Vibratory behavior of doubly curved shallow shells of curvilinear planform

A continuum approach based on the principle of minimum total energy is presented to study the free flexural vibration of doubly curved shallow shells of curvilinear planform. The Ritz procedure supplemented with the pb-2 shape functions is employed to seek for an effective numerical algorithm, which is capable of providing computational solutions to a great accuracy. This p-version Ritz method is easily implemented numerically, is versatile in accounting for various boundary conditions, and requires less computing memory and execution time because no domain discretization is involved. The doubly curved shallow shells under consideration spread over a wide class of positive and negative Gaussian curvatures (spherical and hyperbolic paraboloidal shells) and the boundary could be free, simply supported, or clamped. The accuracy of numerical results has been established through a convergence and comparison study of eigenvalues with available published data. Extensive benchmark frequency parameters covering a wide range of shell-shallowness ratios are presented for shells having circular and elliptical planforms. A set of first known vibration mode shapes is included for future reference. © ASCE.