Vibration of Laminated Shallow Shells on Quadrangular Boundary

Abstract

A numerical solution to investigate the free vibrational characteristics of doubly curved laminated angle-ply shallow shells on quadrangular planforms is presented. The first-order composite shell theory is used in the formulation and the rotary inertia and shear deformation terms are included. The shell equation is solved by the Ritz method, in which the admissible displacement fields are defined in terms of the parametric Bezier surface patches. Owing to the special characteristics of Bezier functions, treatment of the geometric boundary conditions at a particular edge becomes very simple and straightforward by manipulating the coefficients that control the shape of the Bezier surface patch. Rapid convergence of the solution algorithm is found with only the fifth-order function. The natural frequencies are calculated for the four-layer angle-ply cantilevered cylindrical shells on square, rhombic, and trapezoidal boundaries. The numerical comparison indicates that the present solution method yields more accurate results than the ones obtained by the finite-element method using the eight-noded isoparametric shallow-shell element.