Dynamic Characteristics of Reticulated Domes Built of Composite Elastic/Viscoelastic Rods Modeled by the Fractional Zener Model

Abstract

The new method for the determination of the dynamic characteristics of reticulated domes is proposed. Reticulated domes are built of composite rods. Each rod contains two layers made of elastic and viscoelastic materials, respectively. The viscoelastic material is modeled using the Zener model with fractional derivatives. A new formulation for the composite rod is proposed. The natural frequencies, the non-dimensional damping ratios and the modes of vibration are obtained as a solution to the nonlinear eigenvalue problem, which is solved using the continuation method. Moreover, the frequency response functions are determined in the usual way. The results of representative calculations are also presented and briefly discussed.