Sixth order differential equation for sandwich beam deflection including transverse shear

Abstract

A 6th order differential equation for the dynamic analysis of the deflection of a three-layer sandwich beam with a viscoelastic middle layer is developed. Transverse shear deformation as well as rotational inertia effects of the covering layers are taken into account. The same boundary conditions as in the Euler–Bernoulli case are used for the covering layers, making the method straightforward to use. The material in the viscoelastic layer is modeled using a fractional derivative material model. The parameters of the model are fit to experimental data for a rubber in industrial use. A cantilever beam is analyzed, and it is shown that taking the effects of transverse shear and rotational inertia into account can have a significant effect on the response at the resonances even if length to thickness ratio is over 30 for the covering layers.