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Статті в журналах з теми "Effects of geometrical nonlinear term"
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.
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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.
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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.
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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.
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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.
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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.
Дисертації з теми "Effects of geometrical nonlinear term"
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AUGELLO, RICCARDO. "Advanced FEs for the micropolar and geometrical nonlinear analyses of composite structures." Doctoral thesis, Politecnico di Torino, 2021. http://hdl.handle.net/11583/2872330.
Повний текст джерела
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Farajpour, Ouderji Ali. "Nonlinear scale-dependent deformation behaviour of beam and plate structures." Thesis, 2021. http://hdl.handle.net/2440/130767.
Повний текст джерелаАнотація:
Improving the knowledge of the mechanics of small-scale structures is important in many
microelectromechanical and nanoelectromechanical systems. Classical continuum mechanics cannot
be utilised to determine the mechanical response of small-scale structures, since size effects become
significant at small-scale levels. Modified elasticity models have been introduced for the mechanics
of ultra-small structures. It has recently been shown that higher-order models, such as nonlocal strain
gradient and integral models, are more capable of incorporating scale influences on the mechanical
characteristics of small-scale structures than the classical continuum models. In addition, some scaledependent
models are restricted to a specific range of sizes. For instance, nonlocal effects on the
mechanical behaviour vanish after a particular length. Scrutinising the available literature indicates
that the large amplitude vibrations of small-scale beams and plates using two-parameter scaledependent
models and nonlocal integral models have not been investigated yet. In addition, no twoparameter
continuum model with geometrical nonlinearity has been introduced to analyse the
influence of a geometrical imperfection on the vibration of small-scale beams. Analysing these
systems would provide useful results for small-scale mass sensors, resonators, energy harvesters and
actuators using small-scale beams and plates.
In this thesis, scale-dependent nonlinear continuum models are developed for the time-dependent
deformation behaviour of beam-shaped structures. The models contain two completely different size
parameters, which make it able to describe both the reduction and increase in the total stiffness. The
first size parameter accounts for the nonlocality of the stress, while the second one describes the strain
gradient effect. Geometrical nonlinearity on the vibrations of small-scale beams is captured through
the strain-displacement equations. The small-scale beam is assumed to possess geometrical
imperfections. Hamilton’s approach is utilised for deriving the corresponding differential equations.
The coupled nonlinear motion equations are solved numerically employing Galerkin’s method of
discretisation and the continuation scheme of solution. It is concluded that geometrical imperfections would substantially alter the nonlinear vibrational response of small-scale beams. When there is a
relatively small geometrical imperfection in the structure, the small-scale beam exhibits a hardeningtype
nonlinearity while a combined hardening- and softening-type nonlinearity is found for beams
with large geometrical imperfections. The strain gradient influence is associated with an enhancement
in the beam stiffness, leading to higher nonlinear resonance frequencies. By contrast, the stress
nonlocality is related to a remarkable reduction in the total stiffness, and consequently lower nonlinear
resonance frequencies. In addition, a scale-dependent model of beams is proposed in this thesis to
analyse the influence of viscoelasticity and geometrical nonlinearity on the vibration of small-scale
beams. A nonlocal theory incorporating strain gradients is used for describing the problem in a
mathematical form. Implementing the classical continuum model of beams causes a substantial
overestimation in the beam vibrational amplitude. In addition, the nonlinear resonance frequency
computed by the nonlocal model is less than that obtained via the classical model. When the forcing
amplitude is comparatively low, the linear and nonlinear damping mechanisms predict almost the
same results. However, when forcing amplitudes become larger, the role of nonlinear viscoelasticity
in the vibrational response increases. The resonance frequency of the scale-dependent model with a
nonlinear damping mechanism is lower than that of the linear one.
To simulate scale effects on the mechanical behaviour of ultra-small plates, a novel scale-dependent
model of plates is developed. The static deflection and oscillation of rectangular plates at small-scale
levels are analysed via a two-dimensional stress-driven nonlocal integral model. A reasonable kernel
function, which fulfil all necessary criteria, is introduced for rectangular small-scale plates for the
first time. Hamilton and Leibniz integral rules are used for deriving the non-classical motion
equations of the structure. Moreover, two types of edge conditions are obtained for the linear vibration.
