3D orthogonality relations for the surface waves and the far field evaluation in viscoelastic layered solids with or without fluid loading

Abstract

The 3D surface waves in the linearly viscoelastic layered plates and cylinders are considered either under any of the homogeneous boundary conditions providing energy reflection back into the solid, or in the case of fluid loading. A fundamental property of waves in such structures is their generalized orthogonality, which is deduced and discussed. The eigenmodes of discrete spectrum are orthogonal to each other and to the waves of continuous spectrum (if they exist). A method for the exact calculation of the far field caused by an acoustic source of finite size is suggested. The obtained results can be used for evaluating the fields radiated by ultrasonic transducers of arbitrary aperture and by other realistic sources in the layered plate, cylinder, space or half-space using modal analysis. The results are also applicable to the post processing of the FEM calculations.