Forced non-linear vibration of cylindrical laminated shells by the p-version finite element method

Abstract

A p-version, hierarchical finite element for moderately thick, rectangular, laminated, linear elastic, cylindrical shallow shells is presented. In order to select a reasonably accurate but not too large model, the convergence of the linear natural frequencies with the number of degrees of freedom of the finite element model is studied. Furthermore, the number of degrees of freedom is reduced by neglecting the membrane inertia and changing to modal coordinates. Geometrically non-linear vibrations of laminated shells under the action of transverse forces are described. An algorithm based on the shooting and Newton methods is employed to solve the system of first order differential equations of motion and find their periodic solutions. Results obtained with the reduced and complete models are compared.The curvature radii of the laminated shells are varied and the ensuing alterations in their dynamic behavior analyzed. Interesting modal interactions due to the geometrical nonlinearity and to commensurability of natural frequencies are found in several cases.