Dynamic response of laminated and sandwich composite structures via 1D models based on Chebyshev polynomials

Abstract

This article presents the dynamic response of composite structures via refined beam models. The mode superposition method was used, and the Carrera Unified Formulation was exploited to create the advanced structural models. The finite element method was employed to compute the natural frequencies and modes. The main novelty of this article concerns the use of Chebyshev polynomials to define the displacement field above the cross-section of the beam. In particular, polynomials of the second kind were adopted, and the results were compared with those from analytical solutions and already established Carrera Unified Formulation-based beam models, which utilize Taylor and Lagrange polynomials to develop refined kinematics theories. Sandwich beams and laminated, thin-walled box beams were considered. Non-classical effects such as the cross-section distortion and bending/torsion coupling were evaluated. The results confirm the validity of the Carrera Unified Formulation for the implementation of refined structural models with any expansion functions and orders. In particular, the Chebyshev polynomials provide accuracies very similar to those from Taylor models. The use of high-order expansions, e.g. seventh-order, leads to results as accurate as those of Lagrange models which, from previous publications, are known as the most accurate Carrera Unified Formulation 1D models for this type of structural problems.