均匀热载荷作用下功能梯度圆板的非线性振动

基于经典板理论,研究了热载荷作用下功能梯度圆板的大幅振动问题.在经典板理论下利用物理中面概念,导出了功能梯度圆板的非线性运动方程.利用Ritz?Kantorovich方法消去时间变量,将非线性运动方程转换成了一组关于空间变量的非线性常微分方程.采用打靶法数值求解所得方程,并利用数值结果研究了热载荷作用下功能梯度圆板静态...     

横观各向同性功能梯度材料矩形板的自由振动

考察了沿厚度方向材料和为非均匀的功能梯度横观各向同性矩形板的自由振动。通过引入两个位移函数和两个应力函数导出了两个独立的变系数状态方程,进一步利用分层反似理论,将变系数状态方程为常纱数状态方程并求解,发现存在两类的自由振动形式：第一类对应纯板内振动,第二类对应一般的弯曲振动。给出了数值结果,讨论了材料梯度指标对固有频率的影响。     

热环境下功能梯度环板的谱几何法自由振动解EI北大核心CSCD

采用谱几何法建立了热环境下功能梯度环板自由振动分析模型。首先,在该模型中假设材料特性与温度相关,且沿结构厚度方向呈现连续梯度变化;其次,通过在边界处设置不同类型的边界弹簧来模拟任意边界条件,并且基于一阶剪切变形理论推导出热环境下功能梯度环板结构的能量方程;然后,利用谱几何法和傅里叶正余弦函数来描述结构位移容许函数,进而采用Rayleigh-Ritz法获得功能梯度环板结构热振特性分析理论模型。通过热环境下功能梯度环板频率特性对比算例发现,该模型具有良好的计算准确性,并且适用于多种边界条件。最后,给出功能梯度环板结构的参数化研究,研究结果表明,环境温度、边界条件、梯度指数的变化均会对结构的热振特性产生影响。     

热过屈曲正交异性圆(环)板的自由振动响应

基于vonKármán薄板几何非线性理论,建立了以中面位移为基本未知量的加热极正交异性圆板轴对称大挠度动力学控制方程。然后,将控制方程的响应分解为热过屈曲静态解和振动解两部分,并在小振幅振动假设下得到了板在热过屈曲静平衡构形附近自由振动的线性微分方程。最后,采用打靶法获得了板在热过屈曲前后的固有频率与升温参数之间的特征关系曲线。结果表明,周边面内约束板的前两阶固有频率在热屈曲前随着温度升高而降低,而一旦板进入过屈曲平衡状态,前两阶频率都随着升温而单调增加。     

热环境中功能梯度圆板的非线性动力响应分析

研究了热环境中功能梯度圆板在横向简谐激励作用下的非线性动力响应和动应力问题。针对陶瓷-金属功能梯度圆板, 考虑几何非线性、材料物理性质参数随温度变化及材料组分沿厚度方向按幂律分布的情况, 应用虚功原理给出了热载荷与横向简谐载荷共同作用下的非线性振动偏微分方程。在固支无滑动的边界条件下, 利用伽辽金法得到了达芬型非线性强迫振动方程。通过数值算例, 给出了关于体积分数指数的分岔图, 相图、Poincare映射等响应图以及动应力变化规律图, 讨论了材料体积分数指数和温度场对功能梯度圆板非线性动力响应的影响。结果表明: 热环境中功能梯度圆板随体积分数指数的变化可使系统出现周期响应、倍周期响应和混沌响应。功能梯度圆板中心处动应力在系统发生分岔或出现混沌响应时出现大幅变化, 而且在混沌响应时具有不可预测性。      

热环境下功能梯度材料板的自由振动和动力响应

基于Reddy高阶剪切变形理论和广义Kármán型方程,用双重Fourier级数展开法求得了四边简支功能梯度材料板的自由振动及动力响应的解析解,分析中考虑了热传导以及组分材料热物参数对温度变化的依赖性,讨论了材料组分指数和热环境对固有频率及动力响应的影响。     

