On the Eigenvalue Distribution for a Beam with Attached Masses

Autor:	Kalosha, Julia, Zuyev, Alexander, Benner, Peter
Rok vydání:	2020
Předmět:	Mathematics - Optimization and Control Mathematics - Analysis of PDEs 74H45 35P20 74K10 70J10 93C20
Zdroj:	In: Sklyar G., Zuyev A. (eds) Stabilization of Distributed Parameter Systems: Design Methods and Applications. SEMA SIMAI Springer Series, vol 2, 2021, pp. 43-56
Druh dokumentu:	Working Paper
DOI:	10.1007/978-3-030-61742-4_3
Popis:	We study a mathematical model of a hinged flexible beam with piezoelectric actuators and electromagnetic shaker in this paper. The shaker is modelled as a mass and spring system attached to the beam. To analyze free vibrations of this mechanical system, we consider the corresponding spectral problem for a fourth-order differential operator with interface conditions that characterize the shaker dynamics. The characteristic equation is studied analytically, and asymptotic estimates of eigenvalues are obtained. The eigenvalue distribution is also illustrated by numerical simulations under a realistic choice of mechanical parameters. Comment: Accepted for publication in the special issue "Stabilization of Distributed Parameter Systems: Design Methods and Applications", SEMA SIMAI Springer Series
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2006.00610 Zobrazit plný text záznamu View this record from Arxiv