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Sixty years of stochastic linearization technique

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Abstract

Stochastic linearization technique is a versatile method of solving nonlinear stochastic boundary value problems. It allows obtaining estimates of the response of the system when exact solution is unavailable; in contrast to the perturbation technique, its realization does not demand smallness of the parameter; on the other hand, unlike the Monte Carlo simulation it does not involve extensive computational cost. Although its accuracy may be not very high, this is remedied by the fact that the stochastic excitation itself need not be known quite precisely. Although it was advanced about six decades ago, during which several hundreds of papers were written, its foundations, as exposed in many monographs, appear to be still attracting investigators in stochastic dynamics. This study considers the methodological and pedagogical aspects of its exposition.

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Acknowledgments

Authors express their grateful thanks to Professor P.D. Spanos, Lewis B. Rayon Professor of Mechanical Engineering, Civil Engineering and Materials Science and NanoEngineering, Rice University, for helpful comments. The paper is dedicated to the memory of Professor Stephen Harry Crandall (1920–2013) who could not see it in the published form. Sincere thanks are herewith expressed to anonymous reviewers for their constructive comments.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Florida Atlantic University, Boca Raton, FL, 33431-0991, USA

    Isaac Elishakoff

  2. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Stephen H. Crandall

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  1. Isaac Elishakoff
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  2. Stephen H. Crandall
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Correspondence to Isaac Elishakoff.

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Elishakoff, I., Crandall, S.H. Sixty years of stochastic linearization technique. Meccanica 52, 299–305 (2017). https://doi.org/10.1007/s11012-016-0399-x

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  • DOI: https://doi.org/10.1007/s11012-016-0399-x

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