Three-Dimensional Elasticity Solution for Free Vibrations of Exponentially Graded Plates
Publication: Journal of Engineering Mechanics
Volume 140, Issue 7
Abstract
A three-dimensional exact free vibration solution for plates made of functionally graded materials is provided in the current study. An analytical solution in the form of a power series and numerical results for plates having material with an exponential distribution of properties across the thickness are established. Exact solutions for linearly elastic, simply supported, and rectangular plates based on three-dimensional elasticity theory are derived. A power series method is used to find the natural frequencies. An assumed displacement field identically satisfies all the boundary conditions. Numerical results for frequencies are provided for exponentially graded thick and thin plates. The presented results should serve as benchmark frequencies for exponentially graded plates.
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Published In
Journal of Engineering Mechanics
Volume 140 • Issue 7 • July 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jun 26, 2013
Accepted: Nov 25, 2013
Published online: Nov 27, 2013
Published in print: Jul 1, 2014
Discussion open until: Jul 6, 2014
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