弹性边界径向功能梯度压电环板面内振动

摘要

Based on the two-dimension linear elastic theory,the in-plane free vibration differential equations for radial functionally graded piezoelectric (FGPM) annular plates were derived.Using the differential quadrature method (DQM),the differential equations and boundary conditions were discretized and the characteristic equation of the frequency was obtained.Assuming that the physical parameters of the material vary in the form of a power function,the dimensionless natural frequency of in-plane free vibration of FGPM annular plates were solved numerically.The influence of the gradient exponent p,the inner to outer diameter ratio η,the stiffness of elastic boundaries k and piezoelectric effect of the radial FGPM annular plate on the dimensionless frequency was considered under the combination of elastic boundary and the open electrical boundary.Finally,the modal characteristics of radial FGPM annular plate were studied.%基于二维线弹性体理论,推导了弹性边界径向功能梯度压电(FGPM)环板面内自由振动的控制微分方程,利用微分求积法(DQM)将控制微分方程和边界条件离散化,得到求解频率的特征方程.假设材料的物性参数按幂函数形式变化,通过数值求解得到了径向FGPM环板面内自由振动的无量纲频率.考虑了弹性边界和电学开路组合边界条件下径向FGPM环板的梯度指数p、内外径比η弹性边界的弹性刚度k和压电效应对无量纲频率的影响,最后研究了径向FGPM环板模态特性.