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.     

Functionally graded piezoelectric cantilever beam under load

Summary In the present paper, the problem of a functionally graded piezoelectric cantilever beam subjected to different loadings is studied. The piezoelectric beam is characterized by continuously graded properties for one elastic parameter and the material density. A pair of stress and induction functions in the form of polynomials is proposed and determined. Based on these functions, a set of analytical solutions for the beam subjected to different loadings is obtained. As particular cases, series of solutions for some canonical problems can be directly obtained from the solutions of the present paper, such as for the problems of a piezoelectric cantilever beam with constant body force or without body forces, etc.This research work is supported by the National Natural Science Foundation of China (50272003). Support was also given by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, P.R.C.     

Exact static analysis of a rotating piezoelectric spherical shell

This paper gives an exact analysis of a rotating piezoelectric spherical shell with arbitrary thickness. At first, three displacement functions are introduced to simplify the basic equations of a spherically isotropic, piezoelectric medium. By expanding the displacement functions as well as the electric potential in terms of spherical harmonics, the basic equations of equilibrium are converted to an uncoupled Euler type, second order ordinary differential equation and a coupled system of three second order ordinary differential equations. A general solution to the homogeneous equations of equilibrium is then derived. The static analysis of a rotating spherical shell is then performed and numerical example is presented. The project supported by the National Natural Science Foundation of China, the Zhejiang Provincial Natural Science Foundation, and the Japanese Committee of Culture, Education and Science.     

Non-linear axisymmetric response of functionally graded shallow spherical shells under uniform external pressure including temperature effects

This paper presents an analytical approach to investigate the non-linear axisymmetric response of functionally graded shallow spherical shells subjected to uniform external pressure incorporating the effects of temperature. Material properties are assumed to be temperature-independent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Equilibrium and compatibility equations for shallow spherical shells are derived by using the classical shell theory and specialized for axisymmetric deformation with both geometrical non-linearity and initial geometrical imperfection are taken into consideration. One-term deflection mode is assumed and explicit expressions of buckling loads and load-deflection curves are determined due to Galerkin method. Stability analysis for a clamped spherical shell shows the effects of material and geometric parameters, edge restraint and temperature conditions, and imperfection on the behavior of the shells.     

Transient response of a cracked piezoelectric strip under arbitrary electro-mechanical impact

By using the well-developed integral transform methodology, the dynamic response of stress and electric displacement around a finite crack in an infinite piezoelectric strip are investigated under arbitrary dynamic anti-plane loads. The dynamic stress intensity factors and electric displacement are obtained analytically. It is shown that the dynamic crack-tip stress and electric field still have a square-root singularity. Numerical computations for the dynamic stress intensity factor show that the electric load has a significant influence on the dynamic response of stress field. The higher the ratio of the crack length to the width of the strip, the higher the peak value of the dynamic stress intensity factor is. On the other hand, the dynamic response of the electric field is determined solely by the applied electric load. The electric field will promote or retard the propagation of the crack depending on the time elapse since the application of the external electro-mechanical loads. The project supported by the National Natural Science Foundation of China and the Post-Doctor Science Foundation of China     

含压电材料智能结构动态特性的研究

本文推导了含压电材料智能结构有限元动力方程,讨论了智能结构系统的动态特性,得到了模态形状和相应的模态电压以及考察了具有分布的压电传感器和执行器的四边简支方板的各阶固有频率随以馈增益的变化规律,这些结果将在智能结构控制的优化设计中起到了很大的作用。     

基于压电曲壳单元的结构振动最优控制

曲壳结构已广泛应用于航空航天、航海等领域,结构微小的振动会极大地影响部件性能,抑制曲壳结构的振动就很必要。提出了压电曲壳结构的振动最优控制模型,利用空间曲壳单元理论及多点约束方程实现曲壳基结构壳元和压电壳元的耦合,推导了压电曲壳结构动力学有限元方程,并结合线性二次型最优控制理论,实现了压电作动器对曲壳结构的振动最优控制。数值算例表明,对曲壳结构进行动力分析和振动控制时,在达到同样精度及控制效果的情况下,与平壳相比,曲壳单元及作动器所需数目要少得多。     

具有压电材料薄板弯曲控制的有限元法

考虑一均匀各向同性薄板结构,在其上下表面离散分布状压电执行元件,在横向外载和电压共同作用下,分析板的弯曲变形,并通过变化作用于执行元件上的电压对板的变形进行控制,根据逆压电效应将电压转换成作用于板上的等效作用量,用Ｈａｍｉｌｔｏｎ原理导出压电结构板弯曲变形的有限元公式,并对环形板情况进行数值计算。     

