Calculating dispersion relations for waveguide immersed in perfect fluid - Nečiūnas, Audrius; Patašius, Martynas; Barauskas, Rimantas (Mathematical Modelling and Analysis, 2018)
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.