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.

Accepted for publication in the special issue "Stabilization of Distributed Parameter Systems: Design Methods and Applications", SEMA SIMAI Springer Series

Cited by in corpus (4)

• A Dynamic Observer for a Class of Infinite-Dimensional Vibrating Flexible Structures
• Asymptotic Stabilization of a Flexible Beam with an Attached Mass
• Approximating a flexible beam model in the Loewner framework
• Observer Design for a Flexible Structure with Distributed and Point Sensors