考虑剪切效应的旋转FGM楔形梁刚柔耦合动力学建模与仿真

本文对一类中心刚体-柔性梁系统在大范围转动下的刚柔耦合动力学问题进行了研究. 柔性梁为功能梯度材料(functionally graded materials, FGM)楔形变截面梁,材料体积分数在梁轴向呈幂律分布变化. 以弧长坐标来描述柔性FGM梁的几何位移关系,分别使用倾角和拉伸应变变量描述柔性梁的横向弯曲和纵向拉伸变形,并计及剪切效应. 采用假设模态法离散变形场,运用第二类拉格朗日方程进行方程推导,得到系统考虑剪切效应的刚柔耦合动力学模型. 基于全新的刚柔耦合动力学建模理论,研究不同轴向材料梯度分布的FGM楔形梁,通过数值仿真计算,分析讨论不同的转速、梯度分布规律以及变截面参数对系统动力学特性的影响. 结果表明,剪切效应对大高跨比的FGM楔形梁的变形影响较为明显,不容忽略;材料梯度分布规律和截面参数的选取均会对旋转FGM楔形梁的动力学响应和频率产生较大影响. 本文提出的考虑剪切效应的倾角刚柔耦合动力学模型是对以往非剪切模型的进一步完善,可应用于工程中的 Timoshenko梁结构的动力学问题求解.      

Thermal Buckling Analysis of FGM Sandwich Circular Plates Under Transverse Nonuniform Temperature Field Actions北大核心CSCD

Based on the von Kármán geometric nonlinear plate theory, the displacement⁃type geometric nonlinear governing equations for FGM sandwich circular plates under transverse nonlinear temperature field actions were derived. With the immovable clamped boundary condition, the analytical formula for dimensional critical buckling temperature differences of the system was obtained from the solution of the linear eigenvalue problem. Moreover, the 2⁃point boundary value problem of ordinary differential equations was solved with the shooting method. The effects of geometric parameters, constituent material properties, gradient indexes, temperature field parameters and layer⁃thickness ratios on the critical buckling temperature differences, the thermal postbuckling equilibrium paths, and the buckling equilibrium configurations of FGM sandwich circular plates, were investigated. The results show that, with the increases of the thickness⁃radius ratio, the relative thickness of the FGM layer and the gradient index, the FGM sandwich circular plate's critical buckling temperature difference will increase monotonically. Given a fixed radius and a fixed total thickness, the postbuckling deformation of the FGM sandwich circular plate will decrease significantly with the relative thickness of the FGM layer. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

线性分布荷载作用下梯度功能压电悬臂梁的解

采用逆解法求解了上表面受线性分布荷载作用的压电悬臂梁执行器，其中体积力$F_z$ 呈非线性分布. 首先确定了应力函数和电位移函数的多项式表达式，进而研究了该问题的 通解，以及体积力的不同分布对解答的影响. 常体积力和无体力情况下的解可以由上述 解直接得到. 本文为研究其它类型的压电梯度微观结构提供了一种可行的方法.     

Explicit formulas for the reflection and transmission coefficients of one-component waves through a stack of an arbitrary number of layers

The transmission and reflection of one-component elastic, acoustic, optical waves on a stack of arbitrary number of different homogeneous layers have been intensively studied in the literature. However, all obtained formulas for the reflection and transmission coefficients are in implicit form. In this paper, we provide the explicit formulas for them. From these formulas we immediately arrive at the explicit formulas for the reflection and transmission coefficients of one-component waves through an FGM layer. Based on the obtained exact formulas, approximate formulas for the reflection and transmission coefficients are established for a stack of thin layers and for a thin FGM layer. It is numerically shown that they are good approximations. Since the obtained formulas are totally explicit, they are useful in evaluating, not only numerically but also analytically, the transmission and reflection coefficients of one-component waves.     

弹性地基上转动FGM梁自由振动的DTM分析

基于Euler-Bernoulli梁理论,利用广义Hamilton原理推导得到弹性地基上转动功能梯度材料(FGM)梁横向自由振动的运动控制微分方程并进行无量纲化,采用微分变换法(DTM)对无量纲控制微分方程及其边界条件进行变换,计算了弹性地基上转动FGM梁在夹紧-夹紧、夹紧-简支和夹紧-自由三种边界条件下横向自由振动的无量纲固有频率,再将控制微分方程退化到无转动和地基时的FGM梁,计算其不同梯度指数时第一阶无量纲固有频率值,并和已有文献的FEM和Lagrange乘子法计算结果进行比较,数值完全吻合。计算结果表明,三种边界条件下FGM梁的无量纲固有频率随无量纲转速和无量纲弹性地基模量的增大而增大;在一定无量纲转速和无量纲弹性地基模量下,FGM梁的无量纲固有频率随着FGM梯度指数的增大而减小;但在夹紧-简支和夹紧-自由边界条件下,一阶无量纲固有频率几乎不变。     

基于物理中面FGM板屈曲的有限元分析

基于物理中面的概念，根据最小势能原理推导了功能梯度材料FGM薄板屈曲的有限元控制方程，求得临界荷载的有限元解。利用FGM板的屈曲方程与参考均匀板的屈曲方程之间的相似性，建立了FGM板的临界荷载与参考均匀板的临界荷载之间的相似转换关系式，从而将FGM板临界荷载的计算转变为参考均匀板的临界荷载和材料不均匀系数的计算，极大地提高了计算效率，为FGM的推广起积极的推动作用。通过数值算例，将由有限元法和转换关系式得到的临界荷载进行了比较，并讨论了边界条件、荷载工况、材料组成和几何尺寸等对FGM板临界荷载的影响。     

STABILITY ANALYSIS OF A CAPACITIVE FGM MICRO-BEAM USING MODIFIED COUPLE STRESS THEORY

Based on the Modified Couple Stress Theory,a functionally graded micro-beam under electrostatic forces is studied.The FGM micro-beam is made of two materials and material properties vary continuously along the beam thickness according to a power-law.Dynamic and static pull-in voltages are obtained and it is shown that the static and dynamic pull-in voltages for some materials cannot be obtained using classic theories and components of couple stress must be taken into account.In addition,it is shown that the values of pull-in voltages depend on the variation through the thickness of the volume fractions of the two constituents.     

Contact vibration analysis of the functionally graded material coated half-space under a rigid spherical punch

This paper studies the contact vibration problem of an elastic half-space coated with functionally graded materials (FGMs) subject to a rigid spherical punch. A static force superimposing a dynamic time-harmonic force acts on the rigid spherical punch. Firstly, we give the static contact problem of FGMs by a least-square fitting approach. Next, the dynamic contact pressure is solved by employing the perturbation method. Lastly, the dynamic contact stiffness with different dynamic contact displacement conditions is derived for the FGM coated half-space. The effects of the gradient index, coating thickness, internal friction, and punch radius on the dynamic contact stiffness factor are discussed in detail.     

热荷载作用下Timoshenko功能梯度夹层梁的静态响应

在精确考虑轴线伸长和一阶横向剪切变形的基础上建立了Timoshenko功能梯度夹层梁在热载荷作用下的几何非线性控制方程.采用打靶法数值求解所得强非线性边值问题,获得了两端固支功能梯度夹层梁在横向非均匀升温作用下的静态热过屈曲和热弯曲变形数值解.分析了功能梯度材料参数变化、不同表层厚度和升温参数对夹层梁弯曲变形、拉-弯耦...