Nonlinear dynamic analysis of moving bilayer plates resting on elastic foundations

The aim of this study is to investigate the dynamic response of axially moving two-layer laminated plates on the Winkler and Pasternak foundations. The upper and lower layers are formed from a bidirectional functionally graded(FG) layer and a graphene platelet(GPL) reinforced porous layer, respectively. Henceforth, the combined layers will be referred to as a two-dimensional(2D) FG/GPL plate. Two types of porosity and three graphene dispersion patterns, each of which is distributed through the p...     

Nonlinear vibration of functionally graded graphene-reinforced composite laminated beams resting on elastic foundations in thermal environments

Modeling and nonlinear vibration analysis of graphene-reinforced composite (GRC) laminated beams resting on elastic foundations in thermal environments are presented. The graphene reinforcements are assumed to be aligned and are distributed either uniformly or functionally graded of piece-wise type along the thickness of the beam. The motion equations of the beams are based on a higher-order shear deformation beam theory and von Kármán strain displacement relationships. The beam–foundation interaction and thermal effects are also included. The temperature-dependent material properties of GRCs are estimated through a micromechanical model. A two-step perturbation approach is employed to determine the nonlinear-to-linear frequency ratios of GRC laminated beams. Detailed parametric studies are carried out to investigate the effects of material property gradient, temperature variation, stacking sequence as well as the foundation stiffness on the linear and nonlinear vibration characteristics of the GRC laminated beams.     

Vibration of thermally postbuckled carbon nanotube-reinforced composite beams resting on elastic foundations

This paper investigates the small- and large-amplitude vibrations of thermally postbuckled carbon nanotube-reinforced composite (CNTRC) beams resting on elastic foundations. For the CNTRC beams, uniformly distributed (UD) and functionally graded (FG) reinforcements are considered where the temperature-dependent material properties of CNRTC beams are assumed to be graded in the thickness direction and estimated through a micromechanical model. The motion equations are derived based on a higher order shear deformation beam theory with including the beam-foundation interaction. The initial deflection caused by thermal postbuckling is also included. The numerical illustrations concern small- and large-amplitude vibration characteristics of thermally postbuckled CNTRC beams under uniform temperature field. The effects of carbon nanotube (CNT) volume fraction and distribution patterns as well as foundation stiffness on the vibration characteristics of CNTRC beams are examined in detail.     

复合材料层合板壳的非线性热动态响应分析

本文基于高阶剪切变形理论，考虑同天应变和横向剪切应变的影响，对受热复合材料层合板壳的非线性热动态响应进行分析，计及了转动惯量的影响，给出了通用性较好的Ｃ＾０类有限元公式，文中数值算同现有文献和三维有限元计算结果进行了比较，证明了本文方法的精确、有效性，文中还就层合板的边界条件、纵厚比及铺设角度对非线性热动态响应的影响进行了分析。     

Shear buckling of infinite plates resting on tensionless elastic foundations

The buckling problem of an infinite thin plate resting on a tensionless Winkler foundation and subjected to shearing loads is investigated. The infinite plate is simplified to a one-dimensional mechanical model by assuming a lateral buckling mode function and a borderline function between contact and non-contact regions. After the governing differential equations for the plate sections in the contact and non-contact regions have been solved, the problem reduces to two nonlinear algebraic equations. Buckling coefficients for plates with simply supported edges and clamped edges are determined for a range of relative foundation stiffness factors. Comparison of the results with existing theory and finite element analyses shows good agreement.     

Nonlinear bending analysis of FGM rectangular plates with various supported boundaries resting on two-parameter elastic foundations

In this paper, model of the FGM plates resting on two-parameter elastic foundations is put forward by using on physical neutral surface and high-order shear deformation theory. Material properties are assumed to be temperature dependent and vary along the thickness, while Poisson’s ratio depends weakly on temperature change and position and is assumed to be a constant. It is worth noting that physical neutral surface will be changed with temperature. The character of physical neutral surface higher-order shear deformation plate theory is that the displacements have special forms, stretching-bending couplings are eliminated in constitutive equations, and governing equations have the simple and similar forms as homogeneous isotropic plates. The validity of physical neutral surface higher-order shear deformation plate theory can be confirmed by comparing with related researchers’ results. Nonlinear bending approximate solutions of FGM rectangular plates with six cases of boundary conditions are given out using Ritz method, and influences played by different supported boundaries, foundation stiffnesses, thermal environmental conditions, and volume fraction index are discussed in detail.     

