Analysis of elastic wave propagation in nonlinear beams

Mohammad H. Abedinnasab, Mahmoud I. Hussein

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    1 Scopus citations

    Abstract

    We derive the exact dispersion relations for flexural elastic wave motion in a beam under finite deformation. We employ the Euler-Bernoulli kinematic hypothesis. Focusing on homogeneous waveguides with constant cross-section, we utilize the exact strain tensor and retain all high order terms. The results allow us to quantify the deviation in the dispersion curves when exact large deformation is considered compared to the small strain assumption. We show that incorporation of finite deformation shifts the frequency dispersion curves downwards. Furthermore, the group velocity increases with wavenumber but this trend reverses at high wavenumbers when the wave amplitude is sufficiently high. At sufficiently high wave amplitudes, the group velocity becomes negative at high wavenumbers. This study on nonlinear homogeneous beams lays the foundation for future development to nonlinear periodic beams.

    Original languageEnglish (US)
    Title of host publicationASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011
    Pages207-212
    Number of pages6
    EditionPARTS A AND B
    DOIs
    StatePublished - Dec 1 2011
    EventASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011 - Washington, DC, United States
    Duration: Aug 28 2011Aug 31 2011

    Publication series

    NameProceedings of the ASME Design Engineering Technical Conference
    NumberPARTS A AND B
    Volume1

    Other

    OtherASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011
    Country/TerritoryUnited States
    CityWashington, DC
    Period8/28/118/31/11

    All Science Journal Classification (ASJC) codes

    • Modeling and Simulation
    • Mechanical Engineering
    • Computer Science Applications
    • Computer Graphics and Computer-Aided Design

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