Angle-Ply Laminated Composite Beams under Thermal Environments." Advanced Materials Research 335-336 (September 2011): 182–86. http://dx.doi.org/10.4028/www.scientific.net/amr.335-336.182.
Повний текст джерелаАнотація:
Abstract: On the basis of Reddy’s higher order shear deformation plate theory and the von Kármán’s geometry nonlinear theory, governing equations for nonlinear thermal buckling and post-buckling of symmetry angle-ply laminated composite beam subjected to a temperature rise are derived, in which the stretching-bending coupling terms produced by the non-homogenous distribution of the material properties are included. By using the shooting method to solve the corresponding nonlinear boundary value problem, numerical solutions for thermal post-buckling of symmetry angle-ply shear deformation laminated composite beam with its both ends immovably simply supported under uniform temperature rise are obtained. As an example, equilibrium paths and configurations for laminated composite beam paved in term of 45/90 are presented and characteristic curves of the nonlinear deformation changing with the thermal load were plotted. The effects of the geometric and physical parameters on the deformation of the beam are also examined. The theoretical analysis and numerical results show that different thermal expansion coefficient ratio, elastic moduli ratio, will influence of the non-dimension critical buckling temperature.
21
Chang, Xue Ping, Jun Liu, and Ji Hong Ren. "Thermal Post-Buckling of Heated Cross-Ply Laminated Composite Beams." Applied Mechanics and Materials 105-107 (September 2011): 2321–24. http://dx.doi.org/10.4028/www.scientific.net/amm.105-107.2321.
Повний текст джерелаАнотація:
Abstract: On the basis of Reddy’s higher order shear deformation plate theory and the von Kármán’s geometry nonlinear theory, governing equations for nonlinear thermal buckling and post-buckling of cross-ply laminated composite beam subjected to a temperature rise are derived, in which the stretching-bending coupling terms produced by the non-homogenous distribution of the material properties are included. By using the shooting method to solve the corresponding nonlinear boundary value problem, numerical solutions for thermal post-buckling of cross-ply shear deformation laminated composite beam with its both ends immovably simply supported under uniform temperature rise are obtained. As an example, equilibrium paths and configurations for laminated composite beam paved in term of 0/90/0 are presented and characteristic curves of the nonlinear deformation changing with the thermal load were plotted. The effects of the geometric and physical parameters on the deformation of the beam are also examined. The theoretical analysis and numerical results show that different thermal expansion coefficient ratio, elastic moduli ratio, shear stiffness ratio will influence of the non-dimension critical buckling temperature.
22
Nayfeh, Ali H., and Haider N. Arafat. "Nonlinear Response of Cantilever Beams to Combination and Subcombination Resonances." Shock and Vibration 5, no. 5-6 (1998): 277–88. http://dx.doi.org/10.1155/1998/181460.
Повний текст джерелаАнотація:
The nonlinear planar response of cantilever metallic beams to combination parametric and external subcombination resonances is investigated, taking into account the effects of cubic geometric and inertia nonlinearities. The beams considered here are assumed to have large length-to-width aspect ratios and thin rectangular cross sections. Hence, the effects of shear deformations and rotatory inertia are neglected. For the case of combination parametric resonance, a two-mode Galerkin discretization along with Hamilton’s extended principle is used to obtain two second-order nonlinear ordinary-differential equations of motion and associated boundary conditions. Then, the method of multiple scales is applied to obtain a set of four first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the two excited modes. For the case of subcombination resonance, the method of multiple scales is applied directly to the Lagrangian and virtual-work term. Then using Hamilton’s extended principle, we obtain a set of four first-order nonlinear ordinary-differential equations governing the amplitudes and phases of the two excited modes. In both cases, the modulation equations are used to generate frequency- and force-response curves. We found that the trivial solution exhibits a jump as it undergoes a subcritical pitchfork bifurcation. Similarly, the nontrivial solutions also exhibit jumps as they undergo saddle-node bifurcations.
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Lubis, Asnawi, and Jamiatul Akmal. "Nonlinear Analysis of Pressurized Piping Elbows Subjected to Out-of-Plane Bending." Key Engineering Materials 306-308 (March 2006): 351–56. http://dx.doi.org/10.4028/www.scientific.net/kem.306-308.351.
Повний текст джерелаАнотація:
The behavior of piping elbows under bending and internal pressure is more complicated than expected. The main problem is that the coupling of bending and internal pressure is nonlinear; the resulting stress and displacement cannot be added according to the principle of superposition. In addition, internal pressure tends to act against the effect caused by the bending moment. If bending moment ovalise the elbow cross-section, with internal pressure acting against this deformation, then the ovalised cross section deform back to the original circular shape. It is then introduced the term “pressure reduction effect”, or in some literature, “pressure stiffening effect”. Current design piping code treats the pressure reduction effect equally for in-plane (closing and opening) moment and outof- plane moment. The aim of this paper is to present results of a detailed finite element analysis on the non-linear behavior of piping elbows of various geometric configurations subject to out-of-plane bending and internal pressure. Specifically the standard Rodabaugh & George nonlinear pressure reduction equations for in-plane closing moment are checked in a systematic study for out-of-plane moment against nonlinear finite element analysis. The results show that the pressure stiffening effects are markedly different for in-plane and out-of-plane bending.
