Nonlinear free vibration analysis of shell-type structures by the variational differential quadrature method in the context of six-parameter shell theory

Abstract

In the present paper, an attempt is made to adopt the variational differential quadrature (VDQ) technique for the large-amplitude vibration analysis of shell-type structures based on the six-parameter shell theory. The functional of energy in quadratic form is derived based on Hamilton's principle which is then directly discretized by the VDQ method. Although the derived formulation is general, the focus of paper is on the cylindrical and spherical shells. The nonlinear vibration problem is solved by means of the time periodic discretization method. The results reveal that the present numerical method can solve the problem accurately. It is also easy to implement due to its compact and explicit matrix formulation. Comprehensive numerical results are presented to study the effects of geometrical properties and boundary conditions on the frequency-response curves of cylindrical and spherical shells. Moreover, comparison studies are presented between the results of the six-parameter shell theory and the first-order shear deformation shell theory. © 2018 Elsevier Ltd