A Geometric Approach for Establishing Dynamic Buckling Loads of Autonomous Potential Two-Degree-of-Freedom Systems

[+] Author and Article Information
A. N. Kounadis

National Technical University of Athens, Structural Analysis and Steel Bridges, 42, Patission Street, Athens 106 82, Greece

J. Appl. Mech 66(1), 55-61 (Mar 01, 1999) (7 pages) doi:10.1115/1.2789169 History: Received February 02, 1998; Revised June 04, 1998; Online October 25, 2007


Nonlinear dynamic buckling of autonomous potential two-degree-of-freedom nondissipative systems with static unstable critical points lying on nonlinear primary equilibrium paths is studied via a geometric approach. This is based on certain salient properties of the zero level total potential energy “surface” which in conjunction with the total energy-balance equation allow establishment of new dynamic buckling criteria for planar systems. These criteria yield readily obtained “exact” dynamic buckling loads without solving the highly nonlinear initial-value problem. The simplicity, reliability, and efficiency of the proposed technique is illustrated with the aid of various dynamic buckling analyses of two two-degree-of-freedom models which are also compared with those obtained by the Verner-Runge-Kutta scheme.

Copyright © 1999 by The American Society of Mechanical Engineers
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