Calculating dispersion relations for waveguide immersed in perfect fluid

Abstract

Conventional finite element method (FEM) is capable of obtaining wave solutions, but large discretized structures at high frequency require high computational resources, the computational domain can be reduced by combining FEM with analytical assumption for guided wave. Semi Analytical Finite Element (SAFE) formulation for immersed waveguide in perfect fluid is used for acquiring propagating wave modes as dynamic equilibrium states. Modes are solutions to eigenvalue problem and provide with important characteristic features of the guided waves – phase velocity, attenuation, wave structure, etc. The effect of surrounding leaky medium is modeled via traction boundary condition, which is based on assumption of the continuity of stresses at solid-fluid interface. The boundary condition causes wave attenuation due to energy leakage into outer medium. The derivation of the eigen-problem takes into account complex wavenumbers of leaky wave in fluid and guided wave in a three-dimensional waveguide. Linearization procedure for solving nonlinear eigenvalue problem is used. Dispersion relations for immersed waveguide with Rayleigh damping are obtained. The limits of applications of Rayleigh damping and convergence analysis of immersed waveguide model are discussed.

Keywords

• semi analytical finite element
• eigenvalue problem
• complex wavenumber