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de Boer, J. D., J. M. A. Noël, and J. P. St.-Maurice. "The effects of mesoscale regions of precipitation on the ionospheric dynamics, electrodynamics and electron density in the presence of strong ambient electric fields." Annales Geophysicae 28, no. 6 (June 23, 2010): 1345–60. http://dx.doi.org/10.5194/angeo-28-1345-2010.
Повний текст джерелаАнотація:
Abstract. We have developed a new high resolution two-dimensional model of the high latitude ionosphere in which nonlinear advection terms are closely coupled with the electrodynamics. The model provides a self-consistent description of the ionospheric feedback on the electrodynamical perturbations produced by auroral arc-related particle precipitation in regions with strong ambient electric fields. We find in particular that a heretofore neglected ion Pedersen advection term can introduce considerable changes in the electron density profile, the current density distribution, the conductivities and the electron temperatures. We find that the convective effects can carry the ionisation more than 150 km outside the precipitation region in a few minutes, with attendant large changes in the current distribution and E-region densities that become enhanced outside the region of particle precipitation. The production of a tongue of ionisation that slowly decays outside the auroral boundaries contrasts with the sharp geometric cut-off and associated stronger current densities found in previous studies.
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Abdeddine, E., A. Majid, N. Bouzida, Z. Beidouri, and Kh Zarbane. "Numerical investigation of geometrically nonlinear clamped uniform rods and rods with sections varying exponentially free vibration." Journal of Achievements in Materials and Manufacturing Engineering 112, no. 2 (June 1, 2022): 49–63. http://dx.doi.org/10.5604/01.3001.0016.0703.
Повний текст джерелаАнотація:
The present paper is intended to investigate the problem of linear and non-linear longitudinal free vibration of uniform rods and rods whose cross-sections vary exponentially at large vibration amplitudes. The method adopted consists in discretizing the energy term on linear kij and non-linear rigidity tensor bijkl, as well as the mass tensor mij. Therefore, the formulation of this structure is based on Lagrange equations and the harmonic balance method so as to obtain the nonlinear algebraic equations. These latter are solved numerically and analytically through the explicit and linearized method. The response of Clamped-Clamped uniform and non-uniform rods on our structure are highlighted in the amplitude frequency and associated first three mode shapes. Moreover, this research leads to study the influence of the exponential slope on the maximum displacement, thus emphasizing the non-uniform bars usefulness. The obtained results are then compared with the available literature with a view to validating this theory. As a perspective, the method used in this paper would be pushed to study the FDM material, taking into account other parameters related to additive manufacturing, and later to be validated experimentally. Longitudinal vibrations are important in mechanical structures; therefore, the determination of their dynamic behaviour needs to be understood. In the present study, the effect of the displacement amplitude on the exponential slope of the structure was analysed, which led to the determination of the reduction range of the vibration amplitude under resonance. However, this should be taken into account in the design process. Besides, the usefulness of the non-linearity geometric effects was demonstrated to examine these structures by considering all the parameters involved. A linearized procedure is used to solve a nonlinear algebra equation. The use of this method leads to reduce calculation time contrary to iterative methods.
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Bég, Anwar, S. Rawat, J. Zueco, L. Osmond, and R. S. R. Gorla. "Finite element and network electrical simulation of rotating magnetofluid flow in nonlinear porous media with inclined magnetic field and hall currents." Theoretical and Applied Mechanics 41, no. 1 (2014): 1–35. http://dx.doi.org/10.2298/tam1401001b.
Повний текст джерелаАнотація:
A mathematical model is presented for viscous hydromagnetic flow through a hybrid non-Darcy porous media rotating generator. The system is simulated as steady, incompressible flow through a nonlinear porous regime intercalated between parallel plates of the generator in a rotating frame of reference in the presence of a strong, inclined magnetic field A pressure gradient term is included which is a function of the longitudinal coordinate. The general equations for rotating viscous magnetohydrodynamic flow are presented and neglecting convective acceleration effects, the two-dimensional viscous flow equations are derived incorporating current density components, porous media drag effects, Lorentz drag force components and Hall current effects. Using an appropriate group of dimensionless variables, the momentum equations for primary and secondary flow are rendered nondimensional and shown to be controlled by six physical parameters-Hartmann number (Ha), Hall current parameter (Nh), Darcy number (Da), Forchheimer number (Fs), Ekman number (Ek) and dimensionless pressure gradient parameter (Np), in addition to one geometric parameter-the orientation of the applied magnetic field (? ). Several special cases are extracted from the general model, including the non-porous case studied earlier by Ghosh and Pop (2006). A numerical solution is presented to the nonlinear coupled ordinary differential equations using both the Network Simulation Method and Finite Element Method, achieving excellent agreement. Additionally very good agreement is also obtained with the earlier analytical solutions of Ghosh and Pop (2006). for selected Ha, Ek and Nh values. We examine in detail the effects of magnetic field, rotation, Hall current, bulk porous matrix drag, second order porous impedance, pressure gradient and magnetic field inclination on primary and secondary velocity distributions and also frictional shear stresses at the plates. Primary velocity is seen to decrease with an increase in Hall current parameter (Nh) with the converse observed for the secondary velocity.
