引入减基法的压电层合板瞬态响应分析

摘要：用减基法（RBM）结合有限元法、傅里叶变换和Newmark直接积分法,研究了压电层合板在机电耦合载荷下的瞬态响应。用层单元将层合板沿厚度方向进行离散,得到时间域内的运动方程,通过傅里叶变换得到波数域内的控制方程。应用Newmark直接积分法求解波数域内的位移和电势,并在Newmark法求解过程嵌入减基法,构造减基空间,把结构的等效刚度矩阵、质量矩阵和载荷列向量映射到减基空间降阶,得到减缩的Newmark增量式,从而快速求解得到原结构波数域响应,通过傅里叶逆变换得到时域内的响应。以PZT-5A/0°PVDF铺层两相材料复合压电层合板为算例,分析了机电耦合线载荷激励下,位移场和电势场的瞬态响应情况。计算结果表明,求解过程引入减基法能更快得到结构的瞬态响应,并保证了精度。     

热载荷作用下层合板瞬态响应分析

本文研究了层合板在热载作用下的瞬态响应,推导出考虑横向剪切变形影响的运动方程,以简支的正交铺层板为例,对横向剪切的影响作了分析.     

压电层合板层间应力新研究

综述了压电层合板数值分析方面的一些进展，在一般层合板理论的基础上提出一个多层压电层合板单元，依据线性压电理论建立压电层合板单元的杂交元模型，利用三维8节点块状单元建立多层压电层合板的有限元列式，解决了压电层合板层间应力的连续性。     

基于广义混合有限元的压电复合材料层合板的数值分析

将纯弹性体的广义混合有限元法引入到压电材料的静力学分析中。由于采用了8节点六面体非协调实体单元对整体结构进行离散求解,摒弃了板壳理论中的诸多人为假设。非协调项的加入使该方法比同类协调元显示出更好的数值性能。本文方法将应力边界条件和位移边界条件同时考虑,并且求解过程中将层间应力和平面内应力分开处理,按每层的本构关系求解平面内应力,这样求得的层间应力和平面内应力都更加接近精确解。通过几个有代表性的层合板的数值算例说明了本文方法的精度,相较于传统的解析法和数值法,本文方法在适用性和有效性方面都具有优势。     

四边简支压电层合板灵敏度分析的精确解

为了应用弹性力学中的Hamilton 正则方程研究压电材料的灵敏度系数问题,基于压电材料的H-R(Hellinger-Reissner) 变分原理,简要地导出Hamilton正则方程算子表达式,建立了四边简支板静力学控制方程。根据灵敏度定义,在静力学控制方程的基础上联立灵敏度控制方程,得到了增维的齐次压电材料静力响应和灵敏度系数混合控制方程。应用该方程可以同时求得压电层合板的力学、电学参量及其灵敏度。该算法过程简单、运算效率和稳定性好。数值算例结果与有限差分法的结果比较表明本文方法切实有效。      

电压激励下四边简支压电层合板的振动分析

以压电陶瓷-金属-压电陶瓷对称层合板为研究对象,依据小挠度弯曲理论,根据Hamilton原理和Rayleigh-Ritz法推导出了电压激励下压电层合薄板的振动方程。以四边简支的压电层合薄板为算例,用ANSYS软件建立有限元模型并对其进行模态分析、瞬态动力学分析,仿真结果与理论值基本相符,验证了本文理论的正确性;通过改变电压幅值的大小分析其对中心节点位移响应幅值以及x,y方向应力幅值的影响。通过改变阻尼大小分析其对薄板横向位移的影响。数值模拟了薄板中心处节点x,y方向应力随时间的变化规律,并分析了薄板最大应力出现位置及随时间的变化规律,所得结论可为压电振子的设计和分析提供一定的理论参考。     

具有压电材料铺层的自适应层合板的分析

如果把压电材料作为复合材料层合板的铺层之一, 层合板就变成所谓的压电自适应层合板, 它除了具有承载能力外, 还具有检测、动作等功能。本文将压电元件的驱动效应等效为力学载荷, 并用经典层合板理论对压电自适应层合板进行了分析, 理论分析结果和实验结果非常符合。      

