Axisymmetric Vibrations of Homogeneous and Sandwich Spherical Caps

[+] Author and Article Information
B. Koplik

Department of Mechanical Engineering, Polytechnic Institute of Brooklyn, Brooklyn, N. Y.

Yi-Yuan Yu

Voyager Program, General Electric Space Technology Center, Valley Forge, Pa.

J. Appl. Mech 34(3), 667-673 (Sep 01, 1967) (7 pages) doi:10.1115/1.3607759 History: Received March 23, 1966; Revised September 12, 1966; Online September 14, 2011


From the generalized variational equation of motion is derived a complete system of equations for sandwich as well as homogeneous spherical shells including the effect of thickness-shear deformation. Based on these equations the exact solution is obtained for the natural frequencies of axisymmetric vibrations of homogeneous and sandwich spherical caps with clamped edges. Emphasis in our investigation is on the transition from the vibrations of a circular disk to those of a spherical cap, for both homogeneous and sandwich cases, with numerical results showing the effects of thickness-shear and of curvature.

Copyright © 1967 by ASME
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