Scattering Of Flexural Waves In An Infinite Piezoelectric Thin Plate With Holes

The piezoelectric material can be widely used in aviation,aerospace,industrial production and other engineering practices and people's lives because of its inherent force-electric coupling characteristics.It is undeniable that the stress concentration phenomenon will occur at the holes,inclusions,cracks and composite defects,which will lead to the failure or destruction of materials,and piezoelectric materials are no exception.The piezoelectric thin plate is the most widely used piezoelectric structure,so it is of great theoretical and engineering significance to study the problem of the flexural wave scattering in infinite piezoelectric thin plate with holes.Based on Kirchhoff's thin plate hypothesis and linear piezoelectric dynamic theory,the scattering of flexural wave and dynamic stress concentration of an infinite piezoelectric plate with a hole are studied by using wave function expansion method,complex function and conformal mapping in this paper.Firstly,the analytical expression of dynamic moment concentration factor(DMCF)of the flexural wave scattering of the infinite piezoelectric plate with a circular hole is derived.Secondly,the conformal mapping can be used to obtain the analytical expression of dynamic moment concentration factor of the flexural wave scattering of the infinite piezoelectric thin plate with an elliptical hole.Finally,in order to illustrate the problem,takes PZT-4 as an example to discuss the effects of the applied electric field,ratio of two semi-axes' length of the elliptical hole,inclination angle of the elliptical hole and frequency of incident wave on the scattering of flexural waves in an infinite piezoelectric thin plate with a circular hole or an elliptical hole,and the numerical results of the dynamic moment concentration factor of an infinite piezoelectric thin plate with a circular hole and an elliptical hole are given,respectively.The research contents and specific works of this article are mainly divided into two parts as follows:(1)The scattering problem of flexural wave in an infinite piezoelectric plate with a circular hole is solved.Firstly,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,based on the relationship between the internal force and the deflection of the thin plate,the expressions of the stress and moment of the infinite piezoelectric thin plate are derived,and the analytical solution of the dynamic moment concentration factor is obtained;Finally,based on a numerical example,by changing the frequency of the incident wave and the applied electric field,the influence of each parameter change on the DMCF around the circular hole is discussed.(2)The scattering problem of flexural wave in an infinite piezoelectric plate with an elliptical hole is solved.Firstly,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,by using the classical complex function and conformal transformation method,the expressions of stress and moment in infinite piezoelectric thin plate are derived,and the analytical solution of dynamic moment concentration factor is obtained;finally,based on a numerical example,the influence of each parameters change on the dynamic moment concentration factor around the elliptical hole is discussed by changing the inclination angle of the elliptical hole,the ratio of two semi-axes' length of the elliptical hole,the frequency of the incident wave,and the applied electric field.In this paper,the scattering problem of flexural wave in infinite piezoelectric thin plate with a hole is studied,and hopes that the research results can provide a certain reference for industrial production and engineering applications.