Virginia Tech
    • Log in
    View Item 
    •   VTechWorks Home
    • ETDs: Virginia Tech Electronic Theses and Dissertations
    • Doctoral Dissertations
    • View Item
    •   VTechWorks Home
    • ETDs: Virginia Tech Electronic Theses and Dissertations
    • Doctoral Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Nonlinear Vibrations of Cantilever Beams and Plates

    Thumbnail
    View/Open
    Thesis.pdf (2.086Mb)
    Downloads: 14253
    Date
    2003-07-03
    Author
    Malatkar, Pramod
    Metadata
    Show full item record
    Abstract
    A study of the nonlinear vibrations of metallic cantilever beams and plates subjected to transverse harmonic excitations is presented. Both experimental and theoretical results are presented. The primary focus is however on the transfer of energy between widely spaced modes via modulation. This phenomenon is studied both in the presence and absence of a one-to-one internal resonance. Reduced-order models using Galerkin discretization are also developed to predict experimentally observed motions. A good qualitative agreement is obtained between the experimental and numerical results. Experimentally the energy transfer between widely spaced modes is found to be a function of the closeness of the modulation frequency to the natural frequency of the first mode. The modulation frequency, which depends on various parameters like the amplitude and frequency of excitation, damping factors, etc., has to be near the natural frequency of the low-frequency mode for significant transfer of energy from the directly excited high-frequency mode to the low-frequency mode. An experimental parametric identification technique is developed for estimating the linear and nonlinear damping coefficients and effective nonlinearity of a metallic cantilever beam. This method is applicable to any single-degree-of-freedom nonlinear system with weak cubic geometric and inertia nonlinearities. In addition, two methods, based on the elimination theory of polynomials, are proposed for determining both the critical forcing amplitude as well as the jump frequencies in the case of single-degree-of-freedom nonlinear systems. An experimental study of the response of a rectangular, aluminum cantilever plate to transverse harmonic excitations is also conducted. Various nonlinear dynamic phenomena, like two-to-one and three-to-one internal resonances, external combination resonance, energy transfer between widely spaced modes via modulation, period-doubled motions, and chaos, are demonstrated using a single plate. It is again shown that the closeness of the modulation frequency to the natural frequency of the first mode dictates the energy transfer between widely spaced modes.
    URI
    http://hdl.handle.net/10919/28301
    Collections
    • Doctoral Dissertations [15781]

    If you believe that any material in VTechWorks should be removed, please see our policy and procedure for Requesting that Material be Amended or Removed. All takedown requests will be promptly acknowledged and investigated.

    Virginia Tech | University Libraries | Contact Us
     

     

    VTechWorks

    AboutPoliciesHelp

    Browse

    All of VTechWorksCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    Log inRegister

    Statistics

    View Usage Statistics

    If you believe that any material in VTechWorks should be removed, please see our policy and procedure for Requesting that Material be Amended or Removed. All takedown requests will be promptly acknowledged and investigated.

    Virginia Tech | University Libraries | Contact Us