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Kahlen, Katrin, and Hartmut Stützel. "Estimation of Geometric Attributes and Masses of Individual Cucumber Organs Using Three-dimensional Digitizing and Allometric Relationships." Journal of the American Society for Horticultural Science 132, no. 4 (July 2007): 439–46. http://dx.doi.org/10.21273/jashs.132.4.439.
Повний текст джерелаАнотація:
The objective of this study was to estimate geometric attributes and masses of individual cucumber (Cucumis sativus L.) organs in situ. Using three-dimensional (3D) digitizing techniques, geometric data were obtained that were used to establish allometric relationships between geometric organ attribute and organ mass. Moreover, the authors were looking for the effects of ontogeny and the influence of environmental factors on the allometric relationships in cucumber. If such an allometric relationship did not exist, they alternatively tested the relationship between organ dry weight and organ number counted from the top of the plant downward. Lastly, they included allometric relationships based on biomechanical approaches focused on lamina mass and petiole attributes. The digitizing method provided accurate data for the calculation of geometric plant part attributes, such as length, area, and volume. Based on these data it was possible to describe the relationships between plant part dry weight and plant part geometry by allometric functions except for internode length. Apart from this exception, two different kinds of allometric equations were used: a simple power function with two parameters and a linear function without intercept. Information about more than one dimension of the considered plant part (e.g., area or volume) led to a simple linear relationship, whereas knowledge of just one dimension, like plant part length, resulted in more complex nonlinear relationships. Ontogeny led, in general, to a reduction in the scaling exponent or in the scaling factor, whereas changes of the environment distributed these values. Considering these effects makes it possible to determine dry matter partitioning on organ scale nondestructively and investigate long-term processes on intact plants.
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SAN, OMER, and ANNE E. STAPLES. "AN IMPROVED MODEL FOR REDUCED-ORDER PHYSIOLOGICAL FLUID FLOWS." Journal of Mechanics in Medicine and Biology 12, no. 03 (June 2012): 1250052. http://dx.doi.org/10.1142/s0219519411004666.
Повний текст джерелаАнотація:
An improved one-dimensional mathematical model based on the Pulsed Flow Equations (PFE) is derived by integrating the axial component of the momentum equation over the transient Womersley velocity profile, providing a dynamic momentum equation whose coefficients are smoothly varying functions of the spatial variable. The resulting momentum equation along with the continuity equation and pressure-area relation form our reduced-order model for physiological fluid flows in one dimension and are aimed at providing accurate and fast-to-compute global models for physiological systems represented as networks of quasi one-dimensional fluid flows. The consequent nonlinear coupled system of equations is solved by the Lax-Wendroff scheme and is then applied to an open model arterial network of the human vascular system containing the largest 55 arteries. The proposed model with functional coefficients is compared with current classical one-dimensional theories which assume steady state Hagen-Poiseuille velocity profiles, either parabolic or plug-like, throughout the whole arterial tree. The effects of the nonlinear term in the momentum equation and different strategies for bifurcation points in the network, as well as the various lumped parameter outflow boundary conditions for distal terminal points are also analyzed. The results show that the proposed model can be used as an efficient tool for investigating the dynamics of reduced-order models of flows in physiological systems and would, in particular, be a good candidate for the one-dimensional, system-level component of geometric multiscale models of physiological systems.
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Беляев, И., I. Belyaev, Е. Жорова, E. Zhorova, В. Калистратова, V. Kalistratova, И. Парфенова, I. Parfenova, Г. Тищенко та G. Tishchenko. "Dioxide Plutonium-239 in the Lung. Report 3: Different Effect of Vitamins A, C and β-carotene on the Long-term Consequences of Incorporation". Medical Radiology and radiation safety 63, № 2 (5 квітня 2018): 5–14. http://dx.doi.org/10.12737/article_5ac618209e5301.92255096.
