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| Scattering of Flexural Waves in an Infinite Piezoelectric Thin Plate with a Non-circular Hole |
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Abstract 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.
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Received: 01 December 2020
Published: 27 August 2021
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2021, Vol. 42 
