摘要
区别于已有的换能器等效电路分析方法,基于机械系统振动理论,结合本构方程,分析了换能器的径向振动特性。将压电陶瓷复合超声换能器简化为由压电陶瓷圆管与金属预应力管组成的组合厚壁筒力学模型,建立了由压电陶瓷圆管与金属预应力管径向耦合振动波动方程、组合厚壁筒径向振动连续性条件与边界条件组成的换能器径向振动数学模型。建立了换能器径向振动固有频率方程及振型函数,固有频率计算结果与参考文献实验测量值具有较高的符合率。分别基于解析法与差分法求建立了换能器径向振动的数值仿真模型,给出了换能器径向振动的幅频特性与位移响应。仿真结果表明:两种方法所得幅频特性曲线相同、位移响应相同,验证了仿真结果的正确性。通过仿真分析,给出了换能器结构尺寸对其径向振动固有频率的影响规律:当金属预应力管与压电陶瓷圆管壁厚一定时,换能器径向振动固有频率随压电陶瓷圆管内径的增大而减小;当金属预应力管外径与压电陶瓷圆管内径一定时,换能器径向振动固有频率随压电陶瓷圆管与金属预应力管壁厚比值的增大而减小。
Being different from existing transducer equivalent circuit analysis methods, based on the mechanical system vibration theory, combined with the constitutive equation, radial vibration characteristics of a piezoelectric ceramic composite ultrasonic transducer were analyzed. It was simplified into the mechanical model of a combined thick-walled cylinder composed of a piezoelectric ceramic tube and a metal prestressed one. The radial vibration mathematical model of the transducer was established including radial vibration-wave coupled equation of a piezoelectric ceramic tube and a metal prestressed one, and the combined thick-walled cylinder’s radial vibration continuity condition and boundary conditions. The transducer’s natural frequency equation and mode shape function were derived. The calculation results of its natural frequencies have a higher coincidence rate with experimental measurement values published in references. Based on the analytical method and the difference method, numerical simulation models for the transducer’s radial vibration were established, and the amplitude-frequency characteristics and displacement responses of the transducer’s radial vibration were simulated. The simulation results showed that amplitude-frequency characteristics curves and displacement responses obtained using the two methods, respectively are the same to verify the correctness of the simulation results. Through simulation analysis, it was shown that the effect laws of structure size of the transducer on its radial vibration natural frequency are as follows: if the thickness of metal prestressed tube and piezoelectric ceramic one is constant, the transducer’s natural frequencies decrease with increase in inner diameter of piezoelectric ceramic tube;if the outer diameter of metal prestressed tube and the inner diameter of piezoelectric ceramic one are constant, the transducer’s natural frequencies decrease with increase in thickness ratio of piezoelectric ceramic tube to metal prestressed one.
作者
张超
董世民
刘天明
张敬祥
贾贺通
柳青扬
ZHANG Chao;DONG Shimin;LIU Tianming;ZHANG Jingxiang;JIA Hetong;LIU Qingyang(School of Mechanical Engineering,Yanshan University,Qinhuangdao 066004,China)
出处
《振动与冲击》
EI
CSCD
北大核心
2020年第21期217-225,240,共10页
Journal of Vibration and Shock
基金
河北省自然科学基金(E2017203101)。
关键词
径向振动
压电陶瓷
换能器
固有频率
幅频特性
radial vibration
piezoelectric ceramic
transducer
natural frequency
amplitude-frequency characteristics
