A 1D Ritz–Jacobi formulation for the modal analysis of 3D anisotropic laminated composite and soft-core sandwich beam structures through 2D polynomials

Abstract

The present article deals with the computation of natural frequencies of 3D fibre-reinforced anisotropic laminated composite and soft-core sandwich beams by using a 1D Ritz–Jacobi formulation. Generalised higher-order beam models, based on both 2D Taylor and 2D Chebyshev polynomials, are employed in the investigation. The weak-form of the governing equations (GEs) is derived via the classical Hamilton’s principle. Jacobi polynomials are selected to be the admissible functions used to solve the GEs. Various subsets of these polynomials are considered: Legendre polynomials, Lobatto polynomials, Gegenbauer polynomials (or Ultraspherical polynomials) and Chebyshev polynomials of 1st, 2nd, 3rd and 4th kind. Convergence and stability of both cross sectional functions and admissible functions are thoroughly analysed. Several parametric analyses are performed and the effect of some relevant parameters, e.g. lamination angle, boundary condition, stacking sequence, slenderness ratio and composite type, is studied.