Повний текст джерелаАнотація:
Purpose: Testing of vitamin preparations as a means of prophylaxis long-term effects of destruction of incorporated radionuclides. Analysis of experimental material about the influence of L-ascorbic acid, retinol palmitate and β-carotene on the long-term effects inside the lungs of incorporation dioxide plutonium-239. Material and methods: The studies were performed on 628 white nonlinear male rats. Plutonium dioxide was administered to white nonlinear male rats once intratracheally in the amount of 100 kBq/kg body weight. The diet was enriched by L-ascorbic acid, retinol palmitate or synthetic β-carotene. The analysis of pathological effects inside the lungs of incorporation of the plutonium dioxide was carried out by groups formed based on individual absorbed doses in the range of their geometric means between 32 and 212 Gy. Test animals were observed for life. Radiometric, histological and statistical methods were used. Indicators of the pathology of the organ of respiration were inflammatory, sclerotic, premalignant and malignant changes in the lungs. Indicators of breathing pathology: inflammatory, sclerotic, premalignant and malignant changes in the lungs are quantified. Results: Long-term consumption of vitamins C, A and β-carotene in intact rats did not affect the life span of animals and the total frequency of the identified types of lung cancer. We found a significant increase in the frequency of pneumosclerosis in groups of rats received vitamin A (27 %) or β-carotene (29 %) compared with intact animals (11 %). Multidirectional effect of vitamins A, C and β-carotene on selected indicators of long-term effects inside the lungs of incorporation 239PuO2 has been marked. Vitamin A and β-carotene intensified the sclerotic processes in the organ of respiration, and vitamin A largely (67 %) than β-carotene (57 %) with 46 % in controls. When enriching the ration of animals with the studied vitamin preparations, the regularity of increasing the number of rats with tumors localized in the lungs was preserved. Both positive and negative influence on radiation carcinogenesis and the lack of effect depending on the absorbed dose was noted. With the increase of absorbed dose from 32 to 212 Gy not only the frequency but also the spectrum of tumors localized in the lungs has varied. Against the background of increasing the total number of tumors has increased the number of rats with tumors of epithelial origin and decreased with gematosarcoma. No effect is investigated vitamin preparations on the metabolism of plutonium dioxide-239 installed. Consumption of the studied drugs did not affect the lifespan of rats with intra-lungs the introduction of dioxide of plutonium-239 and the process of formation of absorbed doses in the lungs. Conclusions: Vitamin A and β-carotene stimulate the development of pulmonary fibrosis in rats of intact and affected 239PuO2 ones. The result of the use of vitamins A, C and β-carotene showed the different (positive and negative) effect on the formation of lung tumors induced 239PuO2 in various ranges of absorbed doses. In the studied forms, doses and schemes assign vitamins A, C and β-carotene cannot be recommended for the prevention of spontaneous and 239PuO2-induced pathological changes in the lung.
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Liu, Zhilin, Simeng Song, Shouzheng Yuan, Yingkai Ma, and Zongxun Yao. "ALOS-Based USV Path-Following Control with Obstacle Avoidance Strategy." Journal of Marine Science and Engineering 10, no. 9 (August 28, 2022): 1203. http://dx.doi.org/10.3390/jmse10091203.
Повний текст джерелаАнотація:
Path following and obstacle avoidances are used in heading control and path replanning for unmanned surface vessels (USVs), which have attracted the interest of many researchers over the years. This paper investigates the path-following and obstacle avoidance problems for USVs. First, on the basis of the current position and desired path, an adaptive line-of-sight (ALOS) algorithm is used to obtain the desired heading angle, and the sideslip angle compensation is considered. Then, to ensure that the USV follows the desired path. Model predictive control (MPC) is used to reduce the lateral error. The event-triggered mechanism (ETM) strategy is utilized to reduce the computational cost of MPC. Moreover, to obtain accurate state quantities in real time, a linear extended state observer (LESO) is used to counteract the effects of external disturbances and the nonlinear term of the model. Furthermore, an improved obstacle avoidance algorithm based on the geometric relationship is proposed. This method can better ensure USV navigation safety and reduce consumption and computation. Lastly, multiple simulation experiments illustrate that the algorithm improves the path-following capability and security and ensures smooth input changes by setting input constraints. Therefore, the designed controller has better feasibility and robustness.
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Cartailler, J., Z. Schuss, and D. Holcman. "Geometrical Effects on Nonlinear Electrodiffusion in Cell Physiology." Journal of Nonlinear Science 27, no. 6 (May 24, 2017): 1971–2000. http://dx.doi.org/10.1007/s00332-017-9393-2.
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CASTELLA, F., and E. DUMAS. "HIGH FREQUENCY BEHAVIOR OF THE MAXWELL–BLOCH MODEL WITH RELAXATION: CONVERGENCE TO THE SCHRÖDINGER-RATE SYSTEM." Journal of Hyperbolic Differential Equations 09, no. 03 (September 2012): 355–401. http://dx.doi.org/10.1142/s0219891612500129.
