Free Vibration Analysis of a Rotating Thin Pretwisted and Delaminated Composite Strip

Free vibration analysis of rotating composite strip with delamination is presented. The analysis is based on the framework developed using variational asymptotic method, which is used to reduce the three-dimensional (3D) composite strip with delamination problem into a two-dimensional (2D) cross-sectional analysis and a one-dimensional (1D) problem. This approach, in combination with the sublaminate method, delivers homogenized nonlinear cross-sectional stiffness of the delaminated strip with explicit delamination representation. For the purpose of free vibration study, only the linear cross-sectional stiffness obtained from zeroth-order analysis is used in the 1D problem. The 1D problem is set up by using the Hamilton's principle to derive the dynamic equilibrium equations of motion of a rotating composite strip used in the determination of its natural frequencies. The approach presented is applied to composite strips of different layup configurations and delamination size to investigate their effect on the modal behavior of the strips. The efficacy of the results obtained from the model is validated in comparison with experimental data, other theories, and 3D finite element analysis. Apart from being computationally efficient, due to the closed-form analytical determination of the strip cross-sectional stiffness constants, the approach is capable of providing insight into the strip modal behavior by directly relating structural response with appropriate cross-sectional stiffness constants.