The first type is the well-known classical boundary condition while the second type is the nonclassical
edge condition associated with the curvature nonlocality. The differential quadrature
technique as a powerful numerical approach for implementing complex boundary conditions is used.
It is found that while the Laplacian-based nonlocal model cannot predict size influences on the bending of small-scale plates subject to uniform lateral loading, the bending response is remarkably
size-dependent based on the stress-driven plate model. When the size influence increases, the
difference between the resonance frequency obtained via the stress-driven model and that of other
theories substantially increases. Moreover, the resonance frequency is higher when the curvature
nonlocality increases due to an enhancement in the plate stiffness. It is also concluded that more
constraint on the small-scale plate causes the system to vibrate at a relatively high frequency. In
addition to the linear vibration, the time-dependent large deformation of small-scale plates
incorporating size influences is studied. The stress-driven theory is employed to formulate the
problem at small-scale levels. Geometrical nonlinearity effects are taken into account via von
Kármán’s theory. Three types of edge conditions including one conventional and two nonconventional
conditions are presented for nonlinear vibrations. The first non-classical edge condition
is associated with the curvature nonlocality while the second one is related to nonlocal in-plane strain
components. A differential quadrature technique and an appropriate iteration method are used to
compute the nonlinear natural frequencies and maximum in-plane displacements. Molecular
dynamics simulations are also performed for verification purposes. Nonlinear frequency ratios are
increased when vibration amplitudes increase. Furthermore, the curvature nonlocality would cause
the small-scale pate to vibrate at a lower nonlinear frequency ratio. By contrast, the nonlocal in-plane
strain has the opposite effect on the small-scale system.
The outcomes from this thesis will be useful for engineers to design vibrating small-scale resonators
and sensors using ultra-small plates.Thesis (Ph.D.) -- University of Adelaide, School of Mechanical Engineering, 2021
Книги з теми "Effects of geometrical nonlinear term"
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Nimmo, J. J. C. Geometrical and diffusive effects in nonlinear acoustic propagation over long ranges. London: Royal Society, 1986.
Знайти повний текст джерелаЧастини книг з теми "Effects of geometrical nonlinear term"
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Bahouri, Hajer, and Patrick Gérard. "Concentration effects in critical nonlinear wave equation and scattering theory." In Geometrical Optics and Related Topics, 17–30. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-2014-5_2.
Повний текст джерела
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Roca González, Joaquín, M. Vallverdú-Ferrer, P. Caminal-Magrans, F. Martínez-González, J. Roca-Dorda, and J. A. Álvarez-Gómez. "Effects of propofol anesthesia on nonlinear properties of EEG: Lyapunov exponents and short-term predictability." In IFMBE Proceedings, 1272–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-89208-3_303.
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Epstein, Irving R., and John A. Pojman. "Stirring and Mixing Effects." In An Introduction to Nonlinear Chemical Dynamics. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780195096705.003.0021.
Повний текст джерелаАнотація:
In almost everything that we have discussed so far, we have assumed, explicitly or implicitly, either that the systems we are looking at are perfectly mixed or that they are not mixed at all. In the former case, concentrations are the same everywhere in the system, so that ordinary differential equations for the evolution of the concentrations in time provide an appropriate description for the system. There are no spatial variables; in terms of geometry, the system is effectively zero-dimensional. At the other extreme, we have unstirred systems. Here, concentrations can vary throughout the system, position is a key independent variable, and diffusion plays an essential role, leading to the development of waves and patterns. Geometrically, the system is three-dimensional, though for mathematical convenience, or because one length is very different from the other two, we may be able to approximate it as one- or two-dimensional. In reality, we hardly ever find either extreme—that of perfect mixing or that of pure, unmixed diffusion. In the laboratory, where experiments in beakers or CSTRs are typically stirred at hundreds of revolutions per minute, we shall see that there is overwhelming evidence that, even if efforts are made to improve the mixing efficiency, significant concentration gradients arise and persist. Increasing the stirring rate helps somewhat, but beyond about 2000 rpm, cavitation (the formation of stirring-induced bubbles in the solution) begins to set in. Even close to this limit, mixing is not perfect. In unstirred aqueous systems, as we have seen in Chapter 9, it is difficult to avoid convective mixing. Preventing small amounts of mechanically induced mixing requires considerable effort in isolating the system from external vibrations, even those caused by the occasional truck making a delivery to the laboratory stockroom. It is possible to suppress the effects of convection and mechanical motion in highly viscous media, such as the gels used in the experiments on Turing patterns as discussed in the previous chapter. There, we can finally study a pure reaction-diffusion system. Systems in nature—the oceans, the atmosphere, a living cell—are important examples in which chemical reactions with nonlinear kinetics occur under conditions of imperfect mixing.
