Analytical investigation on the free vibration behavior of rotating FGM truncated conical shells reinforced by orthogonal eccentric stiffeners

This article presents an analytical investigation on the free vibration behavior of rotating functionally graded truncated conical shells reinforced by stringers and rings with the change of spacing between stringers. Using the Donnell shell theory, smeared stiffeners technique, and taking into account the influences of centrifugal force and Coriolis acceleration, the governing equations are derived. These variable coefficient partial differential equations are studied by the Galerkin method. The sixth-order polynomial equation of natural frequency is obtained. Numerical results show effects of stiffener and input parameters on the frequency of shell.     

Buckling analysis of moderately thick FG carbon nanotube reinforced composite conical shells under axial compression by DQM

A semi-analytical method is presented to study the buckling of moderately thick carbon nanotube reinforced composite conical shells under axial compression. Material properties are assumed to be graded across the shell thickness. In order to derive the equilibrium equations of the shell, first-order shear deformation theory is used. Then, the partial differential equations are transformed to algebraic type by using the differential quadrature method. To validate the results obtained in this study, comparisons are made with the outcomes of previous studies. Finally, the effects of the geometry of the shell, circumferential mode number, volume fraction of the carbon nanotube, and boundary conditions are studied.     

四边固支功能梯度板中波的传播

摘要：考虑剪切变形和转动惯性的影响,采用一阶剪切变形板理论和小应变的应变－位移关系,利用Hamilton原理推得运动控制方程,并应用特征值方程得到频散方程。给出了波在功能梯度板中传播的频散,相速度和群速度随波数变化的曲线,分析了不同的功能梯度材料指数对波传播的影响规律。     

基于一阶剪切变形理论的功能梯度球环振动特性

提出一种半解析法分析了一般边界条件下中等厚度功能梯度球环结构的自由振动特性。基于一阶剪切变形理论推导了中等厚度功能梯度球环结构公式,其中位移函数用改进傅里叶级数表示以消除边界的不连续性,并利用弹簧参数法来模拟一般边界条件;利用里兹法求解得到功能梯度球环结构的固有频率;在收敛性分析的基础上,将本文结果与有限元法、试验数据和文献数据进行了对比,并探讨相关参数的影响。研究表明,本文提出的方法收敛性好,求解精度高;功能梯度球环结构频率参数随厚度和剪切修正系数的增大而增大。     

含裂纹缺陷的预扭壳结构非线性振动特性研究

基于扩展等几何方法和一阶壳体剪切变形理论建立了含裂纹缺陷的功能梯度预扭壳结构的非线性振动控制方程.控制方程中考虑了预扭壳结构的预扭角度及几何非线性,应用扩展等几何方法,采用反映位移变化的富集函数来描述裂纹的位置及长度,一方面可以提高计算精度,另一方面可以避免在裂纹处的网格加密,提高计算效率.采用了直接迭代法求解非线性振动控制方程.通过与现有文献结果对比,证明了本文方法的正确性和稳定性.在此基础上,探究裂纹对功能梯度预扭壳结构非线性振动频率的影响,研究了预扭角度、裂纹位置及长度和材料的功能梯度指数等参数对预扭壳非线性振动特性的影响规律.     

功能梯度材料梁在后屈曲构型附近的自由振动

基于轴线可伸长杆的几何非线性理论,建立了由陶瓷和金属两种材料组成的功能梯度(FGM)梁在轴向载荷作用下后屈曲横向自由振动的精确模型,采用打靶法数值求解了一端可移简支一端固定的功能梯度梁在后屈曲附近的小振幅自由振动,获得了线性振动的响应,给出了不同梯度指标下FGM梁前三阶固有频率与载荷之间的特征关系曲线.数值结果表明,屈曲前各阶频率随轴向力的增加而降低,而屈曲后轴向力对各阶频率影响不同     

Differential quadrature method for nonlocal nonlinear vibration analysis of a boron nitride nanotube using sinusoidal shear deformation theory

This article presents a nonlocal sinusoidal shear deformation beam theory (SDBT) for the nonlinear vibration of single-walled boron nitride nanotubes (SWBNNTs). The surrounding elastic medium is simulated based on nonlinear Pasternak foundation. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the SWBNNTs are derived using Hamilton's principle. Differential quadrature method (DQM) for the nonlinear frequency is presented, and the obtained results are compared with those predicted by the nonlocal Timoshenko beam theory (TBT). The effects of nonlocal parameter, vibrational modes, length, and elastic medium on the nonlinear frequency of SWBNNTs are considered.     

Three-dimensional static and dynamic analyses of the functionally graded cylinder bonded to the laminated plate under general loading

A graded finite element method code based on Rayleigh–Ritz energy formulation is developed and implemented to study the elastic behavior of a layered plate loaded by a solid isotropic cylinder and a functionally graded interlayer. The applied nonaxisymmetric loading to the inner cylinder induces a stress concentration in the flexible part of the joint. The effects of different thicknesses and power law exponents of functionally graded interlayer on the distribution of displacements and stresses are investigated, which verifies the ability of functionally graded material to control the stress and displacement waves. The time-dependent response of the structure is also obtained based on Newmark's time integration method.     

