Nonlinear vibration of shear deformable FGM cylindrical shells surrounded by an elastic medium

This paper investigates the large amplitude vibration behavior of a shear deformable FGM cylindrical shell of finite length embedded in a large outer elastic medium and in thermal environments. The surrounding elastic medium is modeled as a Pasternak foundation. Two kinds of micromechanics models, namely, Voigt model and Mori-Tanaka model, are considered. The motion equations are based on a higher order shear deformation shell theory that includes shell-foundation interaction. The thermal effects are also included and the material properties of FGMs are assumed to be temperature-dependent. The equations of motion are solved by a two step perturbation technique to determine the nonlinear frequencies of the FGM shells. Numerical results demonstrate that in most cases the natural frequencies of the FGM shells are increased but the nonlinear to linear frequency ratios of the FGM shells are decreased with increase in foundation stiffness. The results confirm that in most cases Voigt model and Mori-Tanaka model have the same accuracy for predicting the vibration characteristics of FGM shells.     

低速冲击下含损伤层合中厚浅球壳的非线性动力响应分析

基于中厚壳几何非线性理论和损伤理论 , 采用应变描述的失效准则 , 导出了层合浅球壳含基体损伤和纤维2基体剪切损伤的损伤本构关系 , 建立了低速冲击下轴对称正交对称铺设层合中厚浅球壳的非线性运动控制方程。对未知函数在空间域采用正交配置法离散 , 时间域采用 Newmark2 β方法离散 , 对整个问题进行迭代求解。数值结果表明 , 损伤、 冲击物的初速度以及结构的几何参数都在不同程度上影响着低速冲击下结构所受的冲击载荷和结构的非线性动力响应。      

Dynamic behaviour of edge-cracked shear deformable functionally graded beams on an elastic foundation under a moving load

This paper studies the dynamic response of functionally graded beams with an open edge crack resting on an elastic foundation subjected to a transverse load moving at a constant speed. It is assumed that the material properties follow an exponential variation through the thickness direction. Theoretical formulations are based on Timoshenko beam theory to account for the transverse shear deformation. The cracked beam is modeled as an assembly of two sub-beams connected through a linear rotational spring. The governing equations of motion are derived by using Hamilton’s principle and transformed into a set of dynamic equations through Galerkin’s procedure. The natural frequencies and dynamic response with different end supports are obtained. Numerical results are presented to investigate the influences of crack location, crack depth, material property gradient, slenderness ratio, foundation stiffness parameters, velocity of the moving load and boundary conditions on both free vibration and dynamic response of cracked functionally graded beams.     

ALE方法模拟爆炸载荷作用下球壳反直观行为

本文利用任意拉格朗日与欧拉（ALE）方法,模拟了球壳在爆炸载荷作用下的动力反直观行为,得到了球壳中点位移时程曲线以及最终变形模式等动力响应。在研究中,考虑了材料的应变率效应,并对球壳的矢高和厚度对其反直观行为的影响进行了参数分析。结果表明,只有炸药距球壳距离在特定范围内,球壳才能发生反直观行为;当炸药当量一定时,球壳发生反直观行为的爆心距区域段随球壳矢高增加而减少,矢跨比大于一定值后,将不会发生反直观行为     

Static and dynamic analysis of an FGM doubly curved panel resting on the Pasternak-type elastic foundation

The static, dynamic, and free vibration analysis of a functionally graded material (FGM) doubly curved panel are investigated analytically in the present paper. The FGM Panel is originated from a rectangular planform and its principle curvatures are considered to be constant. All mechanical properties of the FGM panel are assumed to vary continuously through the thickness according to a power law formulation except Poisson’s ratio, which is kept constant. A Pasternak-type elastic foundation containing damping effects is considered to be in contact with the panel during deformation. The elastic foundation reacts in both compression and tension. Equations of motion are established based on the first order shear deformation and the modified Sanders shell theories. Following the Navier type solution, the established equations are reduced to time-dependent ordinary differential equations. Using the Laplace transform, the time-dependency of the problem is eliminated. The solutions are obtained analytically in the Laplace domain and then are inverted to the time domain following an analytical procedure. Finally, the analytical results are verified with those reported in the literature.     

