Free vibration of advanced anisotropic multilayered composites with arbitrary boundary conditions

Advanced composite stratified structures are of particular interest in numerous industrial areas such as the aerospace and aircraft industries. The main feature of these anisotropic materials is their ability to be tailored for specific applications by optimizing design parameters such as stacking sequence, ply orientation and performance targets. Designing through optimization principles requires the knowledge of an objective function which integrates all the unknowns of the materials therefore an accurate component-level modeling of stratified structures is necessary. Classical formulation available in the literature typically assumes a number of unknowns that increases with the number of layers and this sets serious limitations when trying to solve practical problems. As an alternative an advanced generalized modeling of multilayered composites with arbitrary boundary conditions is proposed in the present paper. This formulation is of a hybrid type which combines the advantages of both single-layer of the First Shear Deformation Theory and multi-layered approach. The number of unknowns is completely independent of the number of layers and a rigorous transfer matrix approach is developed from the interface conditions, which allows the parameters of the last layer to be iteratively related to those of the first layer. The Rayleigh–Ritz method is used in conjunction with a non-orthogonal polynomial basis to establish the free vibration. The model is then validated under free–free boundary conditions against data available in the literature in the case of isotropic, anisotropic angle-ply composites. Excellent agreement is obtained with a relative error less than 1 % , which assesses the validity of the present model. In addition a sensitivity analysis is performed on the boundary stiffness required to model boundary conditions to illustrate the complexity associated with the arbitrary boundary conditions when using artificial springs.