Reduced Basis Technique for Nonlinear Vibrations of Composite Panels

by Ahmed K. Noor, Univ of Virginia, Hampton, United States,
C. M. Andersen, Univ of Virginia, Hampton, United States,
Jeanne M. Peters, Univ of Virginia, Hampton, United States,

Abstract: A reduced basis technique and a computational procedure are developed for the nonlinear free vibrations of composite panels. The computational procedure can be conveniently divided into two distinct phases. The first phase involves determination of the linear free vibration frequencies and mode shapes by solving a linear eigenvalue problem. For each pair of eigenvalue-eigenvector, Linstedt-Poincare method is used to generate perturbation vectors. In the second phase the perturbation vectors are selected as basis vectors and a direct variational technique is applied to generate a set of reduced nonlinear algebraic equations which approximate the governing equations of the structure. The unknowns in the reduced equations are the amplitudes of the basis vectors and the nonlinear frequency of vibration. The analytical formulation is based on a form of the geometrically nonlinear shallow shell theory with the effects of transverse shear deformation, rotatory inertia and anisotropic material behavior included. The panel is discretized by using mixed finite element models with the fundamental unknowns consisting of both the nodal displacements and the stress-resultant parameters of the panel. The potential of the proposed technique is discussed and its effectiveness is demonstrated by means of a numerical example.

Subject Headings: Vibration | Finite element method | Vector analysis | Panels (structural) | Material properties | Computing in civil engineering | Composite materials | Linear functions

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