Повний текст джерелаАнотація:
We study the Maxwell–Bloch model, which describes the propagation of a laser through a material and the associated interaction between laser and matter (polarization of the atoms through light propagation, photon emission and absorption, etc.). The laser field is described through Maxwell's equations, a classical equation, while matter is represented at a quantum level and satisfies a quantum Liouville equation known as the Bloch model. Coupling between laser and matter is described through a quadratic source term in both equations. The model also takes into account partial relaxation effects, namely the trend of matter to return to its natural thermodynamic equilibrium. The whole system involves 6 + N(N + 1)/2 unknowns, the six-dimensional electromagnetic field plus the N(N + 1)/2 unknowns describing the state of matter, where N is the number of atomic energy levels of the considered material. We consider at once a high frequency and weak coupling situation, in the general case of anisotropic electromagnetic fields that are subject to diffraction. Degenerate energy levels are allowed. The whole system is stiff and involves strong nonlinearities. We show the convergence to a nonstiff, nonlinear, coupled Schrödinger-rate model, involving 3 + N unknowns. The electromagnetic field is eventually described through its envelope, one unknown vector in ℂ3. It satisfies a Schrödinger equation that takes into account propagation and diffraction of light inside the material. Matter on the other hand is described through a N-dimensional vector describing the occupation numbers of each atomic level. It satisfies Einstein's rate equation that describes the jumps of the electrons between the various atomic energy levels, as induced by the interaction with light. The rate of exchange between the atomic levels is proportional to the intensity of the laser field. The whole system is the physically natural nonlinear model. In order to provide an important and explicit example, we completely analyze the specific (two-dimensional) Transverse Magnetic case, for which formulae turn out to be simpler. Technically speaking, our analysis does not enter the usual mathematical framework of geometric optics: it is more singular, and requires an ad hoc Ansatz.
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Rosén, T., F. Lundell, and C. K. Aidun. "Effect of fluid inertia on the dynamics and scaling of neutrally buoyant particles in shear flow." Journal of Fluid Mechanics 738 (December 13, 2013): 563–90. http://dx.doi.org/10.1017/jfm.2013.599.
Повний текст джерелаАнотація:
AbstractThe basic dynamics of a prolate spheroidal particle suspended in shear flow is studied using lattice Boltzmann simulations. The spheroid motion is determined by the particle Reynolds number (${\mathit{Re}}_{p} $) and Stokes number ($\mathit{St}$), estimating the effects of fluid and particle inertia, respectively, compared with viscous forces on the particle. The particle Reynolds number is defined by ${\mathit{Re}}_{p} = 4G{a}^{2} / \nu $, where $G$ is the shear rate, $a$ is the length of the spheroid major semi-axis and $\nu $ is the kinematic viscosity. The Stokes number is defined as $\mathit{St}= \alpha \boldsymbol{\cdot} {\mathit{Re}}_{p} $, where $\alpha $ is the solid-to-fluid density ratio. Here, a neutrally buoyant prolate spheroidal particle ($\mathit{St}= {\mathit{Re}}_{p} $) of aspect ratio (major axis/minor axis) ${r}_{p} = 4$ is considered. The long-term rotational motion for different initial orientations and ${\mathit{Re}}_{p} $ is explained by the dominant inertial effect on the particle. The transitions between rotational states are subsequently studied in detail in terms of nonlinear dynamics. Fluid inertia is seen to cause several bifurcations typical for a nonlinear system with odd symmetry around a double zero eigenvalue. Particle inertia gives rise to centrifugal forces which drives the particle to rotate with the symmetry axis in the flow-gradient plane (tumbling). At high ${\mathit{Re}}_{p} $, the motion is constrained to this planar motion regardless of initial orientation. At a certain critical Reynolds number, ${\mathit{Re}}_{p} = {\mathit{Re}}_{c} $, a motionless (steady) state is created through an infinite-period saddle-node bifurcation and consequently the tumbling period near the transition is scaled as $\vert {\mathit{Re}}_{p} - {\mathit{Re}}_{c} {\vert }^{- 1/ 2} $. Analyses in this paper show that if a transition from tumbling to steady state occurs at ${\mathit{Re}}_{p} = {\mathit{Re}}_{c} $, then any parameter $\beta $ (e.g. confinement or particle spacing) that influences the value of ${\mathit{Re}}_{c} $, such that ${\mathit{Re}}_{p} = {\mathit{Re}}_{c} $ as $\beta = {\beta }_{c} $, will lead to a period that scales as $\vert \beta - {\beta }_{c} {\vert }^{- 1/ 2} $ and is independent of particle shape or any geometric aspect ratio in the flow.
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DEVECCHI, F. P., and M. L. FROEHLICH. "3D GRAVITY AND NONLINEAR COSMOLOGY." Modern Physics Letters A 21, no. 05 (February 20, 2006): 445–50. http://dx.doi.org/10.1142/s0217732306018974.
