Frequency simulation of viscoelastic multi-phase reinforced fully symmetric systems

Abstract

Honeycomb structures have the geometry of the lattice network to allow the minimization of the amount of used material to reach minimal material cost and minimal weight. In this regard, this article deals with the frequency analysis of imperfect honeycomb core sandwich disk with multiscale hybrid nanocomposite (MHC) face sheets rested on an elastic foundation. The honeycomb core is made of aluminum due to its low weight and high stiffness. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite layers. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of the generalized differential quadrature method (GDQM). Afterward, a parametric study is done to present the effects of the orientation of fibers ( $$\theta_{{\text{f}}} /\pi$$ ) in the epoxy matrix, Winkler–Pasternak constants ( $$K_{{\text{w}}}$$ and $$K_{{\text{p}}}$$ ), thickness to length ratio of the honeycomb network ( $$t_{{\text{h}}} /l_{{\text{h}}}$$ ), the weight fraction of CNTs, value fraction of carbon fibers, angle of honeycomb networks, and inner to outer radius ratio on the frequency of the sandwich disk. The results show that it is true that the roles of $$K_{{\text{w}}}$$ and $$K_{{\text{p}}}$$ are the same as an enhancement, but the impact of $$K_{{\text{w}}}$$ could be much more considerable than the effect of $$K_{{\text{p}}}$$ on the stability of the structure. Additionally, when the angle of the fibers is close to the horizon, the frequency of the system improves.