An analytical model for the scattering of guided waves by partly through-thickness cavities with irregular shapes in 3D

Ludovic Moreau , Mihaï Caleap (1) , Alexander Velichko , Paul D. Wilcox

1 Department of Mechanical Engineering

This paper presents an analytical model for the three-dimensional scattering of Lamb and SH waves by a partly through-thickness, flat-bottomed cavity with an irregular shape. In this model, both the scattered field and the standing field in the thinner plate beneath the cavity are decomposed on the basis of Lamb and SH waves, by including propagating and evanescent modes. The amplitude of the modes is calculated after writing the nullity of the total stress at the boundary of the cavity, and the continuity of the stress and displacement vectors under the cavity. In the boundary conditions, the functions depend on the through-thickness coordinate, z, and on the angular coordinate, θ, because the cavity is not circular. This is dealt with by projecting the z-dependent functions onto the basis of the guided waves displacements vectors, and by expanding the θ-dependent functions in Fourier series. Example results are presented for the scattering of the S0, SH0 and A0 modes by elliptical cavities of varying depth, and the scattering of the S0 mode by a cavity with an arbitrary shape. Validation is made by comparison with a finite element model.

Mots clés: Scattering; Guided waves; analytical; 3D

Domaines: Acoustique [physics.class-ph]

Ludovic Moreau, Mihaï Caleap, Alexander Velichko, Paul D. Wilcox. An analytical model for the scattering of guided waves by partly through-thickness cavities with irregular shapes in 3D. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00810970⟩