A layerwise p-version finite element formulation for free vibration analysis of thick composite laminates with curvilinear fibres

Herein, modes of vibration of a novel type of composite laminates, manufactured by tow-placement machines and which are called Variable Stiffness Composite Laminates (VSCL), are of interest. Layerwise theory is chosen, because it leads to an accurate prediction of displacements through the thickness of laminates, even when these are thick. Furthermore, it naturally has the capability of modelling the bending-membrane coupling that occurs on free vibration of VSCL plates with unsymmetric stacking sequences. The continuity of displacements at layer interfaces is imposed and in-plane displacements vary in a zig-zag fashion along the thickness. The accuracy of the model is confirmed by testing Constant Stiffness Composite Laminates (CSCL) analysed in the literature by others, who employed either Equivalent Single Layer (ESL) or layerwise theories. Abaqus commercial finite element software is as well employed in order to test the present approach. Finally, published natural frequencies of VSCLs, which were studied by an ESL theory, are compared with frequencies resulting from the present layerwise theory. The verification of the proposed model is followed by an investigation on the effect of curvilinear fibre orientation parameters on natural frequencies of thin to thick composite plates, with symmetric and unsymmetric lay-ups.