Spectrum and stability for elastic systems with global or local Kelvin-Voigt damping

Shuping Chen, Kangsheng Liu, Zhuangyi Liu

Research output: Contribution to journalArticlepeer-review

78 Scopus citations

Abstract

In this paper, we study the mathematical properties of a variational second order evolution equation, which includes the equations modelling vibrations of tile Euler-Bernoulli and Rayleigh beams with the global or local Kelvin-Voigt (K-V) damping. In particular, our results describe the semigroup setting, the strong asymptotic stability and exponential stability of the semi-group, the analyticity of the semigroup, as well as characteristics of the spectrum of the semigroup generator under various conditions on the damping. We also give an example to show that the energy of a vibrating string does not decay exponentially when the K-V dancing is distributed only on a subinterval which has one end coincident with one end of the string.

Original languageEnglish (US)
Pages (from-to)651-668
Number of pages18
JournalSIAM Journal on Applied Mathematics
Volume59
Issue number2
DOIs
StatePublished - Jan 1 1998

Fingerprint

Dive into the research topics of 'Spectrum and stability for elastic systems with global or local Kelvin-Voigt damping'. Together they form a unique fingerprint.

Cite this