压电层合梁静动力学分析的高精度梁单元

给出了一个对复合材料压电层合梁进行数值分析的高精度压电层合梁单元。基于Shi三阶剪切变形板理论的位移场和Layer-wise理论的电势场,用力-电耦合的变分原理及Hamilton原理推导了压电层合梁单元列式。采用拟协调元方法推导了一个可显式给出单元刚度矩阵的两节点压电层合梁单元,并应用于压电层合梁的力-电耦合弯曲和自由振动分析。计算结果表明,该梁单元给出的梁挠度和固有频率与解析解吻合良好,并优于其它梁单元的计算结果,说明了本文所给压电层合梁单元的可靠性和准确性。研究结果可为力-电耦合作用下压电层合梁的力学分析提供一个简单、精确且高效的压电层合梁单元。     

二维复合材料结构模态分析的边界元法

将边界元方法用于分析二维复合材料结构的自由振动模态，利用特解处理体积力（惯性力）仅需静态基本解就可求解问题，对一各向同性悬臂梁，用该法得到的结果与用有限元或各向性边界元法得到的结果符合得很好，但该法可解各向异性问题，对层状复合材料简支梁，用该法得到了数值结果与用一维层状复合材料梁的理论解的比较表明，当结构的长厚比大于２０时，二者符合得很好，当结构的长厚比小于２０时，一维层状材料梁的理论将产生很大的     

AN EXACT ANALYSIS OF THERMAL BUCKLING OF PIEZOELECTRIC LAMINATED PLATES

In this paper,the governing differential equations of elastic stability problems in ther-mopiezoelectric media are deduced.The solutions of the thermal buckling problems for piezoelectriclaminated plates are presented in the context of the mathematical theory of elasticity.Owing to thecomplexity of the eigenvalue problem involved,the critical temperature values of thermal bucklingmust be solved numerically.The numerical results for piezoelectric/non-piezoelectric laminated platesare presented and the influence of piezoelectricity upon thermal buckling temperature is discussed.     

Boundary element method for model analysis of 2-D composite structure

The boundary element method is used for the modal analysis of free vibration of 2-D composite structures in this paper. Since the particular solution method is used to treat the terms of body forces (inertial forces) in the equation of motion, only static fundamental solutions are needed in solving the problem. For an isotropic cantilever beam, the numerical results obtained by using the BEM presented in this paper are in good agreement, with, those of using FEM or other BEM, but this BEM can also be used to analyze problems for anisotropic materials. For simply supported composite laminated beams, the comparisons of the numerical reslts obtained by this method with the analytical results obtained by 1-D laminated beam theory indicate that if the ratio of length/thickness is greater than 20, the results of the two methods are in good agreement, but if the ratio of length/thickness is less than 20, big errors will occur for 1-D laminated beam theory.     

压电层合板热屈曲问题的精确分析

本文在作者们以前工作的基础上导出了热压电介弹性稳定性问题的控制微分方程，提出了热压电层合板热屈曲问题的数学和学解法。由于最后所得特征值问题的复杂性，热屈曲临界必须数值求解。文中对不同压电材非压电材料层构成的层合板作了具体计算，考虑了压电性对屈曲温度的影响。     

Free vibration analyses of axially loaded laminated composite beams based on higher-order shear deformation theory

The dynamic stiffness matrix method is introduced to solve exactly the free vibration and buckling problems of axially loaded laminated composite beams with arbitrary lay-ups. The Poisson effect, axial force, extensional deformation, shear deformation and rotary inertia are included in the mathematical formulation. The exact dynamic stiffness matrix is derived from the analytical solutions of the governing differential equations of the composite beams based on third-order shear deformation beam theory. The application of the present method is illustrated by two numerical examples, in which the effects of axial force and boundary condition on the natural frequencies, mode shapes and buckling loads are examined. Comparison of the current results to the existing solutions in the literature demonstrates the accuracy and effectiveness of the present method.     

Creep buckling and post-buckling analysis of the laminated piezoelectric viscoelastic functionally graded plates

The creep buckling and post-buckling of the laminated piezoelectric viscoelastic functionally graded material (FGM) plates are studied in this research. Considering the transverse shear deformation and geometric nonlinearity, the Von Karman geometric relation of the laminated piezoelectric viscoelastic FGM plates with initial deflection is established. And then nonlinear creep governing equations of the laminated piezoelectric viscoelastic FGM plates subjected to an in-plane compressive load are derived on the basis of the elastic piezoelectric theory and Boltzmann superposition principle. Applying the finite difference method and the Newmark scheme, the whole problem is solved by the iterative method. In numerical examples, the effects of geometric nonlinearity, transverse shear deformation, the applied electric load, the volume fraction and the geometric parameters on the creep buckling and post-buckling of laminated piezoelectric viscoelastic FGM plates with initial deflection are investigated.     

