A physically based averaging procedure is applied to a general form of a nonlinear single-degree-of-freedom equation, with nonwhite random excitation, leading to a one-dimensional continuous Markov model for the energy envelope. It is demonstrated that, in combination with an energy-based technique for estimating the potential energy function, the Markov model can be used as the basis of a stochastic identification method for estimating the spectrum of the excitation, the static nonlinear restoring characteristic, and the nonlinear damping function, from measurements of the response alone. Moreover it is shown that, by combining results for two levels of stochastic excitation, it is possible to obtain good estimates of damping and stiffness parameters, both linear and nonlinear. [S0021-8936(00)02304-7]
Energy-Based Stochastic Estimation for Nonlinear Oscillators With Random 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, June 23, 1999; final revision, Aug. 14, 2000. Associate Technical Editor: A. A. Ferri. Discussion on the paper should be addressed to the Technical Editor, Professor 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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Roberts , J. B., and Vasta, M. (August 14, 2000). "Energy-Based Stochastic Estimation for Nonlinear Oscillators With Random Excitation ." ASME. J. Appl. Mech. December 2000; 67(4): 763–771. https://doi.org/10.1115/1.1330546
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