A Variational Asymptotic Method Based Free Vibration Analysis of a Thin Pretwisted and Delaminated Anisotropic Strip

Abstract

An asymptotically exact cross-sectional model coupled with geometrically nonlinear one-dimensional (1D) theory of modelling partial delamination in composite beams has been proposed and implemented using the finite element method. This analytical model is based on the dimensional reduction of laminated shell theory to non-linear 1D theory using the variational asymptotic method. Delamination was included in the model by following the sub laminate approach. The final results from this approach will include linear as well as non-linear stiffness terms that account for the delamination length and location in closed form. Ability of the model to capture the trapeze effect, in the healthy and delaminated strip, is demonstrated and the results have been compared with experimental observations. The stiffness terms obtained from the non-linear beam analysis were used in the dynamic analysis. As a first step, only linear stiffness quantities have been used within the 1D linear finite element methods (FEM) that has been adopted to investigate the modal behaviour of the strip. The utility of the model was demonstrated by determining the natural frequencies and mode shapes of a pre twisted and delaminated anisotropic and, where possible, compared to full 3D FEM in order to validate the present approach. The approach shows good agreement with experimental and analytical results.