新修正偶应力层合板理论中的几个基本假设对自由振动计算的影响

基于新修正偶应力理论,在对微细观尺度的复合材料层合梁/板进行力学响应计算时,往往采用一系列假设来简化模型。现有文献都全部或部分应用了这些假设,但对这些假设是否会对计算结果造成影响尚未进行充分讨论分析。本文建立了未经简化的新修正偶应力Reddy层合板模型,并对其自由振动进行了分析。通过数值算例的对比,讨论了常用的几个简化假设对微细观复合材料四边简支方板自振频率的影响以及适用范围。算例结果表明,常用的几个简化假设对于微尺度层合薄板自由振动的影响很小,对于厚板的低阶频率影响也很小,但对厚板的高阶频率影响显著。     

一维六方准晶层合简支梁自由振动与屈曲的精确解

伪Stroh型公式能够将多场耦合材料的控制方程转化为线性特征系统来求解，从而获得多层结构简支边界条件的精确解.本文利用伪Stroh型公式，研究一维六方准晶层合简支梁的自由振动和屈曲问题，通过传递矩阵法，获得准晶层合梁自由振动固有频率与临界屈曲载荷的精确解.通过与已有梁的剪切变形理论结果比较，验证了本文伪Stroh型公式的正确性和有效性.通过数值算例，分析由两种不同准晶材料组成的三明治层合梁的叠层方式、高跨比、层厚比及层数对梁的固有频率、临界屈曲载荷及其模态的影响规律.结果表明，叠层顺序和梁的高跨比、层厚比对准晶层合梁的自由振动固有频率和临界屈曲载荷有很大影响，可通过调整梁的几何尺寸和叠层顺序得到准晶层合梁的最佳固有频率和临界屈曲载荷.本文给出的精确解可为工程上研究准晶梁的各种数值解法和实验方法提供理论参考.     

带剪切型压电激励器的板的高阶剪切变形理论

利用压电材料固有的正，逆压电效应可以对结构变形和振动进行控制。与外加电场与极化方向平行于板厚度的压电材料的拉伸作动机制相比，外加电场与极化方向垂直的压电材料的剪切作动机制可以在作动器内产生较小的应力，从而降低作动器边界产生分层破坏的危险。本文对于压电材料的剪切作动机制进行研究，应用三阶剪切变形理论建立带剪切型压电激励器的智能层合板模型。采用哈密顿原理导出带剪切型压电激励器的层合板的控制方程。采用空间法得到了各种边界条件组合条件下板的解析解。数值算例对一三层板采用高阶和一阶剪切变形理论进行计算，结果表明两种理论所得的变形曲线很相似。但对于厚度剪切型激励器而言，由于激励器是引起板的剪切变形，而高阶剪切变形理论比一阶剪切变形理论能更好地反映结构的剪切应变能，因此高阶剪切变形理论可以提供板变形的更为精确的解。因此，对于厚度剪切型激励器，剪切变形理论的选取对于板变形结果的好坏有重要的作用。     

复合材料层合梁的屈曲

本文在铁摩辛柯梁理论基础上,利用迭合刚度方法及Hamilton原理建立了层合梁屈曲问题控制方程,并用此控制方程求解了在具体边界条件下层合梁的屈曲问题,得出了无论在什么边界条件下层合梁的最小屈曲载荷不会大于等效剪切刚度系数C的结论.     

Double Hopf bifurcation of composite laminated piezoelectric plate subjected to external and internal excitations

The double Hopf bifurcation of a composite laminated piezoelectric plate with combined external and internal excitations is studied. Using a multiple scale method, the average equations are obtained in two coordinates. The bifurcation response equations of the composite laminated piezoelectric plate with the primary parameter resonance, i.e.,1:3 internal resonance, are achieved. Then, the bifurcation feature of bifurcation equations is considered using the singularity theory. A bifurcation diagram is obtained on the parameter plane. Different steady state solutions of the average equations are analyzed.By numerical simulation, periodic vibration and quasi-periodic vibration responses of the composite laminated piezoelectric plate are obtained.     

Buckling and post-buckling analyses for an axially compressed laminated cylindrical shell of FGM with PFRC in thermal environments

In this paper, investigation on buckling and post-buckling behaviors of a laminated cylindrical shell of functionally graded material (FGM) with the piezoelectric fiber reinforced composite (PFRC) actuators subjected to thermal and axial compressed loads is presented. Based on the Donnell assumptions, the material properties of the FGM layer vary smoothly through the laminated cylindrical shell thickness according to a power law distribution of the volume fraction of constituent materials. In the present study, a numerical procedure for the laminated cylindrical shell is used based on the Ritz energy method and the nonlinear strain–displacement relations. Some useful discussion and numerical examples are presented to show various effects of temperature field, volume fraction and geometric parameters on the buckling and post-buckling behaviors of the laminated cylindrical shell with PFRC.     

Free axisymmetric vibration of transversely isotropic piezoelectric circular plates

Based on three-dimensional elastic theory of piezoelectric materials, the axisymmetric state space formulation of piezoelectric laminated circular plates is derived. Finite Hankel transforms are used and the boundary variables in free terms are replaced, for two kinds of boundary conditions, to obtain ordinary differential equations with constant coefficients. Regarding the axisymmetric free vibration problem, two exact solutions for two different boundary conditions are found. Discarding piezoelectric effect, the exact solutions for transversely isotropic circular laminates are also obtained through the same procedure. Numerical examples are given and compared with those of Finite Element Method (FEM) .     