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Newnham, Robert E. "Nonlinear optics." In Properties of Materials. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198520757.003.0031.
Повний текст джерелаАнотація:
In most dielectrics, the linear relation between electric polarization and applied electric field is accurately obeyed even for fairly large fields of 107 V/m. The reason is that the atomic displacements are extremely small, in the range of nuclear sizes—millions of times smaller than the size of atoms. Though nonlinear effects such as electrostriction have been known for some time, it was not until the invention of the laser that sufficiently large optical fields became available to produce sizeable nonlinear optical effects. The induced polarization P can be written as a power series in an electric field, . . . P = χE + dE2 +· · · , . . . where χ is the linear electric susceptibility, and the higher-order terms lead to nonlinear effects such as second harmonic generation. The electric field associated with the incident light is sinusoidal, E = E0 sin ωt, and when E is substituted in the expression for P, a power series in sin ωt results. The second term is dE20 sin2 ωt = 1/2dE20 (1 − cos 2ωt), which includes a component of polarization with twice the frequency of the impressed field E. This rapidly oscillating induced dipole moment is the source of second harmonic light. The intensity of the light depends on the size of d, the second order coefficient. Crystal symmetry is a major factor in the second-order effect. The one-dimensional polar chain in Fig. 29.2 illustrates the origin of the quadratic term. When the applied field is directed to the left, the ions and bonding electrons are in very close contact and the displacements will be small because of short range repulsive forces. These forces do not oppose motion in the opposite direction, so that fields directed to the right give larger motions and larger polarizations. A centric chain does not show this effect. Such a chain can give rise to odd-order terms producing saturation but not to even power terms in the P(E) relation. This means that centric crystals are useless as second harmonic generators.
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Darwin, Charles. "Struggle for Existence." In On the Origin of Species. Oxford University Press, 2008. http://dx.doi.org/10.1093/owc/9780199219223.003.0005.
Повний текст джерелаАнотація:
Bears on natural selection—The term used in a wide sense—Geometrical powers of increase—Rapid increase of naturalised animals and plants—Nature of the checks to increase—Competition universal—Effects of climate—Protection from the number of individuals—Complex relations of all animals and plants throughout nature—Struggle for life most severe between...
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Abdoulkary, Saïdou, and Alidou Mohamadou. "Soliton Like-Breather Induced by Modulational Instability in a Generalized Nonlinear Schrödinger Equation." In The Nonlinear Schrödinger Equation [Working Title]. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.100522.
Повний текст джерелаАнотація:
We consider the nonlinear Schrödinger equation modified by a rational nonlinear term. The model appears in various studies often in the context of the Ginzburg-Landau equation. We investigate modulational instability by means of a linear stability analysis and show how the nonlinear terms affect the growth rate. This analytical result is confirmed by a numerical simulation. The latter analysis shows that breather-like solitons are generated from the instability, and the effects of the nonlinear terms are again clearly seen. Moreover, by employing an auxiliary-equation method we obtain kink and anti-kink soliton as analytical solutions. Our theoretical solution is in good agreement with our numerical investigation.
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Manjula, S. H., and Palle Kiran. "Thermo-Rheological Effect on Weak Nonlinear Rayleigh-Benard Convection under Rotation Speed Modulation." In Boundary Layer Flows - Modelling, Computation, and Applications of Laminar, Turbulent Incompressible and Compressible Flows [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.105097.
Повний текст джерелаАнотація:
The effects of rotation speed modulation and temperature-dependent viscosity on Rayleigh-Benard convection were investigated using a non-autonomous Ginzburg-Landau equation. The rotating temperature-dependent viscous fluid layer has been considered. The momentum equation with the Coriolis term has been used to describe finite-amplitude convective flow. The system is considered to be rotating about its vertical axis with a non-uniform rotation speed. In particular, we assume that the rotation speed is varying sinusoidally with time. Nusselt number is obtained in terms of the system parameters and graphically evaluated their effects. The effect of the modulated system diminishes the heat transfer more than the un-modulated system. Further, thermo-rheological parameter VT is found to destabilize the system.
