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 third-order 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 $\Delta H$ and $\theta$ 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 ($\gamma$) 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 $\gamma$ 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.

摘要

机械系统，尤其是环形盘，在工程、农业和医学等不同领域有许多应用。在这方面，多尺度混合纳米复合环形系统（MHCAS）在湿热环境下并受到机械载荷的大振幅振动。此外，该结构覆盖有弹性基础。基体材料分别用纳米或宏观尺度的碳纳米管或碳​​纤维增强。利用三阶剪切变形理论和冯卡门非线性壳理论，得到了多尺度叠片盘非线性振动的位移应变。利用Hamilton原理建立运动控制方程，通过广义微分求积法和微扰法求解。最后，$\Delta H$和$\theta$参数和边界条件的刚度导致结构频率的增加。此外，当非线性参数的值 ($\gamma$) 是正的和负的，系统的动态行为倾向于分别具有硬化和软化行为，并且看不到任何影响$\gamma$MHCAS共振振动最大振幅的参数。最后但不是列表通过增加结构的刚度，系统可能容易产生不稳定的响应。呈现的输出可用于结构健康监测。