压电材料矩形板的热振动分析

Thermal Vibration Analysis of Piezoelectric Materials Rectangular Plates

为保证压电材料结构在高温环境中安全工作,以压电材料矩形板为研究对象,根据弹性力学有限变形基本理论推导出了其在外激励和恒定温度场共同作用下的振动方程和协调方程.利用Bubnov-Galerkin原理,并引入瑞利阻尼得到热振动的非线性动力学方程.进一步运用多尺度法求得矩形板主共振时的幅频响应方程和相频响应方程.用ANSYS软件进行模态、谐响应及瞬态动力学分析,讨论了温度对横向位移的影响,分析了速度、加速度和最大应力值的变化规律以及最大应力的出现位置,结果表明温度升高和长宽比减小都会使系统的固有振动频率减小,且前者使弯曲挠度增大,后者使弯曲挠度减小.

In order to ensure the safety of piezoelectric structure in high temperature environment,piezoelectric materials rectangular plate as the research object,the non-linear vibration equation and the coordination equation in a coupled environment of external excitation and temperature field were derived based on the basic theory of finite deformation of elastic mechanics.The non-linear dynamic equations of thermal vibration were obtained by introducing the Bubnov-Galerkin principle and Rayleigh damping.Further,the amplitude frequency response equation and the phase frequency response equation of rectangular plates were obtained by multi-scale method when the primary resonance occurred.The modal,harmonic response and transient dynamics response of system were analyzed by using ANSYS software.The effect of temperature on the transverse displacement response was analyzed.The variations of velocity and acceleration and the characteristics of maximum stress value,maximum stress position were also discussed.The results show that the natural vibration frequency of the rectangular plate decreases with the increase of temperature and the decrease of the length width ratio.The former makes the bending deflection increase but the latter makes it decrease.These conclusions are valuable to engineering practice.