弯曲波在含非圆孔洞无限压电薄板中的散射

基于线性压电动力学理论，采用波函数展开法、保角映射以及复变函数，对含非圆孔洞无限大压电薄板弹性波的散射及动应力集中问题进行了分析，给出了其动弯矩集中系数（DMCF）的解析表达式。为说明问题，以PZT-4为例，讨论了外加电场、椭圆孔长短半轴比、椭圆孔倾角以及入射波频率对含圆孔和椭圆孔无限大压电薄板弹性波散射的影响，并分别给出了无限压电薄板开圆孔和椭圆孔动弯矩集中系数的数值结果。

Scattering of Flexural Waves in an Infinite Piezoelectric Thin Plate with a Non-circular Hole

The scattering and dynamic stress concentration of flexural waves in an infinite piezoelectric thin plate with a non-circular hole are studied. First, according to Kirchhoff's thin plate hypothesis, the displacement and strain are assumed to be linearly distributed along the thickness direction of the infinite piezoelectric thin plate. Then, the linear piezoelectric dynamics theory, wave function expansion method, complex function and conformal mapping are used and based on the relationship between the internal force and deflection of the thin plate bending, the expressions of the stress, moment and other fields of the infinite piezoelectric thin plate are derived, and the analytical expressions of the dynamic moment concentration factor(DMCF) are obtained. Finally, to illustrate the problem, takes PZT-4 as an example, the effects of the applied electric field, the ratio of two semi-axes' length of the elliptical hole, the inclination angle of the elliptical hole and the frequency of the incident wave on the elastic wave scattering of the infinite piezoelectric thin plate with a circular hole and an elliptical hole are discussed, and the numerical results of the dynamic moment concentration factors of infinite piezoelectric thin plate with a circular hole and an elliptical hole are given, respectively. The numerical results show that the greater the applied electric field, the greater the dynamic moment concentration factor near the defect is, and it is obviously larger than that of ordinary elastic materials, but with the increase of incident wave frequency, the influence of the change of the applied electric field on DMCF gradually decreases. For different incident wave frequencies, the peak value of the dynamic moment concentration factor mainly occur atand. With the increase of incident wave frequency, the value of dynamic moment concentration factor decreases. When the inclination angle of the elliptical hole is larger or the elliptical hole is flatter, the value of the dynamic moment concentration factor is correspondingly larger. Therefore, in contrast, the dynamic moment concentration factor of the circular hole is the smallest. In this paper, the scattering of flexural waves in an infinite piezoelectric thin plate with a hole is studied. The research results can provide some reference for theoretical application and engineering practice.