Large amplitude response of circular plates on elastic foundations

The von Kármán type partial differential equations governing non-linear dynamic behaviour of circular plates resting on Winkler and Pasternak elastic foundations have been analysed analytically. The space and time-wise integrations have been carried out employing the Chebyshev polynomials and implicit Houbolt techniques, respectively. The influence of foundation parameters K and G on the large amplitude response of circular plates subjected to step function loads has been studied for both the clamped immovable as well as simply supported immovable edge conditions. Foundation parameters K and G have been determined for the minimax central response. For all values of K,values of G should be between 30 and 40 for the clamped circular plates and the value of G should be a maximum for the simply supported circular plates.     

Bending of a fiber-reinforced viscoelastic composite plate resting on elastic foundations

Composite structures on an elastic foundation are being widely used in engineering applications. Bending response of inhomogeneous viscoelastic plate as a composite structure on a two-parameter (Pasternak’s type) elastic foundation is investigated. The formulations are based on sinusoidal shear deformation plate theory. Trigonometric terms are used in the present theory for the displacements in addition to the initial terms of a power series through the thickness. The transverse shear correction factors are not needed because a correct representation of the transverse shear strain is given. The interaction between the plate and the foundation is included in the formulation with a two-parameter Pasternak’s model. The effective moduli and Illyushin’s approximation methods are used to derive the viscoelastic solution. The effects played by foundation stiffness, plate aspect ratio, and other parameters are presented.     

Nonlinear vibrations of FGM rectangular plates in thermal environments

Geometrically nonlinear vibrations of FGM rectangular plates in thermal environments are investigated via multi-modal energy approach. Both nonlinear first-order shear deformation theory and von Karman theory are used to model simply supported FGM plates with movable edges. Using Lagrange equations of motion, the energy functional is reduced to a system of infinite nonlinear ordinary differential equations with quadratic and cubic nonlinearities. A pseudo-arclength continuation and collocation scheme is used and it is revealed that, in order to obtain the accurate natural frequency in thermal environments, an analysis based on the full nonlinear model is unavoidable since the plate loses its original flat configuration due to thermal loads. The effect of temperature variations as well as volume fraction exponent is discussed and it is illustrated that thermally deformed FGM plates have stronger hardening behaviour; on the other hand, the effect of volume fraction exponent is not significant, but modal interactions may rise in thermally deformed FGM plates that could not be seen in their undeformed isotropic counterparts. Moreover, a bifurcation analysis is carried out using Gear’s backward differentiation formula (BDF); bifurcation diagrams of Poincaré maps and maximum Lyapunov exponents are obtained in order to detect and classify bifurcations and complex nonlinear dynamics.     

Nonlinear dynamic stability of composite laminated plates

Catastrophe theory was applied to the investigation of nonlinear dynamic stability of composite laminated plates. The influence of large deflection, initial imperfection,support conditions and ply-angle of the fibers were considered. The catastrophic models and the critical conditions of dynamic buckling of composite laminated plates are obtained.     

Dynamic response of elastic plates on viscoelastic foundations to moving loads

Summary The steady-state response of an inifinite plate strip on a foundation of Kelvin material to a moving harmonic line load is presented. The line of application of the load is perpendicular to the infinite edges of the plate, and the load moves parallel to the edges at constant speed. The equations of motion for the plate are those of Mindlin, and they are solved by the integral transform technique. The uniqueness and existence of the physically reasonable solution for any speed of the moving load are discussed. The transient response of the same plate, but with semi-infinite length, is formulated as a mixed initial-boundary value problem. A numerical solution by the method of characteristics is proposed. The propagation of stress discontinuities along wave fronts is also investigated.

