Global/local analytical and numerical free vibration analysis of sandwich columns

Abstract

Sandwich structures are increasingly applied in many industrial fields of application, due to their lightweight combined with favorable mechanical properties. Despite this, such structures are subject to specific failure modes, such as buckling or vibratory resonance. In both cases, due to the presence of thin and stiff skins, global but also local modes may be of great interest when dimensioning such composite structures, which makes it impossible to use classical models. In this paper, the free vibration problem of classical sandwich columns (with homogeneous core materials) is investigated, using special kinematic models, so as to deal with both global and local eigenmodes in an effective and precise way. First, the problem is addressed analytically, where the two faces are represented by Euler-Bernoulli beams and the core material is considered as a 2D continuous solid, in small strain elasticity. Then, an enriched 1D finite element formulation is developed, so as to handle efficiently more general configurations encountered in practice. The homogeneous core layer is here described using hyperbolic functions, in accordance with the modal displacement fields obtained analytically. The present analytical and numerical solutions (natural frequencies and vibration modes) are contrasted against each other and compared to 2D reference numerical results.