通过Stroh方法和B-L积分建立压电体单侧接触周期界面波通解形式及应用举例

Establishing the general solution and giving application example for periodic wave at unilateral contact interface between two piezoelectric materials by stroh formalism and B-L integration

Stroh方法将各项异性材料的本构、几何及平衡方程转化为求解特征值问题,给出了由特征值和特征向量表示的关于位移和应力的一般解,并且通过引入辅助向量直接建立了应力和位移之间的关系。B-L积分又解决了Stroh方法对于某些"退化"材料不适用的问题。单侧接触界面只能承受压力,不能承受拉力,当弹性波作用到界面上时,如果强度足够界面会发生局部分离或滑移,边界条件具有很强的非线性,导致问题的解决非常困难。将Stroh方法应用到压电材料弹性动力学稳态问题中,结合傅立叶分析,给出了压电材料弹性动力学的Stroh基本解,表达式简洁优美,对解决因边界非线性问题带来的困难提供了方便,举例进行了证明。

The constitutive,geometry and equilibrium equations for anisotropic materials are transformed to solving the characteristic value problem by Stroh formalism,and the general solution for displacement and stress expressed by eigenvalues and eigenvectors are given too,and more the relationship of displacement and stress is established directly by the introduction of auxiliary vector.B-L integration solves the problem that the stroh method can not apply to some degenerated materials.If the wave is strong enough the interface will separate or slip in local areas when the elastic wave propagate at a unilateral contact interface,because only pressure not tension can generate in the interface,and non-linearity（boundary non-linearity）will be brought to the problem so that the solving to the question is very difficult.The Stroh formalism is applied to elastic dynamic stability problem for the piezoelectric material in the article,and Stroh dynamics solutions are given by combining Fourier analysis,the expressions are concise and beautiful and they are convenient to solve the difficulties caused by the nonlinear boundary.Finally the application of the Stroh formalism is introduced by an example.