Abstract

A high-performance semi-analytical formulation based on the three-dimensional piezoelectricity theory for bending response and free vibration analysis of circular cylindrical piezoelectric panel subjected to the mechanical and electrical loads is presented. To ensure the accuracy and reliability for the proposed method, a normalized formulation is applied for the constitutive equation of the circular cylindrical piezoelectric panel. By using the scaled boundary finite element method (SBFEM), the normalized dynamic equilibrium equation of cylindrical piezoelectric panel structures in the absence of body force and electric charge is derived into a second-order ordinary differential equation with the analytical form through the weighted residual technique. Under the formulation of the SBFEM, meshes only employed to the boundary of computational domain lead to a reduction of the spatial dimensions by one, so that computation costs can be significantly cut down. After then, the dynamic stiffness equation of whole system is obtained by introducing an intermediate variable. For the static responses, in order to accurately describe the bending behaviors involving the generalized strains and stresses through the thickness, a quadratic function is performed to approximate the generalized displacement vector in the radial direction. For the analysis of free vibrations, the governing equation of motion is rewritten in the expanded form and a condensation of the electric potential degree of freedom is conducted in the system. In this way, the free vibration response of the circular cylindrical piezoelectric panel can be determined by solving the associated eigenvalue problem. Studies of validation and convergence are presented by comparing with those of the published work in which both static and free vibration tests are taken into consideration, and the results show good and convergent performances. Finally, effects of geometric parameters as well as loading conditions on the response characteristics of system are discussed in detail.

摘要

提出了一种基于三维压电理论的高性能半解析公式，用于圆柱压电板在机械和电气负载下的弯曲响应和自由振动分析。为了确保所提出方法的准确性和可靠性，对圆柱形压电面板的本构方程应用了归一化公式。采用标度边界有限元法（SBFEM），通过加权残差技术，将圆柱压电板结构在无体力和无电荷情况下的归一化动态平衡方程推导出为具有解析形式的二阶常微分方程. 在SBFEM的制定下，网格仅用于计算域的边界导致空间维度减少一，从而可以显着降低计算成本。然后，通过引入一个中间变量，得到整个系统的动刚度方程。对于静态响应，为了准确描述在厚度方向上涉及广义应变和应力的弯曲行为，执行二次函数来近似径向方向上的广义位移矢量。为了分析自由振动，将运动控制方程改写为扩展形式，并在系统中进行电势自由度的压缩。这样，圆柱压电板的自由振动响应可以通过求解相关的特征值问题来确定。通过与已发表的同时考虑静态和自由振动测试的工作进行比较，提出了验证和收敛的研究，结果显示出良好的收敛性能。最后，详细讨论了几何参数和加载条件对系统响应特性的影响。