Asymptotic stabilization of a flexible beam with an attached mass

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


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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How to Cite
Kalosha, J. I., and A. L. Zuyev. “Asymptotic Stabilization of a Flexible Beam With an Attached Mass”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 10, Oct. 2021, pp. 1330-41, doi:10.37863/umzh.v73i10.6750.
Research articles