On the vibrations of the imperfect sandwich higher-order disk with a lactic core using generalize differential quadrature method

Abstract This article presents the frequency responses of a sandwich disk with a lactic core (honeycomb), two middle layers containing SMA fiber, and two outer layers (multi-scale hybrid nanocomposite (MHC)). 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). Compatibility equations are considered for modeling the interface between the layers of the sandwich disk. Afterward, a parametric study is done to present the effects of SMA fiber, boundary conditions, outer to inner radius ratio, honeycomb network angle, thickness to length ratio of the honeycomb, fibers angle, weight fraction of CNTs, honeycomb to face sheet thickness ratio on the frequency of the multi-phase sandwich disk. The results show that employing the honeycomb network as the core of the structure improves the dynamic response of the structure, impressively. Another consequence is that if there are C-C, C-S boundary conditions, by ever-increase in the θ h / π , the dynamic response tends to decline.