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Smeresky, Brendon, and Alex Rizzo. "Modern Control System Learning." In Deterministic Artificial Intelligence. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.90198.
Повний текст джерелаАнотація:
This manuscript will explore and analyze the effects of different controllers in an overall spacecraft’s attitude determination and control system (ADCS). The experimental setup will include comparing an ideal nonlinear feedforward controller, a feedback controller, and a combined ideal nonlinear feedforward + feedback controller within a Simulink simulation. A custom proportional, derivative, integral controller was implemented in the feedback control, adding an additional term to account for the nonlinear coupled motion. Consistent proportional, derivative, and integral gains were used throughout the duration of the experiment. The simulated results will show that the ideal nonlinear feedforward controller lacked an error correction mechanism and took extra time to execute, the feedback controller faired only slightly better, but the combined ideal nonlinear feedforward controller with feedback correction yielded the highest accuracy with the lowest execution time. This highlights the potential effectiveness for a learning control system.
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Sheng, Xin, and Rangan Gupta. "Oil Price Shocks and Income Inequality." In Handbook of Research on Energy and Environmental Finance 4.0, 144–58. IGI Global, 2022. http://dx.doi.org/10.4018/978-1-7998-8210-7.ch005.
Повний текст джерелаАнотація:
This study, using the local projections, investigates linear and nonlinear impulse responses of the United States (US) household income inequality to oil price shocks. Oil price shocks are disaggregated according to the origin to test the dynamic response of income inequality to oil price structural shocks which are contingent on the status of oil dependence in individual US states. The results, based on the linear projection model, show that oil supply shocks lead to higher income inequality in the short term, but lower-income inequality in the medium and long terms. Moreover, economic activity shocks and oil inventory demand shocks mainly exert negative impacts on income inequality over time. Both positive and negative effects of oil consumption demand shocks on income inequality are observed. The nonlinear impulse response results reveal some evidence of heterogeneous responses of income inequality to oil price shocks between high- and low-oil-dependent US states.
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Grenfell, Bryan, and Matthew Keeling. "Dynamics of infectious disease." In Theoretical Ecology. Oxford University Press, 2007. http://dx.doi.org/10.1093/oso/9780199209989.003.0013.
Повний текст джерелаАнотація:
Host–pathogen associations continue to generate some of the most important applied problems in population biology. In addition, as foreshadowed in Chapter 5 of this volume, these systems give important insights into the dynamics of host– natural enemy interactions in general. The special place of pathogens in the study of host–natural enemy dynamics arises partly from excellent longterm disease-incidence data, reflecting the public health importance of many infections. However, we argue that host–pathogen dynamics are also distinctive because the intimate association between individual hosts and their pathogens is often reflected with particular clarity in the associated population dynamics. Throughout this chapter we focus in parallel on the population dynamics of host–pathogen interactions and the insights that host–pathogen dynamics can provide for population biology in general. Population-dynamic studies of infectious disease have a long history, which predates the modern foundations of ecology (Bernoulli, 1760). During the twentieth century, the preoccupation of population ecologists with the balance between extrinsic and intrinsic influences on population fluctuations and the role of nonlinearity and heterogeneity (Bjørnstad and Grenfell, 2001) find strong parallels in epidemiological studies of human diseases (Bartlett, 1956; Anderson and May, 1991). In terms of the ecological effects of parasitism, the traditional view held that ‘welladapted’ parasites would not have a consistent impact on the ecology of their hosts (Grenfell and Dobson, 1995). The 1970s saw a new departure, when Anderson and May pointed out the potential of infectious agents to exert nonlinear—regulatory or destabilizing—influences on the population dynamics of their hosts (Anderson and May, 1978, 1979; May and Anderson, 1978, 1979). There has since been an explosion of work on the population biology of human, animal, and plant pathogens. This work spans a huge range: from highly applied to basic theoretical work; from within-host to the metapopulation scale; from short-term population dynamics to long-term evolutionary processes. In this chapter we first outline the simple theory of epidemiological models; we then refine this picture to illustrate the potential impact of pathogens on the population dynamics of their hosts, as well as aspects of host–pathogen interactions which provide important insights into more general ecological dynamics.
