TY - JOUR
T1 - Spectrum and stability for elastic systems with global or local Kelvin-Voigt damping
AU - Chen, Shuping
AU - Liu, Kangsheng
AU - Liu, Zhuangyi
PY - 1998
Y1 - 1998
N2 - 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.
AB - 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.
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U2 - 10.1137/s0036139996292015
DO - 10.1137/s0036139996292015
M3 - Article
AN - SCOPUS:0032202102
SN - 0036-1399
VL - 59
SP - 651
EP - 668
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
IS - 2
ER -