含压电片层合壳的有限元分析与控制仿真

本文首先针对含压电材料的一般结构，推导了按位移和电位移求解时的混合变分原理，在此基础上，通过对面电荷取变分，直接得到了含按电压驱动压电片层合壳的有限元方程，最后给出了利用压电片进行静变形和振动控制的仿真算例，并进行了分析。结果表明，本文建立的有限元方程准确、可靠。     

Single-frequency vibrations and vibrational heating of a piezoelectric circular sandwich plate under monoharmonic electromechanical loading

The forced monoharmonic bending vibrations and dissipative heating of a piezoelectric circular sandwich plate under monoharmonic mechanical and electrical loading are studied. The core layer is passive and viscoelastic. The face layers (actuators) are piezoelectric and oppositely polarized over the thickness. The plate is subjected to harmonic pressure and electrical potential. The viscoelastic behavior of the materials is described by complex moduli dependent on the temperature of heating. The coupled nonlinear problem is solved numerically. A numerical analysis demonstrates that the natural frequency, amplitude of vibrations, mechanical stresses, and temperature of dissipative heating can be controlled by changing the area and thickness of the actuator. It is shown that the temperature dependence of the complex moduli do not affect the electric potential applied to the actuator to compensate for the mechanical stress __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 79–89, January 2008.     

ASYMPTOTIC SOLUTIONS OF THE NONLINEAR STABILITY OF A TRUNCATED SHALLOW SPHERICAL SHELL UNDER A CONCENTRATED LOAD

In this paper,the nonlinear stability problem of a clamped truncated shallow sphericalshell with a nondeformable rigid body at the center under a concentrated load is studied bymeans of the singular perturbation method.When the geometrical parameter k is large,theuniformly valid asymptotic solutions are obtained.     

线黏弹性球面发散应力波的频率响应特性

基于线黏弹性球面波Laplace域的理论解, 得到了不同传播距离处粒子速度、粒子位移、应力、应变等力学量的传递函数。以标准线性固体模型为例, 重点讨论了粒子速度频率响应函数的传播特征, 指出随着传播距离的增加, 粒子速度幅频响应函数的高频响应会低于低频响应, 而在理想弹性条件下, 粒子速度幅频响应函数的高频响应一直高于低频响应。以弹性半径为0.025 m的空腔爆炸为例, 采用Laplace数值逆变换方法对粒子速度波形的演化进行了分析, 给出了粒子速度强间断幅值及粒子速度峰值随传播距离变化的衰减规律曲线, 指出黏弹性介质中粒子速度幅值的衰减曲线介于理想弹性介质中粒子速度幅值衰减曲线和黏弹性介质中粒子速度强间断幅值衰减曲线之间。

     

Structural response of stiffened plates in similitude under a turbulent boundary layer excitation

In structural dynamics, similitude laws usually deal with simple configurations as thin flat plates with point forces. Only recently, few papers have analyzed stiffened shells or stochastic pressure loads.This research activity extends the applicability of some similitude laws, developed for thin flat plates under a turbulent boundary layer load, to ribbed plates forced by the same wall pressure fluctuations.The work addresses the problem of designing a scaled experimental test-article and, successively, of re-modulating the measured data in order to get the structural response of an original (unscaled) configuration.Due to the complexity of the structural domain, the design of a scaled configuration leads to a distorted similitude. Then, a simple approach, to circumvent the distortion effects, is proposed.     

模糊桁架结构在模糊激励下的动力响应分析

研究了模糊参数桁架结构在模糊荷载激励下的动力响应分析问题. 不仅模糊桁架结构的物 理参数、几何尺寸具有模糊性,而且外载荷幅值也具有模糊性时,从Duhamel积分式出发,利用模糊因子法、区间运算和振型叠加法求出了结构动力响应模糊变量的表达式. 最后通过算例考察了结构参数和作用荷载的模糊性对结构动力响应的影响,表明所提出的计算模型和 分析方法是正确与可行的.     

