Stochastic free vibration analysis of laminated composite plates using polynomial correlated function expansion

Over the past few decades, composite materials are extensively used in various industries due to their high specific stiffness, strength, weight sensitivity and cost-effectiveness. However, lack of complete control over the manufacturing process results in undesirable uncertainties, which in turn affect the vibrational characteristics of systems. This paper presents a novel approach, referred to as polynomial correlated function expansion (PCFE), for stochastic free vibration analysis of composite laminate. The proposed approach facilitates a systematic mapping between the input and output variables by expressing the output in a hierarchical order of component functions. The component functions are expressed in terms of extended bases and the unknown coefficients associated with the bases are determined by employing homotopy algorithm. The proposed approach has been employed for stochastic free vibration analysis of laminated composite plates. Results obtained using PCFE have been compared with results obtained using radial basis function (RBF) and conventional response surface method (RSM). Compared to RBF and RSM, PCFE yield more accurate result from considerably fewer sample points. Furthermore, case studies with different ply orientations have also been performed. Based on the numerical results, new physical insights have been drawn on dynamic behaviour of composite laminates.