Carrera Unified Formulation for Free Vibration Analysis of Aircraft Structures
Advanced structural models, based on variable one two and three dimensional kinematics, are proposed in this paper and applied to the analysis of the free vibration of reinforced aircraft shell structures. The used models go beyond classical structural theories, that is, Euler Bernoulli (for one dimensional beams) and Kirchhoff (for two dimensional plates) type assumptions. The order of the expansion of the displacement fields over the cross section (one dimensional case) and along the plate thickness (two dimensional case) is, in fact, a free parameter of the problem. In this paper, Lagrange polynomials are used to build such expansions, and as a consequence, only displacements are used as the problem unknowns (no rotations or derivatives of displacements, which are typical of one dimensional/two dimensional classical theories, are introduced) The finite element method is used to provide numerical solutions. The related arrays and the governing dynamical equations are written in terms of a few funda.