Elastic wave simulation based on modal excitation in 3D medium

Abstract

Paper describes a simulation of an elastic wave in homogenous isotropic waveguide with generic cross-section using semi-analytical finite element (SAFE) formulation. The wave is considered a travelling displacement field in the waveguide as a result to forcing excitation and is expressed via modes' superposition. The solutions for modes are obtained solving SAFE governing eigen problem. Attenuation of the medium in SAFE framework differently from prior researchers is simulated via Rayleigh damping. It is shown, that severe damping is not properly supported by the SAFE formulation and revision for properly accepting linear viscosity is needed.

Calculating Dispersion Relations for Waveguide Immersed in Perfect Fluid

“…It can be noted that the Rayleigh damping term presents the attenuation dependent on frequency. It is important to note that the commonly used governing equation of SAFE formulation (2.1) is derived by assuming k * z ≈ k z ; where * denotes complex conjugate [1]. Therefore, the Rayleigh damping model supports just low damping for modes, where Re(k z ) Im(k z ).…”