Exponential decay rate of the energy of a Timoshenko beam with locally distributed feedback

• Autores: De-Xing Feng, Dong-Hua Shi
• Localización: Anziam journal: The Australian & New Zealand industrial and applied mahtematics journal, ISSN 1446-1811, Vol. 44, Nº 2, 2002, págs. 205-220
• Idioma: inglés
• DOI: 10.1017/s1446181100013900
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• Resumen

  • The problem of the energy exponential decay rate of a Timoshenko beam with locally distributed controls is investigated. Consider the case in which the beam is nonuniform and the two wave speeds are different. Then, using Huang's theorem and Birkhoff's asymptotic expansion method, it is shown that, under some locally distributed controls, the energy exponential decay rate is identical to the supremum of the real part of the spectrum of the closed loop system. Furthermore, explicit asymptotic locations of eigenfrequencies are derived.