Тези доповідей конференцій з теми "Effects of geometrical nonlinear term"
1
Filippi, Matteo, Alfonso Pagani, and Erasmo Carrera. "Nonlinear Dynamics of Rotating Structures and Helicopter Blades." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86786.
Повний текст джерелаАнотація:
This work explores the effects of geometrical nonlinearities in the vibration analysis of rotating structures and helicopter blades. Structures are modelled via higher-order beam theories with variable kinematics. These theories fall in the domain of the Carrera Unified Formulation (CUF), according to which the nonlinear equations of motion of rotating blades can be written in terms of fundamental nuclei, whose formalism is an invariant of the theory approximation. The inherent three-dimensional nature of CUF enables one to include all Green-Lagrange strain components as well as all coupling effects due to the geometrical features and the three-dimensional constitutive law. Numerical solutions are considered and opportunely discussed. Also, linearized and full nonlinear solutions for vibrating rotating blades are compared both in case of small amplitudes and in the large deflections/rotations regime.
2
Ceylan, Zekai, and Mohamed B. Trabia. "Optimization of the Closure-Weld Region of Cylindrical Containers for Long-Term Corrosion Resistance." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/dac-21133.
Повний текст джерелаАнотація:
Abstract Welded cylindrical containers usually experience stress corrosion cracking (SCC) in the closure-weld area. Induction coil heating technique may be used to relieve the residual stresses from the closure-weld. This technique involves localized heating of the material by the surrounding coils. The material is then cooled to the 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 parameters of the design are tuned to maximize the compressive stress within a layer of thickness from the outer surface that is equal to the long-term general corrosion of Alloy 22 (Appendix A). The problem is subject to geometrical and stress constraints. Two different solution methods are implemented for this purpose. First, an off-the-shelf optimization software is used to obtain an optimum solution. These results are not satisfactory 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. Examples and discussion are included.
3
Nascimento, Leonardo, Luis Sagrilo, and Gilberto Ellwanger. "Extreme Value Analyses of Dynamic Response Parameters of a Wind Tower Structure Under Short-Term Nonlinear Irregular Seastate." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-61495.
Повний текст джерелаАнотація:
In the assessment of marine structures in shallow waters domain it is important to take into account the nonlinear (or non-Gaussian) nature of the irregular waves when predicting short and long-term responses of such structures. Other sources of nonlinearities in the response are also present due to some nonlinear effects such as: wet-dry surface effects, wind force on dry parts of the structure, drag term in Morison hydrodynamic force equation, etc. The estimation of the characteristic short-term extreme responses requires the extreme value analysis of a non-Gaussian stochastic process. There are many approaches available in literature which can be employed, such as: Hermite-based model, Weibull-fitting model, etc. In this paper two distinct Weibull fitting models (one based on the first two and other based on the first three moments of the response peaks sample) and Hermite-based models using both conventional and linear moments (L-moments) are investigated for the prediction of extreme short-term response of mono-column wind tower installed in a water depth of 20m and subject to wave, current and wind loading. The tower responses (load effects) time-histories are obtained by means of a time-domain finite element-based program using 3-D geometric nonlinear beam elements developed for the dynamic analysis of this type of structure. In this program, the nonlinear behavior of the irregular waves is modelled by means of the second order Sharma and Dean theory [1] and the wind forces are represented by a very simplified load model based on wind velocity simulated time-series and the obstruction area of the tower and blades.
4
Putko, Michele M., and George T. Flowers. "A Study of the Nonlinear Dynamics of a Flap-Lag Rotor Model in Forward Flight." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0102.
