Open AccessAsymptotic stabilization of a flexible beam with an attached mass
Author(s) -
Julia Kalosha,
Alexander Zuyev
Publication year - 2021
Publication title -
ukraïnsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v73i10.6750
Subject(s) - exponential stability , beam (structure) , control theory (sociology) , bernoulli's principle , spring (device) , euler's formula , operator (biology) , actuator , asymptotic analysis , stability (learning theory) , mathematics , mathematical analysis , physics , computer science , engineering , nonlinear system , mechanical engineering , structural engineering , control (management) , biochemistry , chemistry , repressor , quantum mechanics , artificial intelligence , machine learning , transcription factor , gene , thermodynamics
UDC 517.977A 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.