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