Influence of in-plane loading on the vibrations of the fully symmetric mechanical systems via dynamic simulation and generalized differential quadrature framework

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Honeycomb structures are one type of structure that has the geometry of a honeycomb 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 multi-scale hybrid nanocomposite (MHC) face sheets. 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. Afterward, a parametric study is carried out to investigate the effects of the thickness to length ratio of the honeycomb core, honeycomb core thickness to inner radius ratio, value fraction of carbon fibers, radius ration of the disk, the angle of honeycomb network, the weight fraction of CNTs, and tensile and compressive in-plane force on the frequency of the sandwich disk with honeycomb core and MHC. The results show that the critical fiber angle is $$\theta_{{\text{f}}} /\pi =$$ 0.5 for C–C and C–S boundary conditions. Another consequence is that when the structure is fixed with S–S boundary conditions, for $$p =$$ 500 and $$p = 1000$$ , as well as the critical dimensionless angle for fibers is 0.5, there are two more range for critical fiber angle in which they are $$0.275 \le \theta_{{\text{f}}} /\pi \le 0.375$$ and $$0.23 \le \theta_{{\text{f}}} /\pi \le 0.39$$ , respectively. Additionally, the range of the critical dimensionless angle for fibers increases by increasing the applied load. Some new results related to dynamic behavior of an MHC are also presented, which can serve as benchmark solutions for future investigations.