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Optimal control of longitudinal vibrations of composite rods with the same wave propagation time in each part

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Abstract

We consider longitudinal elastic vibrations of a composite rod and find closedform expressions that describe optimal boundary controls bringing the rod from the quiescent state into a state with given displacement function φ(t) and velocity function ψ(t) in time T. We assume that the wave propagation time through each part of the rod is the same and T is a multiple of that time.

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References

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. M. Rogozhnikov

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  1. A. M. Rogozhnikov
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Dedicated to Vladimir Aleksandrovich Il’in, my scientific teacher, an outstanding mathematician

Original Russian Text © A.M. Rogozhnikov, 2013, published in Differentsial’nye Uravneniya, 2013, Vol. 49, No. 5, pp. 633–642.

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Rogozhnikov, A.M. Optimal control of longitudinal vibrations of composite rods with the same wave propagation time in each part. Diff Equat 49, 607–616 (2013). https://doi.org/10.1134/S0012266113050091

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  • DOI: https://doi.org/10.1134/S0012266113050091

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