Asymptotic modelling of the linear dynamics of laminated beams

We study the linear dynamics of a layered elastic beam by means of the asymptotic expansion method. The beam consists of three linearly elastic isotropic layers: the middle layer is considered to be thinner and softer than the upper and lower ones. We characterize the limit models by distinguishing three cases of natural frequencies: the low frequencies associated with flexural vibrations, the mean frequencies associated with axial vibrations and the high frequencies, associated with transversal shear and pinching vibrations.