Title: Modal characteristics of cross-ply laminated smart beams using various beam theories

Authors: Ahmed Adel Khdeir; Easa Darraj; Osama J. Aldraihem

Addresses: Mechanical Engineering Department, King Saud University, P.O. Box 800, Riyadh 11421, Kingdom of Saudi Arabia. ' Mechanical Engineering Department, King Saud University, P.O. Box 800, Riyadh 11421, Kingdom of Saudi Arabia. ' Mechanical Engineering Department, King Saud University, P.O. Box 800, Riyadh 11421, Kingdom of Saudi Arabia

Abstract: Analytical models and solutions are obtained for the free vibration of cross-ply laminated beams with extension piezoelectric actuators. The piezoelectric actuators are bonded along the beam surface. The models are based on the higher-order shear deformation beam theory (HOBT), first-order shear deformation beam theory (FOBT) and the classical Euler-Bernoulli beam theory (CBT). The equations of motion and associated boundary conditions are derived for the beam models using Hamilton's principle. The state-space approach is used to find accurate natural frequencies and mode shapes for arbitrary combinations of boundary conditions. The exact analytical solutions obtained are illustrated numerically in a number of figures and tables revealing the effects of the number of layers, the actuators' thickness, the length to thickness ratio and the character of boundary conditions on the non-dimensional frequencies. Finally comparison of frequencies obtained by CBT, FOBT and HOBT is made to assess the importance of shear deformation.

Keywords: smart beams; cross-ply beams; beam theory; free vibration; exact solutions; state-space approach; arbitrary boundary conditions; automotive structures; modelling; vehicle vibration; piezoelectric actuators; shear deformation.

DOI: 10.1504/IJVNV.2012.048170

International Journal of Vehicle Noise and Vibration, 2012 Vol.8 No.3, pp.200 - 220

Available online: 23 Jul 2012 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article