A Variational Approach to the Dynamics of Structures Having Mixed or Discontinuous Boundary Conditions

[+] Author and Article Information
P. J. Torvik

Department of Aeronautics and Astronautics, Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio 45433

J. Appl. Mech 51(4), 831-836 (Dec 01, 1984) (6 pages) doi:10.1115/1.3167733 History: Received November 01, 1982; Revised February 01, 1984; Online July 21, 2009


A procedure is developed whereby the steady-state forced response and the modes of free vibration for elastic systems having mixed or discontinuous boundary conditions can be determined. Approximate solutions are obtained as a superposition of a set of functions, each of which satisfies the field equations but not the boundary conditions. The coefficients of this expansion are obtained through applying a variational principle developed from Hamilton’s principle which for simple harmonic motion, is equivalent to Reissner’s principle. The reduction from the general elastic solid to the elastic plate is given, as are some results obtained for the first several natural frequencies of an elastic circular plate, free on a portion of the boundary and clamped on the remainder.

Copyright © 1984 by ASME
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