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

摘要

This paper deals with the free flexural vibration of laminated quadrilateral plates and shallow shells using the Rayleigh-Riz method. Equations are derived using the first order shear deformation theory of plates and shells. Nonlinearity is present only in the in-plane strain components. The transverse shear strains, curvature and inertial terms are linear. The geometry is 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 polynomials, the geometric boundary conditions are satisfied. Numerical results are presented for the four-layer angle-ply plates and cylindrical shallow shells supported on trapezoidal boundary. The influences of the large amplitude and also of the geometry on the natural frequency are examined.