电压激励下四边简支压电层合板的振动分析

Vibration Analysis of Simply Supported Piezoelectric Laminated Plates Subjected to Voltage Excitation

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。

With piezoelectric ceramic-metal-piezoelectric ceramic symmetric laminated plate as the research object,forced vibration equation of the piezoelectric laminated thin plates under voltage excitation was established.The establishment was performed on the basis of small deflection bending theory and Hamilton principle and using Rayleigh Ritz method.Taking simulation of four edges simply supported piezoelectric laminated plate as an example,the finite element model was proposed and transient dynamic analysis of the model was conducted by the using ANSYS software.The simulation results were consistent with the theoretical value,which verify the validity of the theory.The influence of the voltage amplitude on transverse displacement and stresses in x and y directions were analyzed.The damping effect on transverse displacement of the plate was discussed.For the center node of the plate,its stresses in x and y directions were estmated by ANSYS software.The maximum stress position of the piezoelectric laminated plate and its time dependence were also studied.The discussion on damping may have a certain referential value for the design and analysis of piezoelectric vibrator.