Повний текст джерелаАнотація:
By the inclusion of an additional term, nonlinear in the scalar curvature R, it is tested if dark energy could rise as a geometrical effect in 3D gravitational formulations. We investigate a cosmological fluid obeying a non-polytropic equation of state (the van der Waals equation) that is used to construct the energy–momentum tensor of the sources, representing the hypothetical inflaton in gravitational interaction with a matter contribution. Following the evolution in time of the scale factor, its acceleration, and the energy densities of constituents it is possible to construct the description of an inflationary 3D universe, followed by a matter-dominated era. For later times it is verified that, under certain conditions, the nonlinear term in R can generate the old 3D universe in accelerated expansion, where the ordinary matter is represented by the barotropic limit of the van der Waals constituent.
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Lee, Sang-Youl. "Parametric effects on geometrical nonlinear dynamic behaviors of laminated composite skew plates." Journal of The Korean Society for Composite Materials 25, no. 6 (December 31, 2012): 217–23. http://dx.doi.org/10.7234/kscm.2012.25.6.217.
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Korepanov, M. A., M. R. Koroleva, E. A. Mitrukova, and A. N. Nechay. "Nonlinear Effects of Krypton Flow in a Micronozzle with a Cylindrical Tube." Nelineinaya Dinamika 18, no. 3 (2022): 411–22. http://dx.doi.org/10.20537/nd220306.
Повний текст джерелаАнотація:
The paper expresses a mathematical model of homogeneous gas motion with respect to formation processes and the growth of condensation nuclei. Since the condensed particles are small, the research is carried out with a single velocity motion model. The results obtained have shown that the application of the cylindrical tube leads to nonlinear flow effects. The flow responds to: the geometrical exposure related to flow transition from the conical diverging nozzle
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Dung, Dao Van, and Vu Hoai Nam. "An analytical approach to analyze nonlinear dynamic response of eccentrically stiffened functionally graded circular cylindrical shells subjected to time dependent axial compression and external pressure. Part 1: Governing equations establishment." Vietnam Journal of Mechanics 36, no. 3 (August 22, 2014): 201–14. http://dx.doi.org/10.15625/0866-7136/36/3/3984.
Повний текст джерелаАнотація:
Based on the classical thin shell theory with the geometrical nonlinearity in von Karman-Donnell sense, the smeared stiffener technique and Galerkin method, this paper deals with the nonlinear dynamic problem of eccentrically stiffened functionally graded circular cylindrical shells subjected to time dependent axial compression and external pressure by analytical approach. The present novelty is that an approximate three-term solution of deflection taking into account the nonlinear buckling shape is chosen, the nonlinear dynamic second-order differential three equations system is established and the frequency-amplitude relation of nonlinear vibration is obtained in explicit form.
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ZHANG, SHENGLI, QI WANG, and ERHU ZHANG. "THE GEOMETRICAL EFFECTS ON ELECTRONIC SPECTRUM AND PERSISTENT CURRENTS IN MESOSCOPIC POLYGON." Modern Physics Letters B 23, no. 02 (January 20, 2009): 191–201. http://dx.doi.org/10.1142/s0217984909017959.
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In this paper, a new mesoscopic polygon which possesses smooth transition at its corners is proposed. Because of the particularity of structure, this kind of mesoscopic polygon can also be a geometrical superlattice. The geometrical effects on the electron states and persistent current are investigated comprehensively in the presence of magnetic flux. We find that the particular geometric structure of the polygon induces an effective periodic potential which results in gaps in the energy spectrum. The changes of gaps show the consistency with the geometrical two-ness of this new polygon. This electronic structure and the corresponding physical properties are found to be periodic with period ϕ0 in the magnetic flux ϕ and can be controlled by the geometric method. We also consider the Rahsba spin-orbit interaction which double the energy levels splitting and leads to an additional small zigzag in one period of the persistent current. These new phenomena may be useful for the applications in quantum device design in the future.
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Phuong, Nguyen Thi, Vu Hoai Nam, Nguyen Thoi Trung, Vu Minh Duc, and Pham Van Phong. "Nonlinear Stability of Sandwich Functionally Graded Cylindrical Shells with Stiffeners Under Axial Compression in Thermal Environment." International Journal of Structural Stability and Dynamics 19, no. 07 (June 26, 2019): 1950073. http://dx.doi.org/10.1142/s0219455419500731.
