Home
Resource
Dispersion relations for elastic waves in plates and rods
PDF
PDF format is widely accepted and good for printing.
Plug-in required
PDF-1(646.17 kb)
Citation & Export
View Usage Statistics
Staff View

Citation & Export
Hide

Simple citation

Amirkulova, Feruza Abdukadirovna. Dispersion relations for elastic waves in plates and rods. Retrieved from https://doi.org/doi:10.7282/T3X63MM6

Export

Click here for information about Citation Management Tools at Rutgers.

Statistics
Hide

Description

TitleDispersion relations for elastic waves in plates and rods
NameAmirkulova, Feruza Abdukadirovna (author); NORRIS, ANDREW (chair); Baruh, Haim (internal member); Benaroya, Haim (internal member); Rutgers University; Graduate School - New Brunswick
Date Created2011
Other Date2011-01 (degree)
SubjectMechanical and Aerospace Engineering, Wave-motion, Theory of, Dispersion relations, Elastic wave propagation
Extentxi, 102 p. : ill.
DescriptionWave 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.
NoteM.S.
NoteIncludes bibliographical references
NoteIncludes vita
Noteby Feruza Abdukadirovna Amirkulova
Genretheses, ETD graduate
Persistent URLhttps://doi.org/doi:10.7282/T3X63MM6
Languageeng
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
Version 8.5.5
Rutgers University Libraries - Copyright ©2024