Vibration modeling of large repetitive sandwich structures with viscoelastic core

A double scale asymptotic method (DSAM) is proposed for vibration modeling of large repetitive sandwich structures with a viscoelastic core. The method decomposes the initial nonlinear vibration problem into two small linear ones The first one is defined on few basic cells while the second is a differential global.. amplitude equation with complex coefficients. Their numerical computations permit determination of the damping properties as well as Pass and stop bands avoiding the direct computation on the whole structure. Viscoelastic frequency dependent core with fractional and anelastic displacement field models are considered The resulting nonclassical problems are solved by asymptotic numerical method coupled with automatic differentiation. Based on the presented method, a large reduction of the needed computational time and memory is obtained. The accuracy and efficiency of the proposed method are validated with comparisons to the direct simulations by discretization of the whole structure using asymptotic numerical method coupled with automatic differentiation.