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

Highlights: •Dispersive properties of viscoelastic waveguides and cavities are computed using a regularized 2.5D BEM. •Linear viscoelasticity is introduced at the constitutive level by means of frequency dependent complex moduli. •A contour integral algorithm is used to solve the nonlinear eigenvalue problem. •The Sommerfeld radiation condition is used to select the permissible Riemann sheets. •Attenuation of surface waves in cavities approaches the attenuation of Rayleigh waves. -- 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 developedmore » 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.« less
Authors:
 [1] ;  [2] ;  [3] ;  [1] ;  [1]
  1. Department of Civil, Chemical, Environmental and Materials Engineering – DICAM, University of Bologna, DICAM Viale del Risorgimento 2, Bologna 40136 (Italy)
  2. (United States)
  3. Civil, Architectural and Environmental Engineering Department, Drexel University, 3141 Chestnut St., Philadelphia, PA 19104 (United States)
Publication Date:
OSTI Identifier:
22230787
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 248; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; ATTENUATION; BOUNDARY ELEMENT METHOD; DAMPING; EIGENVALUES; FREQUENCY DEPENDENCE; NONLINEAR PROBLEMS; RAYLEIGH WAVES; RIEMANN SHEET; SIMULATION; WAVE EQUATIONS; WAVE PROPAGATION; WAVEGUIDES