Journal of Dynamical and Control Systems
Optimal Energy Decay for a Nonhomogeneous Flexible Beam with a Tip Mass
Journal of Dynamical and Control Systems
Stability of a complex network of Euler-Bernoulli beams
WSEAS TRANSACTIONS on SYSTEMS
Spectrum of a complex network of Euler-Bernoulli beams
AMATH'09 Proceedings of the 15th american conference on Applied mathematics
Journal of Dynamical and Control Systems
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This paper studies the basis property and the stability of a distributed system described by a nonuniform Euler--Bernoulli beam equation under linear boundary feedback control. It is shown that there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis for the state Hilbert space. The asymptotic distribution of eigenvalues, the spectrum-determined growth condition, and the exponential stability are concluded. The results are applied to a nonuniform beam equation with viscous damping of variable coefficient as a generalization of existing results for the uniform beam.