Influences of Large Amplitudes, Transverse Shear Deformation, and Rotatory Inertia on Lateral Vibrations of Transversely Isotropic Plates

[+] Author and Article Information
Cheng-Ih Wu, J. R. Vinson

Department of Mechanical and Aerospace Engineering, University of Delaware, Newark, Del.

J. Appl. Mech 36(2), 254-260 (Jun 01, 1969) (7 pages) doi:10.1115/1.3564617 History: Received July 01, 1968; Revised November 26, 1968; Online September 14, 2011


In the present paper, using an improved Reissner’s variational theorem along with Berger’s hypothesis, a set of governing equations which include the effects of transverse shear deformation and rotatory inertia is derived for the large amplitude free vibrations of plates composed of a transversely isotropic material. Applying the possibility of neglecting the rotatory inertia in primarily flexural vibration (discussed in the previous work [1]2 ), the lateral free vibrations of simply supported plates are treated in detail and the solution is compared with those of previous investigators. The free vibration of beams is studied as a special case of plates, while the small amplitude vibrations are treated as a special case of large amplitude vibrations. The numerical results show that the effect of transverse shear deformation is significant when applying to the plate constructions made of pyrolytic graphite-type materials.

Copyright © 1969 by ASME
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