Flexural wave scattering by varying-thickness annular inclusions on infinite thin plates

Abstract

This paper proposes a semi-analytical method for flexural wave scattering by cylindrical annular inclusions of varying thickness on an infinite thin plate. The thickness of inclusions is assumed to vary in arbitrary power form along the radial direction. In the numerical method, analytically linear relationships between expansion coefficients of exciting and scattered fields around each inclusion are firstly derived by means of closed form solutions of a hypergeometric governing equation of varying-thickness thin plates, and boundary conditions at the interface between different media. Then, linear algebraic equations containing only expansion coefficients of exciting fields are set up with the aid of foregoing linear relations. Expansion coefficients of exciting fields are finally solved by a numerical collocation method. Numerical examples of single and multiple scattering are designed to demonstrate the applicability of the method. The results of single scattering show the change of thickness variations allows tuning local resonances of inclusions to specified frequencies. Furthermore, displacement amplitude spectra of flexural waves for multiple scattering have captured the details of stop band formation of square and hexagonal arrangements of varying-thickness inclusions. It is also demonstrated that stop bands of flexural wave propagation can be controlled by changing stiffness gradients of varying-thickness inclusions.