Vibration analysis of laminated anisotropic shells of revolution

Abstract

An efficient computational procedure is presented for the free vibration analysis of laminated anisotropic shells of revolution, and for assessing the sensitivity of their response to anisotropic (nonorthotropic) material coefficients. The analytical formulation is based on a form of the Sanders-Budiansky shell theory including the effects of both the transverse shear deformation and the laminated anisotropic material response. The fundamental unknowns consist of the eight stress resultants, the eight strain components, and the five generalized displacements of the shell. Each of the shell variables is expressed in terms of trigonometric functions in the circumferential coordinate and a three-field mixed finite element model is used for the discretization in the meridional direction. The three key elements of the procedure are: (a) use of three-field mixed finite element models in the meridional direction with discontinuous stress resultants and strain components at the element interfaces, thereby allowing the elimination of the stress resultants and strain components on the element level; (b) operator splitting, or decomposition of the material stiffness matrix of the shell into the sum of an orthotropic and nonorthotropic (anisotropic) parts, thereby uncoupling the governing finite element equations corresponding to the symmetric and antisymmetric vibrations for each Fourier harmonic; and (c) application of a reduction method through the successive use of the finite element method and the classical Bubnov-Galerkin technique. The potential of the proposed procedure is discussed and numerical results are presented to demonstrate its effectiveness.