Повний текст джерелаАнотація:
Abstract For the purposes of stability analyses, it is necessary to describe the dynamic equilibrium state of a rotor blade in forward flight in terms of a Fourier series. Typically, this is assumed to consist of constant and sinusoidal terms that are integer multiples of the rotor speed. Such an approach neglects potentially important dynamics associated with subsynchronous, supersynchronous, and aperiodic responses. The current work investigates the occurrence of such behavior and discusses some conditions where it may be important. Simulation studies are conducted using a simplified nonlinear rotor blade model in forward flight. This model consists of a rigid blade with effective hinges at the root to simulate a hingeless rotor blade. Quasi-steady linear strip theory is used to provide aerodynamic forcing in the model. The nonlinear terms arise from geometrical effects in the structural and aerodynamic modeling procedure. The resulting system of equations is studied using direct numerical integration and harmonic balancing. Nonsynchronous and aperiodic responses are observed for several realistic parameter configurations.
5
Kazemi, Reza, Ali Asghar Jafari, and Mohammad Faraji Mahyari. "The Effect of Drilling Mud Flow on the Lateral and Axial Vibrations of Drill String." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-25309.
Повний текст джерелаАнотація:
In this research, the effects of drilling mud flow and WOB force on the lateral vibration of drill string are investigated. To this goal, the kinetic and potential energy of drill string for axial and lateral vibrations are written in an integral equation. In potential energy equation, the effect of geometrical shortening, which causes nonlinear coupling between axial and lateral vibration, is considered. Drilling mud forces are modeled by Paidoussis formulations. The works done by WOB force, weight of drill string and drilling mud forces are calculated. The mode summation method is employed to convert the continuous system to a discrete one. Dropping and considering third and fourth order tensor of potential energy lead to linear and nonlinear system, respectively. The effects of stabilizers are modeled by a linear stiff spring. The wall contact is modeled by Hertzian contact force. Lagrange equation is employed for finding the equations of motions. First and second natural frequencies of drill string are found for different WOB and drilling mud flow. Also the effects of drilling mud and nonlinear terms on lateral vibration of drill string are investigated. The effect of drilling mud on the post buckling vibration of drill string is also delivered. This formulation can be used for optimization of drilling mud flow, WOB and the number and positions of stabilizer so that the lateral vibration of drill string is minimized.
6
Daghigh, M. "A New Formulation for Equivalent Hydrodynamic Modeling of the Jack-Up Legs." In ASME 2002 21st International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2002. http://dx.doi.org/10.1115/omae2002-28342.
Повний текст джерелаАнотація:
Regulations of offshore structures suggest the application of Morison type equation for the estimation of forces induced by wave and current on the slender bodies of Jacket and Jack-up structures. However, common values of hydrodynamic coefficients are rarely defined in two different regulations. Estimation of global responses of Jack-up structure, the simplified geometrical model is used, therefore we will try to modify the DNV formulations in order to estimate the hydrodynamic forces on equivalent pile. Finally, the forces on the real structure and the equivalent pile model are compared and it has been shown that the approximation of the inertia forces has more accuracy comparing to the drag force, due to the nonlinear effect in drag term.
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Vlaicu, Dan, and Mike Stojakovic. "Probabilistic Models to Approximate Highly Repetitive Linear and Nonlinear Finite Element Analyses of Nuclear Components." In ASME 2009 Pressure Vessels and Piping Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/pvp2009-77220.
Повний текст джерелаАнотація:
In the development and technical support of nuclear plants, Engineers have to deal with highly repetitive finite element analyses that involve modeling of local variations of the initial design, local flaws due to corrosion-erosion effects, material properties degradation, and modifications of the loading conditions. This paper presents the development of generic models that emulate the behavior of a complex finite element model in a simplified form, with the statistical representation based on a sampling of base-model data for a variety of test cases. An improved Latin Hypercube algorithm is employed to generate the sampling points based on the number and the range of the variables that are considered in the design space. Four filling methods of the approximation models are discussed in this study: response surface, nonlinear, neural networks, and piecewise polynomial model. Furthermore, a bootstrapping procedure is employed to improve the confidence intervals of the original coefficients, and the single-factor or double-factor analysis of variance is applied to determine whether a significant influence exists between the investigated factors. Two numerical examples highlight the accuracy and efficiency of the methods. The first example is the linear elastic analysis of a pipe bend under pressure loading. The objective of the probabilistic assessment is to determine the relation between the loading conditions as well as the geometrical aspects of this elbow (pipe wall thickness, outside diameter, elbow radius, and maximum ovality tolerance) and the maximum stress in the elbow. The second example is an axisymmetric nozzle under primary and secondary cycling loads. Variations of the geometrical dimensions, nonlinear material properties, and cycling loading are taken as the input parameters, whereas the response variable is defined in terms of Melan’s theorem translated into the Nonlinear Superposition Method.