四边简支功能梯度矩形板的热屈曲分析

基于经典板理论,假设材料性质为板厚度方向坐标的幂函数,推导了功能梯度材料矩形板在热荷载作用下的平衡方程和稳定方程。给出了四边简支的功能梯度板在均匀受热时临界屈曲温度变化的封闭解,讨论了板的几何外形尺寸、相对厚度、梯度指数以及中面变形等因素对临界屈曲温度变化的影响。     

Winkler地基上功能梯度材料矩形厚板的自由振动

直接从三维弹性力学方程基本出发,利用状态空间法并结合层合模型,分析了Winkler地基上具有横观各向异性的功能梯度矩形厚板的自由振动问题,得出了两类独立的自由振动形式。给出了数值例子,并讨论了材料梯度指标的影响。     

前屈曲耦合变形对FGM圆板稳定性的影响

功能梯度材料结构沿厚度方向具有非均匀性,在其本构关系中会存在拉伸-弯曲耦合效应。在某些条件下,由于这个耦合效应的存在会引起前屈曲耦合变形,因此只要施加面内外载荷,就会伴随该载荷而产生耦合挠度。该文基于经典非线性板理论,导出了计及前屈曲耦合变形时功能梯度圆板稳定性问题的基本方程,并给出了判断功能梯度圆板是否发生屈曲现象的方法。用打靶方法对所得方程进行了数值求解,并利用数值结果研究了在不同边界条件和不同外因素下前屈曲耦合变形对功能梯度圆板稳定性的影响。     

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.     

Large amplitude vibration analysis of functionally graded laminated skew plates in thermal environment

Large amplitude vibration analysis of functionally graded laminated skew plates in thermal environment has been studied. The mechanical properties are assumed to be temperature-dependent and graded in the thickness direction using power-law distribution in terms of the volume fractions of the constituents. The temperature field is uniformly distributed over the plate surface and varied in the thickness direction only. The nonlinear C⁰ finite element equations are obtained using Reddy’s HSDT with von-Karman’s strain assumptions. The convergence and comparison studies have been performed to prove the accuracy of the present model. Results with different design parameters have been presented.     

The effects of large vibration amplitudes on the stresses of thin circular functionally graded plates

Variations of stresses of a thin circular functionally grade plate, due to large vibration amplitudes, are developed in this paper. The plate thickness is constant and temperature dependent functionally graded material (FGM) properties vary through the thickness of the plate. For harmonic vibrations, governing equations are solved. Corresponding results are illustrated in the case of steady-state free vibration. The results show that the variation of volume fraction index is considerable in FGM properties and the amount of stresses.     

Free vibration of functionally graded arbitrary straight-sided quadrilateral plates in thermal environment

As a first endeavor, the free vibration of functionally graded (FG) arbitrary straight-sided quadrilateral plates under thermal environment and based on the first order shear deformation theory (FSDT) is presented. The material properties are assumed to be temperature-dependent and graded in the thickness direction. The initial thermal stresses are evaluated by solving the thermo-elastic equilibrium equations. The solution procedure is based on transformation of the governing equations from physical domain to computational domain and then the discretization of the spatial derivatives by employing the differential quadrature method (DQM) as an efficient and accurate numerical tool. The accuracy of the present method is demonstrated by studying the free vibration of isotropic and FG plates with various shapes and comparing the solutions obtained against existing results in literature. Then, the effects of thickness-to-length ratio, volume fraction index, temperature rise, geometrical shape and the boundary conditions on the frequency parameters of the plate are studied.     

Nonlinear vibration of smart circular functionally graded plates coupled with piezoelectric layers

Nonlinear vibration analysis of thin circular pre-stressed functionally graded (FG) plate integrated with two uniformly distributed piezoelectric actuator layers with an initial nonlinear large deformation are presented in this paper. Nonlinear governing equations of motion are derived based on classical plate theory (CPT) with von-Karman type geometrical large nonlinear deformations. A nonlinear static problem is solved first to determine the initial stress state and pre-vibration deformations of the plate that is subjected to in-plane forces and applied actuator voltage. By adding an incremental dynamic state to the pre-vibration state, the differential equations that govern the nonlinear vibration behavior of pre-stressed piezoelectrically actuated circular FG plate are derived. An exact series expansion method is used to model the nonlinear electro-mechanical vibration behavior of the structure. Control of the FG plate’s nonlinear deflections and natural frequencies using high control voltages are studied and their nonlinear effects are evaluated. In a parametric study the emphasis is placed on investigating the effect of varying the applied actuator voltage as well as gradient index of FG plate on the dynamic characteristics of the structure.     

