Linear and geometrically nonlinear vibrations of fiber reinforced laminated plates and shallow shells

This paper deals with the free flexural vibration of laminated quadrilatera l plates and shallow shells using the Rayleigh-Ritz method. Equations are d erived using the first order shear deformation theory of plates and shells. Nonlinearity is present only in the in-plane strain components. The transv erse shear strains, curvature and inertial terms are linear. The geometry i s mapped using the natural coordinates. Admissible displacement fields are constructed by taking the product of two simple polynomials in each of the two parametric coordinates. By controlling the coefficients of these polyno mials, the geometric boundary conditions are satisfied. Numerical results a re presented for the four-layer angle-ply plates and cylindrical shallow sh ells supported on trapezoidal boundary. The influences of the large amplitu de and also of the geometry on the natural frequency are examined. (C) 2000 Published by Elsevier Science Ltd. All rights reserved.