Accurate Backbone Curves for a Modified-Duffing Equation for Vibrations of Imperfect Structures With Viscous Damping

[+] Author and Article Information
D. Hui

University of New Orleans, Dept. of Mechanical Engineering, Lakefront, New Orleans, LA 70148

J. Vib. Acoust 112(3), 304-311 (Jul 01, 1990) (8 pages) doi:10.1115/1.2930509 History: Received May 04, 1987; Revised November 04, 1987; Online June 17, 2008


This paper deals with the Runge-Kutta numerical solution of the modified-Duffing ordinary differential equation with viscous damping. Accurate backbone curves for the finite-amplitude vibrations of geometrically imperfect rectangular plates and shallow spherical shells are presented. For a structure with a sufficiently large initial imperfection, the well-known soft-spring nature of the backbone curve is confirmed for small vibration amplitude. However, for large vibration amplitude, the backbone curves tend to exhibit the usual hard-spring behavior. The predominantly “inward” deflection response (as viewed from the center of curvature) of an imperfect system is found for undamped systems, but this is not necessarily true for a viscously damped structure. Both the initial-deflection and initial-velocity problems are examined.

Copyright © 1990 by The American Society of Mechanical Engineers
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