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Title Dispersion relations for elastic waves in plates and rods
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Publication Date
Degree MS
Discipline/Department Mechanical and Aerospace Engineering
Degree Level masters
University/Publisher Rutgers University
Abstract Wave propagation in homogeneous elastic structures is studied. Dispersion relations are obtained for elastic waves in plates and rods, for symmetric and antisymmetric modes using different displacement potentials. Some engineering beam theories are considered. Dispersion relations are obtained for phase velocity. The comparison of results based on the fundamental beam theories is presented for the lowest flexural mode. The Rayleigh-Lamb frequency equations are derived for elastic plate using the Helmholtz displacement decomposition. The Rayleigh-Lamb equations are considered in a new way. A new series expansion of frequency to any order of wave number, in principle, is obtained for symmetric and antisymmetric modes using an iteration method. Dispersion relations are shown in graphs for frequency, phase speed and group speed versus wave number. The obtained results are in good agreement with exact solutions. The cutoff frequencies for axial-shear, radial-shear and flexural modes are calculated and taken as starting points in dispersion relations for frequencies versus wave number. Different displacement potential representations are presented and compared. The Pochhammer-Chree frequency equations are derived for elastic rods using two displacement potentials, such as the Helmholtz decomposition for vector fields and Buchwald's vector potentials. Buchwald's representation enables us to find an efficient formulation of dispersion relations in an isotropic as well as anisotropic rods. Analysis of the numerical results on dispersion relations and cutoff frequencies for axial-shear, radial-shear and flexural modes is given.
Subjects/Keywords Wave-motion, Theory of; Dispersion relations; Elastic wave propagation
Contributors Amirkulova, Feruza Abdukadirovna, 1973- (author); NORRIS, ANDREW (chair); Baruh, Haim (internal member); Benaroya, Haim (internal member)
Language en
Country of Publication us
Format xi, 102 p. : ill.
Record ID oai:example.org:rutgers-lib:30991
Other Identifiers rutgers-lib:30991; ETD_3051; doi:10.7282/T3X63MM6
Repository rutgers
Date Indexed 2018-10-11

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