Повний текст джерелаАнотація:
The geometrically nonlinear response of sandwich functionally graded cylindrical shells reinforced by orthogonal and/or spiral stiffeners and subjected to axial compressive loads is investigated in this paper. Two types of sandwich functionally graded material models are considered. The formulations are based on the Donnell shell theory considering geometrical nonlinearity and Pasternak’s elastic foundation. The improved Lekhnitskii’s smeared stiffener technique is used to account for the stiffener effects with both mechanical and thermal stresses. The results obtained indicate that the spiral stiffeners have significantly beneficial influences in comparison with orthogonal stiffeners on the nonlinear buckling behavior of shells. The relatively large effects of temperature change, geometrical and material parameters are also demonstrated in the numerical investigations.
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Khoa, Nguyen Minh, and Hoang Van Tung. "Nonlinear thermo-mechanical stability of shear deformable FGM sandwich shallow spherical shells with tangential edge constraints." Vietnam Journal of Mechanics 39, no. 4 (December 27, 2017): 351–64. http://dx.doi.org/10.15625/0866-7136/9810.
Повний текст джерелаАнотація:
This paper presents an analytical approach to investigate the nonlinear axisymmetric response of moderately thick FGM sandwich shallow spherical shells resting on elastic foundations, exposed to thermal environments and subjected to uniform external pressure. Material properties are assumed to be temperature independent, and effective properties of FGM layer are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Formulations are based on first-order shear deformation shell theory taking geometrical nonlinearity, initial geometrical imperfection, Pasternak type elastic foundations and various degree of tangential constraint of boundary edge into consideration. Approximate solutions are assumed to satisfy clamped boundary condition and Galerkin method is applied to derive closed-form expressions of critical buckling loads and nonlinear load-deflection relation. Effects of geometrical parameters, thickness of face sheets, foundation stiffness, imperfection, thermal environments and degree of tangential edge constraints on the nonlinear stability of FGM sandwich shallow spherical shells are analyzed and discussed.
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Stafström, Sven. "GEOMETRICAL AND ELECTRONIC STRUCTURE OF C60 ANIONS." International Journal of Modern Physics B 06, no. 23n24 (December 1992): 3853–58. http://dx.doi.org/10.1142/s0217979292001924.
Повний текст джерелаАнотація:
The geometrical and electronic structure of various C 60 anions is calculated using a model which couples the bond length to the bond order and to Coulomb interactions between adjacent sites. The total energy of the C 60 anions is minimized with respect to variations in the bond length. The geometrical relaxations of the anions, relative to the neutral molecule, are such that the symmetry of the molecule is lowered (Jahn-Teller distortion). In the case of the mono-anion and the di-anion, the geometrical distortions and the charge are localized to one equatorial line around the spherical molecule. We term this type of self-localized defect a cyclon. The distortions of higher anions are best described as resulting from interacting cyclons. These distortions and the corresponding charges are delocalized over practically the whole system. The Jahn-Teller distortions of the C 60 anions result in a breaking of the degeneracy of the electronic levels and, generally speaking, a broadening of the peaks in the density of states compared to neutral C 60.
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Lashkari, Saleh, Ali Moghimi, Hamid Reza Kobravi, and Mohamad Amin Younessi Heravi. "A Novel Spike-Wave Discharge Detection Framework Based on the Morphological Characteristics of Brain Electrical Activity Phase Space in an Animal Model." International Clinical Neuroscience Journal 8, no. 4 (October 30, 2021): 180–87. http://dx.doi.org/10.34172/icnj.2021.36.
Повний текст джерелаАнотація:
Background: Animal models of absence epilepsy are widely used in childhood absence epilepsy studies. Absence seizures appear in the brain’s electrical activity as a specific spike wave discharge (SWD) pattern. Reviewing long-term brain electrical activity is time-consuming and automatic methods are necessary. On the other hand, nonlinear techniques such as phase space are effective in brain electrical activity analysis. In this study, we present a novel SWD-detection framework based on the geometrical characteristics of the phase space. Methods: The method consists of the following steps: (1) Rat stereotaxic surgery and cortical electrode implantation, (2) Long-term brain electrical activity recording, (3) Phase space reconstruction, (4) Extracting geometrical features such as volume, occupied space, and curvature of brain signal trajectories, and (5) Detecting SDWs based on the thresholding method. We evaluated the approach with the accuracy of the SWDs detection method. Results: It has been demonstrated that the features change significantly in transition from a normal state to epileptic seizures. The proposed approach detected SWDs with 98% accuracy. Conclusion: The result supports that nonlinear approaches can identify the dynamics of brain electrical activity signals.
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Budiman, H. T., and P. A. Lagace. "Nondimensional Parameters for Geometric Nonlinear Effects in Pressurized Cylinders With Axial Cracks." Journal of Applied Mechanics 64, no. 2 (June 1, 1997): 401–7. http://dx.doi.org/10.1115/1.2787322.
