压电圆环径向弯曲振动与激励研究

Study of radial bending vibration and excitation of piezoelectric rings

针对压电圆环换能器的径向弯曲振动问题,从薄壳理论出发进行相关数理推导,讨论了压电效应的影响及电学短路与开路下的弯曲振动方程.进行相关解析求解,给出了两种条件下的多阶谐振频率预测公式,并利用有限元法分析了两式的适用范围.使用模态理论,定义模态权值函数,研究了电学激励条件对多阶弯曲振动模态的具体影响,得到了单模态激励、局部等幅激励和单端激励等作用于多个目标模态的有效方法.经有限元仿真(FEM)、实验与理论对比验证,三者吻合较好,相关结论可以为压电圆环弯曲振动模态识别、模态激励的精细化调控提供理论基础.

Piezoelectric ring transducer is one of the most common underwater transducers,and its radial vibration,bending vibration in-plane r-θand out-of-plane r-θhave been widely studied.However,the current research on the bending vibration in the plane r-z of the ring is insufficient,although it may have a noticeable influence on the applicability of the underwater transducers.In this study,mechanical analysis and related mathematical calculations of the bending vibrations in the plane r-z are carried out by using the thin-shell theory.Herein,the following three aspects are studied:1)free vibration theory solution,2)forced vibration:multi-order modal excitation theory,and 3)related finite element calculations and experimental verification.In this study,the bending vibration equations under electrical short and electric open condition are derived,and the multi-order resonance frequency prediction formulas and shape functions for both conditions are obtained by analytical solution and function fitting.Using the finite element method,the influence of piezoelectric effect and the range of applicability of these two electrical conditions are analyzed.The non-homogeneous equations under forced vibration are solved.By utilizing the orthogonal completeness of the vibration mode function,an integral transformation with the vibration mode function can be defined as the basis vector,so that the equation is solved in a simple positive space,and the results reveal the relationship between the coefficients of the modes of different orders and the voltage distribution.By modal theory,the effects of electrical excitation conditions on the multistep bending vibration modes are investigated,and effective methods such as unimodal excitation,partial excitation and single-ended excitation acting on several different target modes are obtained.The proposed piezoelectric ring unimodal excitation and single-ended excitation methods successfully excite the target modes in the experiments:the unimodal excited ring excites only one of its corresponding bending modes,while the single-ended excitation method excites all the bending modes of the first five orders,and its modal strength characteristics are in accordance with the theoretical predictions.This study involves finite element simulation,experimental and theoretical comparative verification,which are in good agreement.The relevant conclusions can provide a theoretical basis for identifying the vibration modes of piezoelectric ring and the fine tuning of modal excitation.