Nonlinear Dynamics of a Taut String with Material Nonlinearities

[+] Author and Article Information
M. J. Leamy, O. Gottlieb

Faculty of Mechanical Engineering, The Technion-Israel Institute of Technology, Haifa 32000, Israel

J. Vib. Acoust 123(1), 53-60 (Aug 01, 2000) (8 pages) doi:10.1115/1.1325411 History: Received November 01, 1999; Revised August 01, 2000
Copyright © 2001 by ASME
Topics: String , Equations
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Grahic Jump Location
Diagram depicting a small element of the string in both the tensioned and the deformed configuration. Material coordinates (x1,x2,x3) identify a point P0 in the tensioned configuration, which is displaced during deformation to point P and is located in space by the inertial coordinates (z1(t),z2(t),z3(t)). After deformation, the material coordinates form a nonorthogonal curvilinear coordinate system (x1,x2,x3) with covariant base vectors (G1,G2,G3).
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Comparison of predicted longitudinal dynamic response for increasing numbers of included modes. Here, a2=−2,a3=6,ωt=1,N=1,r=4,p=0.08,α1=2/2,C=0, and c1=6.25, corresponding to 1 percent critical damping of the first mode. E represents the square root of the modal energy and is given by the L2 norm of all the included modal amplitudes.
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Frequency response curves for different nonlinear material descriptions. In each, ωt=1,N=1,r=4,p=0.08,α1=2/2,a3=6, and μ=6.25, corresponding to 1 percent critical damping.




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