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A study of nonlinear dynamic equations of higher-order shear deformation plate theories. (English) Zbl 0734.73041

Summary: The nonlinear dynamic equations of the first-order shear deformation theory and the third-order shear deformation plate theory of the second author [J. Appl. Mech. 51, 745-752 (1982; Zbl 0549.73062); Int. J. Solids Struct. 20, 881-896 (1984; Zbl 0556.73064); AIAA J. 21, 621-629 (1983; Zbl 0506.73074)] are reformulated into equations describing the interior and edge-zone problems of rectangular plates. Viscous damping terms are also included. It is shown that, for certain boundary conditions, the number of governing equations can be reduced to three, as in the classical plate theory. Two problems related to static large-deflection and dynamic small-deflection of rectangular plates are considered. Numerical results are presented to demonstrate the effects of nonlinearity, shear deformation, rotatory inertia, damping and sonic boom type loadings.

MSC:

74G60 Bifurcation and buckling
74B20 Nonlinear elasticity
74K20 Plates
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