8
Srinil, Narakorn, Hossein Zanganeh, and Alexander Day. "Experimental Investigation of Two-Degree-of-Freedom VIV of Circular Cylinder With Low Equivalent Mass and Variable Natural Frequency Ratio." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-10239.
Повний текст джерелаАнотація:
This paper presents an experimental investigation and validation of numerical prediction model for a 2-DOF VIV of a flexibly mounted circular cylinder by also accounting for the effect of geometrically nonlinear displacement coupling. A mechanical spring-cylinder system, achieving a low equivalent mass ratio in both in-line and cross-flow directions, is tested in a water towing tank and subject to a uniform steady flow in a sub-critical Reynolds number range of about 2000–50000. A generalized numerical model is based on double Duffing-van der Pol (structure-wake) oscillators which can capture the structural geometrical coupling and fluid-structure interaction effects through system cubic and quadratic nonlinearities. Experimental results are compared with numerical predictions in terms of response amplitudes, lock-in ranges and time-varying trajectories of cross-flow/in-line motions. Some good qualitative and quantitative agreements are found which encourage the use of the proposed numerical model subject to calibration and tuning of empirical coefficients. Various features of figure-of-eight orbital motions due to dual resonances are observed experimentally as well as numerically, depending on the natural frequency ratio of the oscillating cylinder.
9
Leadenham, S., and A. Erturk. "An M-Shaped Asymmetric Nonlinear Oscillator for Broadband Energy Harvesting." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13368.
Повний текст джерелаАнотація:
Nonlinear oscillators have been given growing attention due to their ability to enhance the performance of energy harvesting devices by increasing the frequency bandwidth. Duffing oscillators are a typical type of nonlinear oscillator characterized by a symmetric hardening or softening cubic restoring force. In order to realize the cubic nonlinearity in a cantilever at reasonable excitation levels, often an external magnetic field or mechanical load is imposed, since the inherent geometric nonlinearity would otherwise require impractically high excitation levels to be pronounced. As an alternative to magnetoelastic structures and other forms of symmetric Duffing oscillators, in this paper, an M-shaped bent beam with clamped end conditions is investigated for bandwidth enhancement under base excitation. The M-shaped beam geometry can exhibit significantly asymmetric spring behavior: hardening in one direction and softening in the other. A particular advantage of the M-shaped structure is its well-pronounced nonlinear characteristics without needing an external component to create hardening or softening. The force-displacement relationship of the M-shaped beam with a central lumped mass attachment is experimentally identified and asymmetric nonlinear behavior is verified. The purely elastic system parameters (such as the linear and nonlinear stiffness components) identified from the experiments are used in numerical simulations and compared with the experimental results. A quadratic damping term is included to account for nonlinear dissipative effects. Bandwidth enhancement with increasing base excitation is investigated experimentally and numerically. Very good agreement is observed between the simulated frequency response curves and experimental measurements.
10
Rabinovich, Oded, and Yeoshua Frostig. "High-Order Analysis of Unidirectional Sandwich Panels With Flat and Generally Piecewise Curved Faces and a “Soft” Core." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-2037.
Повний текст джерелаАнотація:
Abstract The bending behavior of a unidirectional sandwich panel with flat and generally piecewise curved faces and a flexible core in the vertical direction is investigated. The studied panels consist of an upper flat face sheet, a core of a variable thickness, and a lower face sheet that can take any geometrical layout described by a piecewise analytical function. The core is assumed to be a two-dimensional elastic medium with vertical and shear rigidities only, and the faces are considered to have membrane and bending rigidities and are made of metallic or composite materials. The field equations and the boundary conditions are rigorously derived using the variational principle of virtual work. The continuity conditions between the various regions of the generally piecewise curved face are presented. Higher order effects in the form of nonlinear deformation distributions through the thickness due to flexibility of the core are incorporated in the proposed analysis. Numerical results in terms of deformations, stresses, and stress resultants are presented for some typical cases of piecewise flat-curved panels. The results demonstrate the capabilities and generality of the proposed model, especially in the ability to predict the high-order localized effects and the high stress concentrations that characterize these panels.