压电复合材料层合板的热压电弹性简化模型研究

为有效分析压电复合材料层合板在热、电和载荷下的单向耦合热电弹性问题,基于变分渐近方法(VAM)建立热电弹性简化模型。首先根据虚功原理推导三维压电复合板总势能泛函。然后基于变分渐近法,利用板固有的小参数将三维总势能泛函渐近扩展为系列二维泛函,同时将近似泛函转换为Reissner形式以便实际工程应用。最后建立三维场重构关系以正确预测沿厚度方向的应力分布。计算结果显示:基于该模型重构的沿厚度方向横向剪切应力较古典层合理论和一阶剪切变形理论精确度更好,与三维有限元精确解相一致,表明该模型在压电复合材料层合板应力预测上的有效性。     

含压电片复合材料层合板的高阶计算模型

给出了一种分析含任意内埋压电片复合材料层合板的高阶耦合模型, 板的位移场采用三阶剪切理论, 并提出了压电片中电势场在厚度方向的三次分布模式, 可以更精确地描述力、电耦合作用下电场的非均匀分布。在平面应力的假设下给出了简化的压电材料本构方程, 推导了基于该模型的压电层合板有限元计算公式, 并对双压电片梁的弯曲和层合板的变形控制进行了计算, 压电梁的弯曲计算结果与解析结果吻合良好, 表明本文的模型和公式是精确有效的。     

压电层合板高阶计算模型

压电复合(层合)结构可应用于结构振动控制、形状保持、健康监测等,建立压电层合结构精确的机电耦合计算模型成为了研究的焦点.针对表面粘贴或内部嵌入压电片的压电层合板结构,基于高阶位移场和高阶电势模型,根据Hamilton原理建立了机电耦合高阶有限元模型.该模型适用于薄板和中厚板,并且能够捕捉压电层内沿厚度方向呈抛物线型分布的诱导电势.以压电双晶片简支板为例,进行了作动器构型和开环、闭环状态传感器构型的数值分析.结果指出,诱导电势对压电传感器有重要影响,而压电作动器可忽略这种电势.     

Vibration of axisymmetric composite piezoelectric shells coupled with internal fluid

This paper presents the theoretical and finite element formulations of piezoelectric composite shells of revolution filled with compressible fluid. The originality of this work lies (i) in the development of a variational formulation for the fully coupled fluid/piezoelectric structure system, and (ii) in the finite element implementation of an inexpensive and accurate axisymmetric adaptive laminated conical shell element. Various modal results are presented in order to validate and illustrate the efficiency of the proposed fluid–structure finite element formulation. Copyright © 2007 John Wiley & Sons, Ltd.     

Nonlinear transient analysis of FGM and FML plates under blast loads by experimental and mixed FE methods

Nonlinear transient behavior of fiber-metal laminated (FML) composite plates under non-ideal blast loads are investigated by both experimental and numerical techniques. In the experiments three plates with different aspect ratios are tested under blast loads and their response is also simulated and compared with both the developed mixed finite element method and the commercial software ANSYS. Furthermore parametric numerical analyses are conducted for nonlinear transient behavior of functionally graded (FGM) thin plates under blast loads with mixed FEM. In these parametric analyses the effect of aspect ratio, load distribution and impulse function in time domain are investigated. In the developed mixed FE formulation, the von Kármán plate theory is used. Nonlinear functional is developed using the Hellinger-Reissner principle and linearized with the incremental formulation. Dynamic analyses are carried using the Newmark method with the Newton-Raphson iterations. Condensation is not performed hence time derivative of internal forces are also calculated during the solutions. Damping is incorporated to the analysis in the sense of the Rayleigh damping. As a result of conducted analyses, there is a good and reliable agreement between the numerical and the experimental results. Moreover, the developed mixed FEM results are almost identical to the ANSYS results.     

A technique for analyzing elastodynamic responses of anisotropic laminated plates to line loads

A new technique is presented to modify the hybrid numerical method (HNM) proposed earlier by the authors for analyzing the responses of anisotropic laminated plates subjected to time-step and time-pulse line loads. In the modified HNM, eigenfrequencies and modal factor functions for wave modes in the plate are computed at equally spaced points on the wavenumber axis. In each interval of the points, the eigenfrequencies and modal factor functions are replaced by straight lines, and the inverse Fourier integrations are then carried out analytically. The proposed modification can significantly reduce the sampling points in the inverse integrations. The modified HNM is much more efficient than the original HNM, and can be used to compute not only near-field and short-time but also far-field and long-time responses for anisotropic laminated plates, without increasing the sampling points. Numerical examples are presented to demonstrate the modified HNM.     

