Abstract
Mechanical systems especially annular disks have many applications in different fields such as engineering, agriculture, and medicine. In this regard, the large amplitude vibrations of multi-scale hybrid nanocomposite annular system (MHCAS) under hygrothermal environment and subjected to mechanical loading. Also, the structure is covered with elastic foundation. The matrix material is reinforced with carbon nanotubes or carbon fibers at the nano- or macro-scale, respectively. The displacement strain of nonlinear vibration of the multi-scale laminated disk via thirdorder shear deformation theory and using von Karman nonlinear shell theory is obtained. Hamilton's principle is employed to establish the governing equations of motion, which is solved by the generalized differential quadrature method and perturbation method. Finally, the results show that increasing the value of the DH and h parameters and the rigidity of the boundary conditions lead to increase in the frequency of the structure. Besides, when the value of the nonlinearity parameter (c) is positive and negative, the dynamic behavior of the system tends to have hardening and softening behaviors, respectively, and could not be seen any effects from c parameter on the maximum amplitudes of resonant vibration of the MHCAS. The last but not the list by increasing the rigidity of the structure, the system can be susceptible to have unstable responses. The presented outputs can be used in the structural health monitoring.