Nosier, A.; Reddy, J. N. A study of nonlinear dynamic equations of higher-order shear deformation plate theories. (English) Zbl 0734.73041 Int. J. Non-Linear Mech. 26, No. 2, 233-249 (1991). 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. Cited in 29 Documents MSC: 74G60 Bifurcation and buckling 74B20 Nonlinear elasticity 74K20 Plates Keywords:interior and edge-zone problems; rectangular plates; Viscous damping terms; static large-deflection; dynamic small-deflection; effects of nonlinearity; shear deformation; rotatory inertia; sonic boom type loadings Citations:Zbl 0549.73062; Zbl 0556.73064; Zbl 0506.73074 PDFBibTeX XMLCite \textit{A. Nosier} and \textit{J. N. Reddy}, Int. J. Non-Linear Mech. 26, No. 2, 233--249 (1991; Zbl 0734.73041) Full Text: DOI