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Übersicht Es wird das Verhalten eines unendlich langen Plattenstreifens auf einem Fundament aus Kelvin-Material unter einer sich bewegenden, harmonisch über die Breite verteilten Linienlast nach Erreichung des Beharrungszustandes beschrieben. Die Angriffslinie der Last steht senkrecht auf den unendlich langen Kanten der Platte; die Last bewegt sich parallel zu den Kanten mit gleichförmiger Geschwindigkeit. Die Bewegungsgleichungen für die Platte sind dieselben wie die von Mindlin; sie werden durch eine Integral-Transformation gelöst. Die Eindeutigkeit und Existenz der physikalisch sinnvollen Lösung für beliebige Geschwindigkeiten der wandernden Last werden diskutiert. Der Einschwingvorgang derselben, von Null bis ins Unendliche erstreckten Platte wird als gemischtes Anfangs-Grenzwert-Problem behandelt. Eine numerische Lösung mit Hilfe des Charakteristiken-Verfahrens wird vorgeschlagen. Das Fortschreiten von Spannungssprüngen längs Wellenfronten wird ebenfalls untersucht.

     

流固冲击载荷下弹性约束加筋板的非线性动力响应

本文在考虑大变形、忽略阻尼影响的情况下,基于高散加筋板模型,对具有弹性约束边界的加筋板在流固冲击载荷下的非线性瞬态响应进行了理论研究.取样条函数作为挠度试函数,运用加权残值法求得加筋板动力响应的控制方程,采用四阶Runge-Kutta法求解该方程,并用Fortran语言编制了相应的计算程序.构造的B样条函数能适应板侧边上的任意弹性转动约束.文中不仅分析了不同的冲击载荷形式对加筋板动力特性的影响,还讨论了载荷峰值、冲击栽荷持续时问、加强筋和弹性转动约束的影响.     

Dynamic response of plates on elastic foundations due to the moving loads

This paper discusses the dynamic response of thin plates on the elastic foundations due to the moving loads by means of the variational calculus. In the text we take the mass of moving loads into account, treat a series of questions such as the forced oscillations, the influence surfaces of the flexions and the influence surfaces of the inner forces, resonance conditions and critical speed and so forth.     

On the simple and mixed first-order theories for functionally graded plates resting on elastic foundations

In this article, the bending response of a functionally graded plate resting on elastic foundations and subjected to a transverse mechanical load is investigated. An accurate solution for the functionally graded plate with simply supported edges resting on elastic foundations is presented. The interaction between the plate and the elastic foundations is considered and included in the equilibrium equations. Pasternak’s model is used to describe the two-parameter elastic foundations, and get a special case of Winkler’s model by considering one-parameter of elastic foundation. A relationship between the simple and mixed first-order transverse shear deformation theories is presented. Numerical results for deflections and stresses of functionally graded plates are investigated. Comparisons between the results of the simple and mixed first-order theories are made, and appropriate conclusion is formulated. Additional boundary conditions at the edges of the present plates are investigated.     

Axisymmetric shells and plates on tensionless elastic foundations

This paper first describes a finite element method for the large deflection analysis of axisymmetric shells and plates on a nonlinear tensionless elastic foundation. Through the use of discrete data points, any form of nonlinear elastic foundation behaviour can be easily modelled. The analysis is then validated by comparison with existing results for circular plates and beams as the only existing results for shells on tensionless foundations are found to be in error. Following this verification, the analysis is applied to investigate the behaviour of shallow spherical shells subject to a central concentrated load on tensionless linear elastic foundations. A number of insightful conclusions regarding the behaviour of such structure-foundation systems are drawn. The numerical results for shells are believed to be the first correct results, which may be useful in benchmarking results from other sources in the future.     

Thick rectangular plates with free edges on elastic foundations

In this paper an accurate solution for the thick rectangular plate with free edges laid onelastic foundation is presented.The superposition method of trigonometric series is used.The method can solve this kind of plates directly and simply.Its results completely satisfythe boundary conditions of the four free edges and nicely agree with the solutions by WangKe-lin and Huang Yi.     

Nonlinear vibrations,bifurcations and chaos of lattice sandwich composite panels on Winkler–Pasternak elastic foundations with thermal effects in supersonic airflow

Meccanica - This paper is devoted to investigate the nonlinear dynamic characteristics of lattice sandwich composite panels resting on Winkler–Pasternak elastic foundations under simultaneous...