Dispersion analysis of leaky guided waves in fluid-loaded waveguides of generic shape

Abstract

A fully coupled 2.5D formulation is proposed to compute the dispersive parameters of waveguides with arbitrary cross-section immersed in infinite inviscid fluids.The discretization of the waveguide is performed by means of a Semi-Analytical Finite Element (SAFE) approach, whereas a 2.5D BEM formulation is used to model the impedance of the surrounding infinite fluid. The kernels of the boundary integrals contain the fundamental solutions of the space Fourier-transformed Helmholtz equation, which governs the wave propagation process in the fluid domain. Numerical difficulties related to the evaluation of singular integrals are avoided by using a regularization procedure. To improve the numerical stability of the discretized boundary integral equations for the external Helmholtz problem, the so called CHIEF method is used.The discrete wave equation results in a nonlinear eigenvalue problem in the complex axial wavenumbers that is solved at the frequencies of interest by means of a contour integral algorithm. In order to separate physical from non-physical solutions and to fulfill the requirement of holomorphicity of the dynamic stiffness matrix inside the complex wavenumber contour, the phase of the radial bulk wavenumber is uniquely defined by enforcing the Snell–Descartes law at the fluid–waveguide interface.Three numerical applications are presented. The computed dispersion curves for a circular bar immersed in oil are in agreement with those extracted using the Global Matrix Method. Novel results are presented for viscoelastic steel bars of square and L-shaped cross-section immersed in water.