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The Quarterly Journal of Mechanics and Applied Mathematics 2002 55(3):345-356; doi:10.1093/qjmam/55.3.345
© 2002 by Oxford University Press
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Long-Wave Vibrations of a Nearly Incompressible Isotropic Plate with Fixed Faces

J. D. Kaplunov1 and E. V. Nolde1

( 1 Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101-1, Moscow 117526, Russia )

The three-dimensional dynamic equations of elasticity are subjected to a two-parameter asymptotic analysis for the case of long-wave vibrations of a nearly incompressible isotropic plate with fixed faces. Two non-standard types of two-dimensional approximations are revealed. The approximation of the first type is not local, as is typical for long-wave vibrations of standard linear isotropic plates and shells, occurring near zero-frequency and thickness resonance frequencies. The relevant governing equations are characterized by the appearance of trigonometric functions of the frequency parameter. The second approximation is localized near the cut-off frequencies of an incompressible plate, which do not represent thickness resonance frequencies. The analysed phenomena are specific only for symmetric motions and are not observed for other boundary conditions on the faces.

Received 24 August 2000. Revised 28 May and 12 October 2001.


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