A 2.5D boundary element formulation for modeling damped waves in arbitrary cross-section waveguides and cavities

Abstract

A regularized 2.5D boundary element method (BEM) is proposed to predict the dispersion properties of damped stress guided waves in waveguides and cavities of arbitrary cross-section. The wave attenuation, induced by material damping, is introduced using linear viscoelastic constitutive relations and described in a spatial manner by the imaginary component of the axial wavenumber. The discretized dispersive wave equation results in a nonlinear eigenvalue problem, which is solved obtaining complex axial wavenumbers for a fixed frequency using a contour integral algorithm. Due to the singular characteristics and the multivalued feature of the wave equation, the requirement of holomorphicity inside the contour region over the complex wavenumber plane is fulfilled by the introduction of the Sommerfeld branch cuts and by the choice of the permissible Riemann sheets. A post processing analysis is developed for the extraction of the energy velocity of propagative guided waves. The reliability of the method is demonstrated by comparing the results obtained for a rail and a bar with square cross-section with those obtained from a 2.5D Finite Element formulation also known in literature as Semi Analytical Finite Element (SAFE) method. Next, to show the potential of the proposed numerical framework, dispersion properties are predicted for surface waves propagating along cylindrical cavities of arbitrary cross-section. It is demonstrated that the attenuation of surface waves approaches asymptotically the attenuation of Rayleigh waves.