Open AccessUniform Exponential Stabilization for Flexural Vibrations of a Solar Panel
Author(s) -
Prasanta K. Nandi,
Ganesh C. Gorain,
Samarjit Kar
Publication year - 2011
Publication title -
applied mathematics
Language(s) - English
Resource type - Journals
eISSN - 2152-7393
pISSN - 2152-7385
DOI - 10.4236/am.2011.26087
Subject(s) - vibration , exponential function , boundary value problem , transverse vibration , euler's formula , transverse plane , bernoulli's principle , boundary (topology) , physics , classical mechanics , mathematical analysis , mechanics , mathematics , structural engineering , acoustics , engineering , thermodynamics
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