基于温度效应的无限长压电圆杆纵波分析

Longitudinal wave analysis of infinite length piezoelectric circular rod based on temperature effect

利用有限变形理论,以无限长压电圆杆为研究对象,考虑了在横向惯性、等效泊松比效应以及在热电弹藕合共同作用下,基于Hamilton原理,并引入Euler方程推导出压电圆杆的纵向波动方程.采用Jacobi椭圆函数展开法,求解压电圆杆的波动方程和对应的解.最后,通过Matlab软件得到不同波速比下的色散曲线.以及温度场对压电圆杆的波形、波幅和波数的影响曲线.数值分析结果表明:随着温度的升高,波速逐渐降低,温度场的改变可影响和控制孤立波的传播特性.

Piezoelectric elements have been commonly used because of their wide applications in sensors,transducers,and some micro intelligent structures.However,in the fields of aviation,aerospace,and automation,some relevant equipment works in a harsh environment and is susceptible to the temperature change,thereby leading its performances to be greatly affected.Therefore,the problem of nonlinear wave relating to piezoelectric circular rods in different temperature fields is studied by modeling and numerical analysis.Firstly,based on the theory of finite deformation,we take infinite piezoelectric circular rod as a research object and consider the effects of transverse inertia and equivalent Poisson’s ratio under the thermoelectric coupling action.Using the Hamilton principle and introducing the Euler equation,the longitudinal wave equation of piezoelectric circular rod is obtained.Secondly,Jacobi elliptic cosine function and Jacobi elliptic sine function expansion method are used to solve the wave equation of the piezoelectric circular rod,and the solitary wave solution and the exact periodic solution of the wave equation are obtained.It is found that the periodic solution can be reduced into a solitary wave solution under certain conditions,and it is proved theoretically that there may be solitary wave stably propagating in a piezoelectric circular rod.Finally,the dispersion curves of different wave velocity ratios and the curves about influences of temperature field on the waveform,amplitude and wave number of the piezoelectric rod are obtained by Matlab.The numerical results show that the wave velocity decreases with the increase of temperature when the wave velocity ratio is constant.Given the temperature is constant,it can be found that with the increase of the ratio,the amplitude of solitary wave gradually increases while the wavelength gradually decreases.In addition,the images obtained show that although temperature change can cause the characteristics of solitary waves to change,the solitary waves are always symmetrical bell shaped waves in the propagation process,reflecting the stability characteristics under the combined action of nonlinear and dispersion effects.Therefore,the variation of temperature field can influence and control some propagation characteristics of solitary waves.Moreover,the wave theory has been widely used in the nondestructive testing of structures and the improving of information transmission quality due to its special stability.