Period Doubling and Chaos in Unsymmetric Structures Under Parametric Excitation

[+] Author and Article Information
W. Szemplińska-Stupnicka

Institute of Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska 21, PL 00-049 Warsaw, Poland

R. H. Plaut, J.-C. Hsieh

Charles E Via, Jr. Department of Civil Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Va. 24061

J. Appl. Mech 56(4), 947-952 (Dec 01, 1989) (6 pages) doi:10.1115/1.3176195 History: Received September 21, 1988; Revised January 31, 1989; Online July 21, 2009


Nonlinear oscillations of a single-degree-of-freedom, parametrically-excited system are considered. The stiffness involves quadratic and cubic nonlinearities and models a shallow arch or buckled mechanism. The excitation frequency is assumed to be close to twice the natural frequency of the system. Numerical integration is used to obtain phase plane portraits, power spectra, and Poincaré maps for large-time motions. Period-doubling bifurcations and several types of limit cycles and chaotic behavior are observed. Approximate analytical techniques are applied to analyze some of the limit cycles and transitions of behavior. The results are used to estimate the parameter region in which chaos may occur.

Copyright © 1989 by ASME
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