Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 11202190)
Received Date:21 May 2020
Accepted Date:14 September 2020
Available Online:18 January 2021
Published Online:05 February 2021
Abstract: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. Keywords:piezoelectric rod/ Hamilton principle/ temperature effect/ solitary wave
图 6 压电圆杆的孤波特性 Figure6. Solitariness of piezoelectric rod.
图7给出了在三种不同温度下, 压电圆杆的波速c和波数k的关系图. 可以看出, 当温度一定时, 随着波数k的增加, 波速c也呈增加趋势, 同样地, 当波数k一定时, 随着温度的升高波速c反而呈减小趋势, 这与表2以及图3和图4的模拟结果相符合. 图 7 三种不同温度下波速c和波数k的关系图 Figure7. Graph of wave velocity c and wave number k at three different temperatures.