Computation of dispersion relations for axially symmetric guided waves in cylindrical structures by means of a spectral decomposition method

Höhne, Christian; Prager, Jens; Gravenkamp, Hauke

doi:10.1016/j.ultras.2015.06.011

Cited by 7 publications

(2 citation statements)

References 36 publications

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“…The origin of the CMT goes back to early 1950 s, first appearing in connection with electromagnetic [2] and acoustic [3] waveguides of varying cross sections (horns). Since then, the CMT has been applied to the study of almost all types of elongated waveguides 2 : microwave and optical waveguides (sometimes under the name generalized telegraphist's equations) [4][5][6]; duct acoustics (horns) [7][8][9]; duct acoustics with mean flow [10]; elastic waveguides [11][12][13]; hydroacoustics [1,Sec. 7.1], [14][15][16][17]; seismology and geophysics [18,19]; water waves [20][21][22][23][24][25][26][27][28][29][30][31]; hydroelasticity [26].…”

Section: Introductionmentioning

confidence: 99%

Exact semi-separation of variables in waveguides with non-planar boundaries

Athanassoulis

Papoutsellis

2017

Proc. R. Soc. A.

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Series expansions of unknown fields n n Z ϕ Φ = å in elongated waveguides are commonly used in acoustics, optics, geophysics, water waves and other applications, in the context of coupled-mode theories (CMTs). The transverse functions n Z are determined by solving localSturm-Liouville problems (reference waveguides). In most cases, the boundary conditions assigned to n Z cannot be compatible with the physical boundary conditions of Φ , leading to slowly convergent series, and rendering CMTs mild-slope approximations. In the present paper, the heuristic approach introduced in (Athanassoulis & Belibassakis 1999 J. Fluid Mech. 389, 275-301) is generalized and justified. It is proved that an appropriately enhanced series expansion becomes an exact, rapidly-convergent representation of the field Φ , valid for any smooth, nonplanar boundaries and any smooth enough Φ . This series expansion can be differentiated termwise everywhere in the domain, including the boundaries, implementing an exact semi-separation of variables for non-separable domains. The efficiency of the method is illustrated by solving a boundary value problem for the Laplace equation, and computing the corresponding Dirichlet-to-Neumann operator, involved in Hamiltonian equations for nonlinear water waves. The present method provides accurate results with only a few modes for quite general domains. Extensions to general waveguides are also discussed.

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Section: Introductionmentioning

confidence: 99%

Exact semi-separation of variables in waveguides with non-planar boundaries

Athanassoulis

Papoutsellis

2017

Proc. R. Soc. A.

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“…Modeling of ultrasonic guided wave propagation and its interaction with damage is of great importance in the process of system identification by Lamb waves [10,11]. Generation of dispersion curves [12], determination of wave-damage interaction coefficients [13], and optimal arrangement of transducer arrays are some of the Lamb wave modeling objectives.…”

Section: Introductionmentioning

confidence: 99%