Out-of-plane free vibration of functionally graded circular curved beams in thermal environment

A first known formulation for the out-of-plane free vibration analysis of functionally graded (FG) circular curved beams in thermal environment is presented. The formulation is based on the first order shear deformation theory (FSDT), which includes the effects of shear deformation and rotary inertia due to both torsional and flexural vibrations. The material properties are assumed to be temperature dependent and graded in the direction normal to the plane of the beam curvature. The equations of motion and the related boundary conditions, which include the effects of initial thermal stresses, are derived using the Hamilton’s principle. Differential quadrature method (DQM), as an efficient and accurate numerical method, is adopted to solve the thermoelastic equilibrium equations and the equations of motion. The formulations are validated by comparing the results, in the limit cases, with the available solutions in the literature for isotropic circular curved beams. In addition, for FG circular curved beams with soft simply supported edges, the results are compared with the obtained exact solutions. Then, the effects of temperature rise, boundary conditions, material and geometrical parameters on the natural frequencies are investigated.     

Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment

The free vibration analysis of rotating functionally graded (FG) cylindrical shells subjected to thermal environment is investigated based on the first order shear deformation theory (FSDT) of shells. The formulation includes the centrifugal and Coriolis forces due to rotation of the shell. The material properties are assumed to be temperature-dependent and graded in the thickness direction. The initial thermo-mechanical stresses are obtained by solving the thermoelastic equilibrium equations. The equations of motion and the related boundary conditions are derived using Hamilton’s principle. The differential quadrature method (DQM) as an efficient and accurate numerical tool is adopted to discretize the thermoelastic equilibrium equations and the equations of motion. The convergence behavior of the method is demonstrated and comparison studies with the available solutions in the literature are performed. Finally, the effects of angular velocity, Coriolis acceleration, temperature dependence of material properties, material property graded index and geometrical parameters on the frequency parameters of the FG cylindrical shells with different boundary conditions are investigated.     

随从力作用下功能梯度矩形板的非线性振动

本文研究了切向均布随从力作用下简支FGM矩形板的非线性振动问题。按照材料组份体积分数的简单幂率分布规律,FGM板的材料常数仅沿厚度连续变化。由大挠度的von Karman理论建立了以应力函数和挠度函数表示的运动偏微分方程组,再由Galerkin法转化成非线性常微分方程。对随从力作用下的四边简支陶瓷/金属矩形板,讨论了随从力、梯度指标和边长比对板的动力特性的影响,得到了各种条件下板中心振幅与非线性基频的关系。     

加热弹性梁在热过屈曲构形附近的自由振动

基于轴向可伸长梁的几何非线性理论建立了弹性直梁在热过屈曲静态大变形附近自由振动的几何非线性模型。在小振幅振动假设下,简化得到热过屈曲梁线性振动的控制方程。采用打靶法分别获得了两端不可移简支(pinned-pinned)和两端固定(fixed-fixed)梁的前四阶固有频率与升温之间的特征关系曲线。数值结果表明,梁在未屈曲时,各阶频率都随升温而单调下降。在过屈曲后,两端不可移简支梁的前两阶频率随升温单调上升,三、四阶频率随升温而单调下降。但是,两端固定梁在过屈曲后的各阶频率都随升温而单调增加。因此,可以通过温度调控来实现对结构固有频率的调整。     

Thermo elasticity solution of functionally graded,solid, circular,and annular plates integrated with piezoelectric layers using the differential quadrature method

Static analysis of functionally graded (FG) solid circular/annular plates imbedded in piezoelectric layers under thermo-electro mechanical load is investigated using the differential quadrature method. The plate has various edge boundary conditions and its material properties are assumed to vary in an exponential law with the Poisson ratio to be constant. The method is validated by comparing numerical results with the results obtained in the literature. The effects of the gradient index, thickness to radius ratio, and edges boundary conditions on the thermoelastic behavior of FG solid circular and annular plates are investigated.