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Free Vibration of Cross Ply Laminated Beams with Multiple Distributed Piezoelectric Actuators

Published online by Cambridge University Press:  22 March 2012

A. A. Khdeir ,
E. Darraj  and
O. J. Aldraihem
A. A. Khdeir*
Affiliation:
Mechanical Engineering Department, King Saud University, Riyadh 11421, Kingdom of Saudi Arabia
E. Darraj
Affiliation:
Mechanical Engineering Department, King Saud University, Riyadh 11421, Kingdom of Saudi Arabia
O. J. Aldraihem
Affiliation:
Mechanical Engineering Department, King Saud University, Riyadh 11421, Kingdom of Saudi Arabia
*
*Corresponding author (khdeir@ksu.edu.sa)
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Abstract

Analytical solution is obtained for the free vibration of cross-ply laminated beams with multiple distributed extension piezoelectric actuators. The piezoelectric actuators are bonded at local position on the beam surface. The beam structure can contain one pair or two pairs or n pairs of piezoelectric actuators and it can be symmetric or unsymmetric about its mid-plane. The equations of motion and associated boundary conditions are derived for the beam model using Hamilton's principle. The state-space approach is used to find accurate natural frequencies and mode shapes for arbitrary combinations of boary conditions. The exact analytical solutions obtained are illustrated numerically in a number of figures revealing the influences of varying some parameters for the symmetric and unsymmetric cross-ply laminated beam for different type of piezoelectric actuators cases. The first order shear deformation beam theory (FOBT) is used to present the effect of actuators position and length on the nondimensional frequencies when one pair and two pairs of piezoelectric actuators are bonded at a local position on the beam surface.

Keywords

Free vibrationSmart beamsMultiple piezoelectric patchesAnalytical solutionsArbitrary boundary conditions
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 1 , March 2012 , pp. 217 - 227
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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References

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