A Ritz vibration analysis of doubly-curved rectangular shallow shells using a refined first-order theory

Integral expressions for strain and kinetic energies in vibration analysis of shear deformable doubly-curved shallow shells are presented. Although the formulation follows the first-order shear deformation theory, the consideration of Lamé parameters for the transverse shear strain through shell thickness, which have been hitherto neglected by other researchers, shows linear distribution functions instead of constant values if the Lamé parameters were dropped. Finite higher-order two-dimensional orthogonal polynomials (pb-2 functions) previously used in thin shell analyses [3-6] have been generalized from three to five degrees to account for the additional rotation fields of a moderately thick shell. These global shape functions satisfy the kinematic boundary conditions at the outset. The excellent performance and versatility of the computational methodology of the pb-2 Ritz method are illustrated in representative numerical simulations. The resultant matrix size is far smaller than other discretization methods and yet accurate solutions can be obtained. The validity of the results is verified through direct comparisons. The discrepancy of various formulations with and without the Lamé parameters is presented and discussed. © 1995.