Christopher L. Lee

University of Michigan, Ann Arbor, Michigan, United States

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Publications (2)6.02 Total impact

  • Source
    Christopher L. Lee, Noel C. Perkins
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    ABSTRACT: The near resonant response of suspended, elastic cables driven by planar excitation is investigated using a three degree-of-freedom model. The model captures the interaction of a symmetric in-plane mode with two out-of-plane modes. The modes are coupled through quadratic and cubic nonlinearities arising from nonlinear cable stretching. For particular magnitudes of equilibrium curvature, the natural frequency of the in-plane mode is simultaneously commensurable with the natural frequencies of the two out-of-plane modes in 1:1 and 2:1 ratios. A second nonlinear order perturbation analysis is used to determine the existence and stability of four classes of periodic solutions. The perturbation solutions are compared with results obtained by numerically integrating the equations of motion. Furthermore, numerical simulations demonstrate the existence of quasiperiodic responses. Peer Reviewed http://deepblue.lib.umich.edu/bitstream/2027.42/43332/1/11071_2004_Article_BF00045006.pdf
    Nonlinear Dynamics 01/1995; · 3.01 Impact Factor
  • Source
    Christopher L. Lee, Noel C. Perkins
    [Show abstract] [Hide abstract]
    ABSTRACT: The near-resonant response of suspended, elastic cables driven by planar excitation is investigated using a two degree-of-fredom model. The model captures the interaction of a symmetric in-plane mode and an out-of-plane mode with near commensurable natural frequencies in a 2:1 ratio. The modes are coupled through quadratic and cubic nonlinearities arising from nonlinear cable stretching. The existence and stability of periodic solutions are investigated using a second order perturbation analysis. The first order analysis shows that suspended cables may exhibit saturation and jump phenomena. The second order analysis, however, reveals that the cubic nonlinearities and higher order corrections disrupt saturation. The stable, steady state solutions for the second order analysis compare favorably with results obtained by numerically integrating the equations of motion. Peer Reviewed http://deepblue.lib.umich.edu/bitstream/2027.42/43323/1/11071_2004_Article_BF00045648.pdf
    Nonlinear Dynamics 01/1992; · 3.01 Impact Factor

Publication Stats

80 Citations
6.02 Total Impact Points

Top Journals

Institutions

  • 1992–1995
    • University of Michigan
      • Department of Mechanical Engineering
      Ann Arbor, Michigan, United States