Asymptotic stabilization of a flexible beam with an attached mass

J. I. Kalosha; A. L. Zuyev

doi:10.37863/umzh.v73i10.6750

J. I. Kalosha Inst. Appl. Math. and Mech. Nat. Acad. Sci. Ukraine, Sloviansk
A. L. Zuyev Inst. Appl. Math. and Mech. Nat. Acad. Sci. Ukraine, Sloviansk; Otto von Guericke Univ. Magdeburg, Max Planck Inst. Dynamics of Complex Techn. Systems, Germany

DOI: https://doi.org/10.37863/umzh.v73i10.6750

Keywords: Euler--Bernoulli beam; stabilization; asymptotic stability; Lyapunov functional

Abstract

UDC 517.977

A mathematical model of a simply supported Euler – Bernoulli beam with attached spring-mass system is considered. The model is controlled by distributed piezo actuators and a lumped force. We address the issue of asymptotic behavior of solutions of this system driven by a linear feedback law. The precompactness of trajectories is established for the operator formulation of the closed-loop dynamics. Sufficient conditions for strong asymptotic stability of the trivial equilibrium are obtained.

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