The moment Lyapunov exponents of a two-dimensional viscoelastic system under bounded noise excitation are studied in this paper. An example of this system is the transverse vibration of a viscoelastic column under the excitation of stochastic axial compressive load. The stochastic parametric excitation is modeled as a bounded noise process, which is a realistic model of stochastic fluctuation in engineering applications. The moment Lyapunov exponent of the system is given by the eigenvalue of an eigenvalue problem. The method of regular perturbation is applied to obtain weak noise expansions of the moment Lyapunov exponent, Lyapunov exponent, and stability index in terms of the small fluctuation parameter. The results obtained are compared with those for which the effect of viscoelasticity is not considered.
Moment Lyapunov Exponents of a Two-Dimensional Viscoelastic System Under Bounded Noise Excitation
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Apr. 24, 2001; final revision, Oct. 2, 2001. Associate Editor: D. A. Siginer. Discussion on the paper should be addressed to the Editor, Prof. Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Xie, W. (May 3, 2002). "Moment Lyapunov Exponents of a Two-Dimensional Viscoelastic System Under Bounded Noise Excitation ." ASME. J. Appl. Mech. May 2002; 69(3): 346–357. https://doi.org/10.1115/1.1445143
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