Random response of integrable Duhem hysteretic systems under non-white excitation

In this study, an integrable Duhem hysteresis model is derived from the mathematical Duhem operator. This model can represent a wide category of hysteretic systems. The stochastic averaging method of energy envelope is then adapted for response analysis of the integrable Duhem hysteretic system subjected to non-white random excitation. Using the integrability of the proposed model, potential energy and dissipated energy of the hysteretic system can be represented in an integration form so that the hysteretic restoring force is separable into conservative and dissipative parts. Based on the equivalence of dissipated energy, a non-hysteretic non-linear system is obtained to substitute the original system, and the averaged Itô stochastic differential equation of total energy is derived with the drift and diffusion coefficients being expressed as Fourier series expansions in space averaging. The stationary probability density of total energy and response statistics are obtained by solving the Fokker–Planck–Kolmogorov (FPK) equation associated with the Itô equation. Verification is given by comparing the computational results with Monte Carlo simulations.     

参数和直接激励下非线性压电俘能器性能分析的多尺度法

考虑几何非线性、阻尼非线性和梁的轴向不可伸长条件,利用Hamilton变分原理,建立了参数激励和直接激励下压电俘能器的非线性力电耦合的运动微分方程;利用Galerkin法,将所建立的动力学偏微分方程降阶为力电耦合的Mathieu-Duffing型方程;采用多尺度法获得了梁的位移和输出电压的解析表达式,给出了解的稳定性条件;利用解析表达式研究了单独参数激励以及参数激励和直接激励共同作用下阻尼系数对压电俘能器性能的影响。结果表明,在参数激励情况下,线性阻尼会显著影响超临界分岔点的位置,非线性二次阻尼不会影响超临界分岔点的位置。参数激励和直接激励的结合可以作为提升压电能量俘获器性能的解决方案。     

Thermo-electromechanical behavior of functionally graded piezoelectric hollow cylinder under non-axisymmetric loads

This paper presents an analytical solution of a thick walled cylinder com- posed of a functionally graded piezoelectric material (FGPM) and subjected to a uniform electric field and non-axisymmetric thermo-mechanical loads. All material properties, except Poisson's ratio that is assumed to be constant, obey the same power law. An exact solution for the resulting Navier equations is developed by the separation of variables and complex Fourier series. Stress and strain distributions and a displacement field through the cylinder are obtained by this technique. To examine the analytical approach, different examples are solved by this method, and the results are discussed.     

Nonlinear stability of truncated shallow spherical shell with variable thickness under uniformly distributed load

I.Intr0ducti0nTheclampedtruncatedshailowsphericalshellwithanondeformablerigidbodyatthecenterisoftenusedinstructureandelasticcomponentofprecisioninstrument.Inthebuildingengineering,wemustpreventtheshelllosingstability.Butintheelasticcomponent0fprecisionins…     

球壳塑性变形下的应变增长现象

应变增长现象会对容器安全形成威胁。以往研究涉及的应变增长现象大多在壳体弹性变形范围内,本文中实验观察到球壳塑性变形时的应变增长现象,应变增长系数(最大应变值与第一个应变峰的比值)最大值达到1.16。实验还获得了容器内壁压力-时间曲线,并利用球壳响应理论分析出应变增长现象是由容器内壁的周期性多脉冲载荷引起的,该载荷存在3个较明显的脉冲,前两个脉冲对应变增长现象起主要作用。     

On the electroelastic interaction of a piezoelectric screw dislocation with an elliptical inclusion in piezoelectric materials

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｉｎｔｅｒａｃｔｉｏｎｏｆｄｉｓｌｏｃａｔｉｏｎｓｗｉｔｈｉｎｃｌｕｓｉｏｎｓｉｓｏｆｃｏｎｓｉｄｅｒａｂｌｅｉｍｐｏｒｔａｎｃｅｆｏｒｕｎｄｅｒｓｔａｎｄｉｎｇｔｈｅｐｈｙｓｉｃａｌｂｅｈａｖｉｏｒｏｆｍａｔｅｒｉａｌｓ.Ｓｕｃｈｓｔｕｄｉｅｓｃａｎｐｒｏｖｉｄｅｄｉｎｆｏｒｍａｔｉｏｎｃｏｎｃｅｒｎｉｎｇｃｅｒｔａｉｎｓｔｒｅｎｇｔｈｅｎｉｎｇｏｒｈａｒｄｅｎｉｎｇｍｅｃｈａｎｉｓｍｓｉｎｎｕｍｂｅｒｏｆｔｒａｄｉｔｉｏｎａｌａｎｄｃｏｍｐｏｓｉｔｅｍａｔｅｒｉ…