压电材料圆形板热弹耦合作用下的主共振

Principal Resonance of Piezoelectric Material Circular Plates under Thermoelastic Coupling

以温度场中的压电材料圆形薄板为研究对象,基于Von Karman大挠度理论及弹性力学基本理论,利用Bubnov-Galerkin原理推导出了压电圆形薄板的非线性动力学方程.利用多尺度法求得系统发生主共振时的幅频、相频响应方程.利用Lyapunov理论对系统稳态解的稳定性进行了分析.借助MATLAB软件分析了板中心温度、阻尼、外激励幅值、板厚对系统主共振响应的影响.研究结果表明:板中心温度增大会引起系统的响应幅值减小,发生跳跃的外激励频率与固有频率的比值增大,板中心温度对系统的影响相当于阻尼的作用,温度场对系统振动特性具有很大的影响;当外激励幅值增大时,系统的响应幅值也会随之增大,共振区域增大,适当地增大外激励幅值可以使系统避开不稳定区域.

The piezoelectric circular thin plate in the temperature field was investigated.Based on the Von Karman large deflection theory and elastic mechanics,the non-linear dynamic equation of piezoelectric circular thin plate was obtained by utilizing Bubnov-Galerkin principle.The amplitude-frequency and the phase-frequency response equation of principal resonance of the system were derived by using the multi-scale method,and the stability of solution was analyzed making use of Lyapunov theory.And some numerical simulations were carried out with the aid of MATLAB,the effect of different parameters such as temperature of plate center,damp,mechanical loads and plate thickness on principal resonance of the system was examined.The results show that increasing the temperature of the plate center leads to the decrease of the amplitude of the system,and the ratio of the external frequency to the natural frequency of jumping toward larger,and the effect of temperature of plate center on the system is equivalent to that of the damper.The influence of the temperature field on the vibration characteristics of the system is considerable;the amplitude and the resonant region of the system increase when increasing the amplitude of the external excitation,but appropriately increasing the amplitude of the external excitation can keep the system away from unstable areas.