A spatial string model incorporating a nonlinear (and nonconservative) material law is proposed using finite deformation continuum mechanics. The resulting model is shown to reduce to the classical nonlinear string when a linear material law is used. The influence of material nonlinearities on the string’s dynamic response to excitation near a transverse natural frequency is shown to be small due to their appearance at high orders only. Material nonlinearities appear at low order in the equations for excitation near a longitudinal natural frequency, and a solution for this case is developed by applying a second order multiple scales method directly to the partial differential equations. The material nonlinearities are found to influence both the degree of nonlinearity in the response and its softening or hardening nature.
Nonlinear Dynamics of a Taut String with Material Nonlinearities
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received Nov. 1999; revised Aug. 2000. Associate Editor: S. C. Sinha.
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Leamy, M. J., and Gottlieb, O. (August 1, 2000). "Nonlinear Dynamics of a Taut String with Material Nonlinearities ." ASME. J. Vib. Acoust. January 2001; 123(1): 53–60. https://doi.org/10.1115/1.1325411
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