On the Eigenvalue Distribution for a Beam with Attached Masses
Abstract
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.
Cite
@article{arxiv.2006.00610,
title = {On the Eigenvalue Distribution for a Beam with Attached Masses},
author = {Julia Kalosha and Alexander Zuyev and Peter Benner},
journal= {arXiv preprint arXiv:2006.00610},
year = {2022}
}
Comments
Accepted for publication in the special issue "Stabilization of Distributed Parameter Systems: Design Methods and Applications", SEMA SIMAI Springer Series