Abstract
We consider the vibrations of a cantilever structure modeled by the standard linear flexible model of viscoelasticity coupled to an expectedly dissipative effect through heat conduction. It is shown that the amplitude of such vibrations is bounded under some restriction of the disturbing force. Using multiplier technique, an uniform exponential stability of the system is obtained directly, when the disturbing force is insignificant.
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Acknowledgments
Octavio Vera thanks the support of Fondecyt projects 1121120. This research was partially supported by PROSUL Project (Chamada II): Sistemas Dinâmicos Controle e Aplicações. Processo: CNPq 490577/2008-3. The authors are grateful to the reviewers for their valuable comments and suggestion in revising the paper.
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Misra, S., Alves, M., Gorain, G.C. et al. Stability of the vibrations of an inhomogeneous flexible structure with thermal effect. Int. J. Dynam. Control 3, 354–362 (2015). https://doi.org/10.1007/s40435-014-0113-6
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DOI: https://doi.org/10.1007/s40435-014-0113-6
Keywords
- Energy decay estimate
- Exponential stability
- Bounded-input bounded-output stability
- C\(_{0}\)-semigroup
- Viscoelastic damping