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.
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January 2001
Technical Papers
Nonlinear Dynamics of a Taut String with Material Nonlinearities
M. J. Leamy, Assoc. Mem. ASME,
M. J. Leamy, Assoc. Mem. ASME
Faculty of Mechanical Engineering, The Technion-Israel Institute of Technology, Haifa 32000, Israel
11
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O. Gottlieb, Assoc. Mem. ASME
O. Gottlieb, Assoc. Mem. ASME
Faculty of Mechanical Engineering, The Technion-Israel Institute of Technology, Haifa 32000, Israel
Search for other works by this author on:
M. J. Leamy, Assoc. Mem. ASME
11
Faculty of Mechanical Engineering, The Technion-Israel Institute of Technology, Haifa 32000, Israel
O. Gottlieb, Assoc. Mem. ASME
Faculty of Mechanical Engineering, The Technion-Israel Institute of Technology, Haifa 32000, Israel
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.
J. Vib. Acoust. Jan 2001, 123(1): 53-60 (8 pages)
Published Online: August 1, 2000
Article history
Received:
November 1, 1999
Revised:
August 1, 2000
Citation
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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