Nonlinear dynamic response and vibration of imperfect shear deformable functionally graded plates subjected to blast and thermal loads

Based on Reddy's higher-order shear deformation plate theory, this article presents an analysis of the nonlinear dynamic response and vibration of imperfect functionally graded material (FGM) thick plates subjected to blast and thermal loads resting on elastic foundations. The material properties are assumed to be temperature-dependent and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. Numerical results for the dynamic response and vibration of the FGM plates with two cases of boundary conditions are obtained by the Galerkin method and fourth-order Runge–Kutta method. The results show the effects of geometrical parameters, material properties, imperfections, temperature increment, elastic foundations, and boundary conditions on the nonlinear dynamic response and vibration of FGM plates.     

Nonlinear eccentric low-velocity impact response of a polymer-carbon nanotube-fiber multiscale nanocomposite plate resting on elastic foundations in hygrothermal environments

In the present article, a nonlinear, eccentric, low-velocity impact response of a polymer-carbon nanotube-fiber multiscale nanocomposite plate on elastic foundations in hygrothermal conditions using the finite element method is performed. In this regard, the governing equations are derived based on higher-order shear deformation plate theory and von Kármán geometrical nonlinearity. Three types of distributions of the temperature field and moisture concentrations, namely, uniformly, linearly, or nonlinearly through the thickness direction of the plates are considered. The effective material properties of the multiphase nanocomposite are calculated using fiber micromechanics and Halpin–Tsai equations in hierarchy. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the matrix. The contact force between the impactor and the plate is obtained with the aid of the modified nonlinear Hertzian contact law models. After examining the validity of the present work, the effects of the weight percentage of CNT, moisture concentration, temperature variations, distribution of temperature and moisture concentration, elastic foundation, and the eccentricity on the contact force, indentation, and central deflection of polymer-CNT-fiber multiscale nanocomposite plate are studied in details.     

Free vibration analysis of FGM cylindrical shell partially resting on Pasternak elastic foundation with an oblique edge

The free vibration characteristics of FGM cylindrical shells partially resting on elastic foundation with an oblique edge are investigated by an analytical method. The cylindrical shell is partially surrounded by an elastic foundation which is represented by the Pasternak model. An edge of an elastic foundation lies in a plane that is oblique at an angle with the shell axis. The motion of shell is represented based on the first order shear deformation theory (FSDT) to account for rotary inertia and transverse shear strains. The functionally graded cylindrical shell is composed of stainless steel and silicon nitride. Material properties vary continuously through the thickness according to a four-parameter power law distribution in terms of volume fraction of the constituents. The equation of motion for eigenvalue problem is obtained using Rayleigh–Ritz method and variational approach. To validate the present method, the numerical example is presented and compared with the available existing results.     

Nonlinear thermo-mechanical response of eccentrically stiffened Sigmoid FGM circular cylindrical shells subjected to compressive and uniform radial loads using the Reddy's third-order shear deformation shell theory

Based on Reddy's third-order shear deformation shell theory, this paper presents an analytical approach to investigate the nonlinear thermo-mechanical response of imperfect Sigmoid FGM circular cylindrical shells surrounded on elastic foundations and reinforced by outside metal stiffeners. The eccentrically stiffened S-FGM shells are subjected to axial compressive load and uniform radial load in thermal environment. Using the stress function, Bubnov–Galerkin method, the paper proposes the formula for forces and moments taking into account the thermal stress in both the shells and stiffeners. The obtained results are validated by comparing with other results reported in the literature.     

Nonlinear free and forced vibration behavior of functionally graded plate with piezoelectric layers in thermal environment

In the present study, finite element formulation based on higher order shear deformation plate theory is developed to analyze nonlinear natural frequencies, time and frequency responses of functionally graded plate with surface-bonded piezoelectric layers under thermal, electrical and mechanical loads. The von Karman nonlinear strain–displacement relationship is used to account for the large deflection of the plate. The material properties of functionally graded material (FGM) are assumed temperature-dependent. The temperature field has uniform distribution over the plate surface and varies in the thickness direction. The considered electric field only has non-zero-valued component E_z. Numerical results are presented to study effects of FGM volume fraction exponent, applied voltage in piezoelectric layers, thermal load and vibration amplitude on nonlinear natural frequencies and time response of FGM plate with integrated piezoelectric layers. In addition, nonlinear frequency response diagrams of the plate are presented and effects of different parameters such as FGM volume fraction exponent, temperature gradient, and piezoelectric voltage are investigated.