广义场作用对电磁弹性结构中弹性波传播的影响

【作者】 吕克朋；

【导师】 陈江义；

【作者基本信息】 郑州大学 ， 机械设计及理论， 2009， 硕士

【摘要】 电磁弹性结构中声表面波的传播特性研究是近年来较新的课题,人们也进行了不断的探索与研究。但对广义场下的情形研究较少,且不系统,特别是电场及磁场下的研究更少。鉴于此,本文将系统的研究广义场下电磁弹性结构中声表面波的传播性能。从基础理论出发,给出横观各向同性电磁弹性介质的力学、电学和磁学基本方程,得出位移、电势和磁势的一般解,并给出无外加场量下电磁弹性结构中声表面波传播的频散方程。在确定广义场量（磁场、电场、应力）下电磁弹性板中耦合初始广义应力（弹性应力、电位移及磁感应强度）的基础上,根据基本方程,通过势函数法与子波技术相结合的方法,得出广义场量下声表面波的传播特性,并分别给出对称模态和反对称模态时的频散方程——波传播速度与波数的关系。最后以由BaTiO₃-CoFe₂O₄材料构成的电磁弹性板模型作为数值算例,结合广义场下电磁弹性结构中表面波的频散方程,借助Matlab软件,绘制了电磁弹性结构中Lamb波传播的对称模态及反对称模态频散曲线,并与无外加场量的情况进行对比。计算结果表明,整体而言广义场对声表面波的传播速度有所改变。在外加电场及磁场下的改变量可达2%-5%,特别是在波数（?）＞10,波速改变更加明显,但是所加电场及磁场比较大。在波数（?）＞10时,电场及磁场对波速的改变不太明显。而对于压力作用下的情形,波速的改变较为稳定,其改变幅度不随波数的改变而改变。更多还原

【Abstract】 The research of propagating characteristics of surface acoustic wave in magneto-electro-elastic structure has been increasingly concerned these days and more and more people are doing related work on the subjects. However, the relevant research of generalized field is rare and unsystematic, especially the research of circumstance in generalized field and magnetic field. So this paper will describe some systematic research on propagating characteristics of surface acoustic wave under generalized field.On the basis of some basic theories and the macroscopic fundamental equation of mechanical , electrical, magnetical quotations relevant to the transversely isotropic medium and dispersive equation of the surface acoustic wave in magneto-electro-elastic structure, we can get the general solution of displacement electric, potential and magnetic potential. Coupled with initial generalized stress of magneto-electro-elastic plate under generalized field, we can get propagating characteristics of the surface acoustic wave through potential function methods and wavelet techniques, which is the relationship between wave number and the velocity of waves（the dispersive quotation including symmetric modes and anti-symmetric modes）Finally, Numerical calculations were carried out for a BaTiO₃-CoFe₂O₄ magneto-electro-elastic plate. With the aid of Matlab, we get the symmetric modes and anti-symmetric curves of Lamb wave propagating in magneto-electro-elastic structure, and compared the results to circumstance where there is no field. In general, the result shows that generalized field has effect on the phase velocity of Lamb wave. In the absence of electric field and magnetic field, the phase velocity is changed by 2 to 5 percent, and it is remarkably changed especially when k is more than 10. While k is less than 10, the phase velocity is not changed obviously. However, the electric field and magnetic field must be strong enough. We also find that the velocity changed stably under pressure and its amplitude of variation did not change with the wave number.更多还原