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).
Grahic Jump Location
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.
Grahic Jump Location
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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