Vibration analysis and active control of nearly periodic two-span beams with piezoelectric actuator/sensor pairs

The piezoelectric materials are used to investigate the active vibration control of ordered/disordered periodic two-span beams. The equation of motion of each sub-beam with piezoelectric patches is established based on Hamilton's principle with an assumed mode method. The velocity feedback control algorithm is used to design the controller. The free and forced vibration behaviors of the two-span beams with the piezoelectric actuators and sensors are analyzed. The vibration properties of the disordered two-span beams caused by misplacing the middle support are also researched. In addition, the effects of the length disorder degree on the vibration performances of the disordered beams are investigated. From the numerical results, it can be concluded that the disorder in the length of the periodic two-span beams will cause vibration localizations of the free and forced vibrations of the structure, and the vibration localization phenomenon will be more and more obvious when the length difference between the two sub-beams increases. Moreover, when the velocity feedback control is used, both the forced and the free vibrations will be suppressed. Meanwhile, the vibration behaviors of the two-span beam are tuned.     

Size-dependent free vibration analysis of composite laminated Timoshenko beam based on new modified couple stress theory

A micro-scale free vibration analysis of composite laminated Timoshenko beam (CLTB) model is developed based on the new modified couple stress theory. In this theory, a new anisotropic constitutive relation is defined for modeling the CLTB. This theory uses rotation–displacement as dependent variable and contains only one material length scale parameter. Hamilton’s principle is employed to derive the governing equations of motion and boundary conditions. This new model can be reduced to composite laminated Bernoulli–Euler beam model of the couple stress theory. An example analysis of free vibration of the cross-ply simply supported CLTB model is adopted, and an explicit expression of analysis solution is given. Additionally, the numerical results show that the present beam models can capture the scale effects of the natural frequencies of the micro-structure.     

有限长压电层合简支板自由振动的三维精确解

基于三维弹性理论和压电理论，导出了有限长矩形压电层合简支板的动力学方程及相应的边界条件，给出了一种求解压电层合板自由振动三维精确解的方法；分析了正、逆向压电效应对层合板振动频率的影响．本文所述的方法和结果对于求解其他三维动态问题，验证、比较其他简化模型、有限元计算结果以及工程应用都有指导意义．     

压电压磁圆柱壳的自由振动分析

本文基于三维弹性理论，结合状态空间理论和离散奇异卷积算法分析了压电压磁圆柱壳的自由振动问题．圆柱壳的厚度方向被作为状态空间理论的传递方向，同时应用离散奇异卷积算法对面内域进行离散．因此，初始的偏微分运动方程被转化为由一阶常微分方程构成的状态方程．离散奇异卷积算法的引入使得本方法可以处理不同边界条件，从而扩展了常规状态空间方法的应用范围．本文对数值算例的计算验证了此方法的有效性和精确度．     

压电压磁复合材料中裂纹对反平面简谐弹性波的散射问题

分析了压电压磁复合材料中裂纹对反平面简谐弹性波的散射问题。利用傅立叶变换,使问题的求解转换为对一对以裂纹表面上的位移差为未知变量的对偶积分方程的求解。为了求解对偶积分方程,把裂纹面上的位移差展开为雅可比多项式形式,进而得到了裂纹长度、入射波波速及入射波频率对裂纹应力强度因子的影响。从数值结果可以看出,压电压磁复合材料中可导通裂纹的反平面问题的动应力奇异性与一般弹性材料中的反平面断裂问题动应力奇异性相同。     

Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment

Free vibration of statically thermal postbuckled functionally graded material （FGM） beams with surface-bonded piezoelectric layers subject to both temperature rise and voltage is studied. By accurately considering the axial extension and based on the Euler-Bernoulli beam theory, geometrically nonlinear dynamic governing equations for FGM beams with surface-bonded piezoelectric layers subject to thermo-electro- mechanical loadings are formulated. It is assumed that the material properties of the middle FGM layer vary continuously as a power law function of the thickness coordinate, and the piezoelectric layers are isotropic and homogenous. By assuming that the amplitude of the beam vibration is small and its response is harmonic, the above mentioned non-linear partial differential equations are reduced to two sets of coupled ordinary differential equations. One is for the postbuckling, and the other is for the linear vibration of the beam superimposed upon the postbuckled configuration. Using a shooting method to solve the two sets of ordinary differential equations with fixed-fixed boundary conditions numerically, the response of postbuckling and free vibration in the vicinity of the postbuckled configuration of the beam with fixed-fixed ends and subject to transversely nonuniform heating and uniform electric field is obtained. Thermo-electric postbuckling equilibrium paths and characteristic curves of the first three natural frequencies versus the temperature, the electricity, and the material gradient parameters are plotted. It is found that the three lowest frequencies of the prebuckled beam decrease with the increase of the temperature, but those of a buckled beam increase monotonically with the temperature rise. The results also show that the tensional force produced in the piezoelectric layers by the voltage can efficiently increase the critical buckling temperature and the natural frequency.