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Stability and control of random rocking motion of a multidimensional structure: the Melnikov approach

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Abstract

This paper investigates the controlled dynamics of a structure consisting of a free standing rigid block with an attached chain of uniaxially moving point masses. Rocking motion is excited by motion of the ground; instability is associated with overturning of the structure as a whole. The control task is to minimize the probability of overturning. The stochastic Melnikov method is used to obtain a necessary condition of instability, estimate an upper bound to the probability of overturning, and find a convenient control strategy. The paper is restricted to the consideration of seismic vulnerability of the structure. A similar approach can be applied to systems with wind or wave excitations.

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Authors and Affiliations

  1. Space Research Institute, Russian Academy of Sciences, 84/32 Profsoyuznaya ul., Moscow, 117997, Russia

    A. Kovaleva

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  1. A. Kovaleva
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Correspondence to A. Kovaleva.

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Kovaleva, A. Stability and control of random rocking motion of a multidimensional structure: the Melnikov approach. Nonlinear Dyn 59, 309–317 (2010). https://doi.org/10.1007/s11071-009-9540-x

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  • DOI: https://doi.org/10.1007/s11071-009-9540-x

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