Influences of elastic foundations and shear deformations on the buckling behavior of functionally graded material truncated conical shells under axial compression

This article presents an investigation on the buckling of functionally graded (FG) truncated conical shells under an axial load resting on elastic foundations within the shear deformation theory (SDT). The governing equations are solved using the Galerkin method, and the closed-form solution of the axial buckling load for FG conical shells on elastic foundations within the SDT is obtained. Various numerical examples are presented and discussed to verify the accuracy of the closed-form solution in predicting dimensionless buckling loads for FG conical shells on the Winkler–Pasternak elastic foundations within the SDT.     

Buckling and vibrations of two-directional FGM Mindlin circular plates under hydrostatic peripheral loading

An analysis is presented for the effect of hydrostatic peripheral loading on the free axisymmetric vibrations of functionally graded moderately thick circular plates on the basis of first-order shear deformation theory. The mechanical properties of the plate material are supposed to vary according to a power-law in both the radial and transverse directions. The numerical solution of the governing differential equation derived by using Hamilton's energy principle for such simply supported and clamped boundary conditions has been obtained employing the harmonic differential quadrature method choosing zeros of Chebyshev–Gauss–Lobatto as the grid points. The effect of different parameters has been analyzed on the frequency parameter for the first three modes of vibration. The critical buckling loads for both the plates have been computed by putting the frequencies to zero. Three-dimensional mode shapes for particular plate have been plotted. Obtained results have been compared.     

功能梯度材料圆板的三维弹性分析

基于线弹性理论的基本方程,选用两个位移分量和两个应力分量作为状态变量,利用状态空间法建立了功能梯度材料轴对称圆板的三维状态方程.根据微分求积法,将状态方程在径向进行离散,考虑周边固支的边界条件,采用打靶法数值求解了材料常数沿板厚按幂率变化的轴对称弯曲问题和自由振动问题,为求解功能梯度材料三维弹性响应提供了一种方法.并且给出了功能梯度材料三维圆板的静动态响应受组分材料分布以及板厚径比变化的影响规律.     

Evaluation of nonlocal higher order shear deformation models for the vibrational analysis of functionally graded nanostructures

Small scale effects in the functionally graded beam are investigated by using various nonlocal higher-order shear deformation beam theories. The material properties of a beam are supposed to vary according to power law distribution of the volume fraction of the constituents. The nonlocal equilibrium equations are obtained and an exact solution is presented for vibration analysis of functionally graded (FG) nanobeams. The accuracy of the present model is discussed by comparing the results with previous studies and a parametric investigation is presented to study the effects of power law index, small-scale parameter, and aspect ratio on the vibrational behavior of FG nanostructures.     

基于物理中面FGM梁的非线性力学行为

当坐标面置于功能梯度材料(FGM)梁的物理中面上时,其本构方程中,面内力与弯矩并不耦合,这使得问题的控制方程以及边界条件得以简化.该文利用物理中面概念,基于一阶非线性梁理论,导出了FGM梁的基本方程,分析研究了热载荷作用下FGM梁的过屈曲、弯曲以及在这些构形上的振动等问题.假设功能梯度材料性质只沿梁厚度方向,并按成分含...     

Electro-magneto temperature-dependent vibration analysis of functionally graded-carbon nanotube-reinforced piezoelectric Mindlin cylindrical shells resting on a temperature-dependent,orthotropic elastic medium

Vibration smart control analysis of a temperature-dependent functionally graded-carbon nanotube-reinforced piezoelectric cylindrical shell embedded in an orthotropic elastic medium is investigated. The mixture law is used for obtaining the material properties of the structure. The structure is subjected to a 2D magnetic field. Considering the first-order shear deformation theory, the motion equations are obtained. Based on an analytical method and differential quadrature method, the frequency is calculated. The effects of applied voltage, magnetic field, volume percent, and distribution type of carbon nanotubes, temperature, orthotropic elastic medium, and length to radius ratio of the shell are shown on system frequency.     

Mechanical buckling of two-dimensional functionally graded cylindrical shells surrounded by Winkler–Pasternak elastic foundation

In this research, buckling analysis of a two-dimensional, functionally graded, cylindrical shell that has been embedded in an outer elastic medium in the presence of combined axial and transverse loading based on third-order shear deformation shell theory is numerically investigated. Variations of the shell properties are considered to be continuous through length and thickness. Winkler–Pasternak foundation and simply supported boundary conditions have been applied. The problem has been solved using the generalized differential quadrature method. Geometrical, load, and foundation parameters beside functionally graded power indexes effects on the critical buckling load have been studied.