Stochastic Response and Stability of a Nonintegrable System |
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Authors: | Deepak Kumar T. K. Datta |
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Affiliation: | 1Research Scholar, Dept. of Civil Engineering, Indian Institute of Technology, Delhi, India. 2Professor, Dept. of Civil Engineering, Indian Institute of Technology, Delhi, India. E-mail: tushar_k_datta@yahoo.com
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Abstract: | For determining the stochastic response and stability of a strongly nonlinear single-degree-of-freedom system using the stochastic averaging technique, the size of excitations should be small such that the response of the system converges weakly to a Markov process. This condition is not often met with practical problems, and therefore, application of this method for obtaining their responses becomes difficult. Further, for systems with nonlinearities that cannot be integrated in closed form, stability analysis by examining the conditions of the two boundaries of the problem is not possible. A semianalytical method along with a weighted residual technique is presented here to circumvent these difficulties and to determine the response and stability of a strongly nonlinear system subjected to sizable stochastic excitation. The weighted residual technique is employed to correct the errors in averaged drift and diffusion coefficients resulting due to the size of the stochastic excitation. Two example problems are solved as illustrations of the method. |
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Keywords: | Stochastic processes Stability Nonlinear systems Markov chains |
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