Uniform Exponential Stabilization for Flexural Vibrations of a Solar Panel

Abstract

Here we study a problem of stabilization of the flexural vibrations or transverse vibrations of a rectangular solar panel. The dynamics of vibrations is governed by the fourth order Euler-Bernoulli beam equation. One end of the panel is held by a rigid hub and other end is totally free. Due to attachment of the hub, its dynamics leads to a non-standard equation. The exponential stabilization of the whole system is achieved by applying an active boundary control force only on the rigid hub. The result of uniform stabilization is obtained by means of an explicit form of exponential energy decay estimate.

Here we study a problem of stabilization of the flexural vibrations or transverse vibrations of a rectangular solar panel. The dynamics of vibrations is governed by the fourth order Euler-Bernoulli beam equation. One end of the panel is held by a rigid hub and other end is totally free. Due to attachment of the hub, its dynamics leads to a non-standard equation. The exponential stabilization of the whole system is achieved by applying an active boundary control force only on the rigid hub. The result of uniform stabilization is obtained by means of an explicit form of exponential energy decay estimate.

Keywords

Solar Panel, Hybrid System, Flexural Vibrations, Uniform Exponential Stabilization, Energy Decay Estimate

Solar Panel, Hybrid System, Flexural Vibrations, Uniform Exponential Stabilization, Energy Decay Estimate

Cite this paper

nullP. Nandi, G. Gorain and S. Kar, "Uniform Exponential Stabilization for Flexural Vibrations of a Solar Panel,"*Applied Mathematics*, Vol. 2 No. 6, 2011, pp. 661-665. doi: 10.4236/am.2011.26087.

nullP. Nandi, G. Gorain and S. Kar, "Uniform Exponential Stabilization for Flexural Vibrations of a Solar Panel,"

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