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.

    A theoretical and experimental investigation of parametrically excited nonlinear mechanical systems

    Thumbnail
    View/Open
    LD5655.V856_1987.Z376.pdf (19.08Mb)
    Downloads: 3085
    Date
    1987
    Author
    Zavodney, Lawrence D.
    Metadata
    Show full item record
    Abstract
    The response of one- and two-degree-of-freedom (SDOF and 2DOF) systems with quadratic and cubic nonlinearities to fundamental, principal, and combination harmonic parametric excitations is investigated theoretically and experimentally. The method of multiple scales (MMS) is used to determine the equations that describe to first and second order the amplitude- and phase-modulations with time. These equations are used to determine the fixed points and their stability. The perturbation results are verified by integrating the governing equations on a digital computer. The analytical results are in excellent agreement with the numerical solutions. In the SOOF systems with quadratic and cubic nonlinearities, the large responses that oscillate about three equilibrium positions are investigated on the digital and analogue computers. The analogue computer is used to generate a bifurcation diagram in the excitation amplitude versus excitation frequency domain. The digital computer is used to obtain Poincare maps of strange attractors, to investigate larger amplitude responses, and to show the transition to a fractal basin of attraction. The system exhibits 2T, 3T, 4T, ST, 6T, 7T, 8T, 12T, 16T, and ∞T period-multiplying bifurcations. The response of a flexible cantilever beam with a concentrated mass to principal parametric base excitation of the first bending mode is analyzed theoretically. The model takes into account the geometric nonlinearities due to large displacements. Galerkin's method is used to reduce the fourth-order nonlinear POE to a second-order ODE having periodic coefficients and cubic nonlinearities. The MMS is used to determine steady-state responses and their stability. Experiments are performed on metallic and composite beams; the results show good qualitative agreement with the theory. Chaotic responses are observed in the response of the composite beam. The response of 2DOF systems with quadratic nonlinearities to a combination parametric resonance in the presence of 2:1 internal resonances is investigated using the MMS. The first-order perturbation solution predicts qualitatively the stable steady-state solutions and illustrates the quenching and saturation phenomena. The reduced equations also predict a transition from periodic to quasi-periodic responses (i.e., Hopf bifurcation). 359 pages, 110 figures.
    URI
    http://hdl.handle.net/10919/76297
    Collections
    • Doctoral Dissertations [14904]

    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