Modeling wave propagation in damped waveguides of arbitrary cross-section

Abstract

This paper deals with a semi-analytical finite element (SAFE) method for modeling wave propagation in waveguides of arbitrary cross-section. The method simply requires the finite element discretization of the cross-section of the waveguide, and assumes harmonic motion along the wave propagation direction. The general SAFE technique is extended to account for viscoelastic material damping by allowing for complex stiffness matrices for the material. The dispersive solutions are obtained in terms of phase velocity, group velocity (for undamped media), energy velocity (for damped media), attenuation, and cross-sectional mode shapes. Knowledge of these properties is important in any structural health monitoring attempt that uses ultrasonic guided waves. The proposed SAFE formulation is applied to several examples, including anisotropic viscoelastic layered plates, composite-to-composite adhesive joints and railroad tracks.