Free Vibration Analysis of Fibre-Metal Laminated Beams via Hierarchical One-Dimensional Models

Abstract EN

This paper presents a free vibration analysis of beams made of fibre-metal laminated beans.

Due to its attractive properties, this class of composites has gained more and more importance in the aeronautic field.

Several higher-order displacements-based theories as well as classical models (Euler-Bernoulli’s and Timoshenko’s ones) are derived, assuming Carrera’s Unified Formulation by a priori approximating the displacement field over the cross section in a compact form.

The governing differential equations and the boundary conditions are derived in a general form that corresponds to a generic term in the displacement field approximation.

The resulting fundamental term, named “nucleus”, does not depend upon the approximation order N, which is a free parameter of the formulation.

A Navier-type, closed form solution is used.

Simply supported beams are, therefore, investigated.

Slender and short beams are considered.

Three- and five-layer beams are studied.

Bending, shear, torsional, and axial modes and frequencies are presented.

Results are assessed for three-dimensional FEM solutions obtained by a commercial finite element code using three-dimensional elements showing that the proposed approach is accurate yet computationally effective.