Повний текст джерелаАнотація:
The effects of geometric nonlinearity on the response of axially cracked cylindrical shells under internal pressure are investigated in a general way. Using the Donnell-Mushtari-Vlasov nonlinear shell equations, the nonlinear response is shown to depend on two nondimensional parameters: the geometrical parameter λ, which is a function of the cylinder geometries and crack length, and the loading parameter η, which depends on the applied pressure, material properties, and cylinder geometries. To assess the applicability of such parameters, nonlinear analyses of different cylindrical configurations were performed using the STAGS finite element code. The results show that the two parameters are able to characterize the nonlinear response of such cylinders. Effects of nonlinearity are then presented in the form of an iso-nonlinear plot showing the percentage difference between the linear and nonlinear stress intensification factors. Using the iso-nonlinear plot, the importance of geometric nonlinearity can thus be assessed once the cylinder geometries, loading parameters, and material properties are known.
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Pletyukhov, M. V., and E. A. Tolkachev. "Evolution of twofold degenerate two-level system. Geometrical effects." Journal of Physics A: Mathematical and General 32, no. 6 (January 1, 1999): 1073–82. http://dx.doi.org/10.1088/0305-4470/32/6/017.
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Soteros, C. E., and S. G. Whittington. "Lattice models of branched polymers: effects of geometrical constraints." Journal of Physics A: Mathematical and General 22, no. 24 (December 21, 1989): 5259–70. http://dx.doi.org/10.1088/0305-4470/22/24/014.
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Hoan, Pham Van, Dao Nhu Mai, Khuc Van Phu, and Le Kha Hoa. "Nonlinear buckling and post-buckling of imperfect FG porous sandwich cylindrical panels subjected to axial loading on elastic foundation." Vietnam Journal of Mechanics 44, no. 4 (December 31, 2022): 514–25. http://dx.doi.org/10.15625/0866-7136/17980.
Повний текст джерелаАнотація:
This paper deals with the nonlinear buckling and post-buckling of sandwich cylindrical panels with non-uniform porous core and functionally graded face sheets. The imperfect sandwich cylindrical panels are subjected to axial loading on elastic foundation. Based on the Donnell shell theory, with von Kármán geometrical nonlinearity, the governing equations are derived. The effects of elastic foundation, various panel geometrical characteristics, porosity parameters, and the thickness of the porous core are investigated. The effects of foundation parameters, porosity parameters, the thickness of the porous core, and material parameters are investigated.
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Van Phu, Khuc, Dao Huy Bich, and Le Xuan Doan. "Nonlinear thermal vibration and dynamic buckling of eccentrically stiffened sandwich-FGM cylindrical shells containing fluid." Journal of Reinforced Plastics and Composites 38, no. 6 (December 1, 2018): 253–66. http://dx.doi.org/10.1177/0731684418814636.
Повний текст джерелаАнотація:
The governing equations for analysing thermal vibration and dynamic buckling of eccentrically stiffened sandwich functionally graded cylindrical shells full filled with fluid and surrounded by elastic foundations in thermal environment are derived by using the classical shell theory, the geometrical nonlinearity in von Karman-Donnell sense, the smeared stiffener technique and Pasternak’s foundation model. Solutions of the problem are established according to the Galerkin’s method and Runge–Kutta method. The effects of fluid pressure, stiffeners, geometrical ratios, temperature and elastic foundation on the dynamic responses of shells are investigated.
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Cong, Pham Hong, Pham Thi Ngoc An, and Nguyen Dinh Duc. "Nonlinear stability of shear deformable eccentrically stiffened functionally graded plates on elastic foundations with temperature-dependent properties." Science and Engineering of Composite Materials 24, no. 3 (May 1, 2017): 455–69. http://dx.doi.org/10.1515/secm-2015-0225.
Повний текст джерелаАнотація:
AbstractThis article investigates the nonlinear stability of eccentrically stiffened moderately thick plates made of functionally graded materials (FGM) subjected to in-plane compressive, thermo-mechanical loads. The equilibrium and compatibility equations for the moderately thick plates are derived by using the first-order shear deformation theory of plates, taking into account both the geometrical nonlinearity in the von Karman sense and initial geometrical imperfections, temperature-dependent properties with Pasternak type elastic foundations. By applying the Galerkin method and using a stress function, the effects of material and geometrical properties, temperature-dependent material properties, elastic foundations, boundary conditions, and eccentric stiffeners on the buckling and post-buckling loading capacity of the eccentrically stiffened moderately thick FGM plates in thermal environments are analyzed and discussed.
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Dippel, S., and S. Luding. "Simulation on Size Segregation: Geometrical Effects in the Absence of Convection." Journal de Physique I 5, no. 12 (December 1995): 1527–37. http://dx.doi.org/10.1051/jp1:1995215.
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Carrera, Erasmo, and Horst Parisch. "An evaluation of geometrical nonlinear effects of thin and moderately thick multilayered composite shells." Composite Structures 40, no. 1 (December 1997): 11–24. http://dx.doi.org/10.1016/s0263-8223(97)00145-1.
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