Three-dimensional thermal buckling analysis of piezoelectric antisymmetric angle-ply laminates using finite layer method

Finite layer method is the most efficient numerical method for 3D analysis of simply supported rectangular plates. Using this method, the 3D analysis is transformed into one dimensional analysis by virtue of the orthogonal properties of trigonometric interpolation functions. In the present study, the finite layer method is extended to the thermal buckling analysis of piezoelectric antisymmetric angle-ply laminates, which may be combined with some symmetrical cross-plies. Full coupling between the thermal, electrical and mechanical fields is taken into consideration. Pre-buckling state is assumed to be steady, and initial thermal stresses are computed accordingly. The geometrical stiffness matrix is then formed, and the critical temperature and buckling mode are obtained. Numerical examples are presented to verify the proposed method. The critical temperature is determined for both the adiabatic and isothermal buckling processes. The thermal buckling behaviours of some piezoelectric laminates and the effects of the thermo-electro-mechanical coupling are investigated.     

An analytical approach for free vibration and transient response of functionally graded piezoelectric cylindrical panels subjected to impulsive loads

In this article, the free vibration and dynamic response of simply supported functionally graded piezoelectric cylindrical panel impacted by time-dependent blast pulses are analytically investigated. Using Hamilton’s principle, the equations of motion based on the first-order shear deformation theory are derived. Also, Maxwell’s electricity equation is taken as one of the governing equations. Three sets of electric surface conditions including closed circuit and two mixtures of closed and open circuit surface conditions are considered. By introducing an analytical approach and using the Fourier series expansions, the Laplace transform and Laplace inverse method, the solution of unknown variables are obtained in the real time domain based on a combination of system frequencies. Finally, the effects of various electric surface conditions, geometric parameters and the material power law index on the free vibration and transient response of functionally graded piezoelectric cylindrical panels subjected to various impulsive loads are examined in detail.     

The transient response of a functionally graded piezoelectric rod subjected to a moving heat source under fractional order theory of thermoelasticity

The transient thermo-piezoelectric response of a functionally graded piezoelectric rod subjected to a moving heat source is investigated in the context of fractional order theory of thermoelasticity proposed by Sherief. The material properties of the functionally graded piezoelectric rod are assumed to vary exponentially along the length, except for the thermal relaxation time and the specific heat, which are taken to be constant. To solve the governing equations of the problem, Laplace transform is applied, eliminating the time effect; the analytical solutions of the displacement, stress, temperature, and electric field in Laplace domain are obtained. Subsequently, the solutions of the considered variables in time domain are obtained by numerical Laplace inversion and illustrated graphically. In calculation, the effect of the fractional order parameter on the variations of the considered variables is presented.     

The transient responses of two-layered cylindrical shells attacked by underwater explosive shock waves

An approximation solution is introduced for the dynamic response of a two-layered cylindrical shell of circular cross-section subjected to an underwater explosive shock wave. The solution is obtained within the framework of the Flugge thin shell theory and the reflected-afterflow-virtual-source (RAVS) method is used to account for the fluid–structure interaction. Detailed numerical computations are carried out, in dimensionless form, for the cases of infinitely long two-layered cylindrical shells. Time histories of nondimensional radial velocity, mid-surface strain, 0th mode radial displacement and 1st mode radial velocity are presented in graphical form and the effects of elastic modulus, shell radius and thickness on the transient response characteristics of the shells are investigated.     

周期复合材料压电问题的双尺度数值模拟

利用渐近展开的方法对具有一般周期结构的复合材料中描述压电现象的电势与位移建立了二阶双尺度渐近展开式及边界层解, 得到了局部单胞内电场与位移场的相互耦合关系, 并给出了复合材料中电势与位移的双尺度结合边界层的有限元计算方法。数值算例表明了该方法的可行性与高效性。      

Transient waves in plates of functionally graded materials

A numerical method is proposed for analysing transient waves in plates of functionally graded material (FGM) excited by impact loads. The material properties of the FGM plate have a gradient in the thickness direction and are anisotropic in the plane of the plate. In the present method, the FGM plate is divided into layer elements in the thickness direction. For an accurate modelling of the variation of the material property of FGM plates, it is expressed by second‐order polynomials in the thickness direction within an element. This can further reduce the number of elements to obtain more accurate results effectively. The principle of virtual work is used to develop approximate dynamic equilibrium equations. The displacement response is determined by employing the Fourier transformation and the modal analysis. As examples, the displacement response of FGM plates excited by line, point and distributed loads is calculated. The computations have shown the efficiency of the present method. Copyright © 2001 John Wiley & Sons, Ltd.