The goal of the current investigation is to determine the dynamic behaviour of double-arch systems: the system is made of two arches reinforced by three different functionally graded patterns of carbon nanotubes and connected with an elastic layer of spring bed. The carbon-nanotube functionally graded patterns considered are uniformly distributed, FG-X and FG-O. Two different boundary conditions of movable and immovable simply supported (named SS1 and SS2) are studied for the reinforced double-arches, where the displacements along the curve-line are constrained for the ends of SS2 arches. Both the Hamilton principle and force-moment technique are utilised to formulate the coupled equations of motion. A series expansion technique is then used to solve the equations. A validation is performed and consistent agreement between the proposed methodology and simplified version of the double-arch system is achieved. One prominent observation arising from this study is that an increase in the opening angle of the double-arch system results in a decline in both the series for the transverse natural frequencies for SS1. Conversely, the systems with SS2 boundary conditions exhibit an initial rise in both the series of natural frequencies as the opening angle increases, followed by a gradual decrease. A thicker carbon-nanotube reinforced functionally graded double-arch system demonstrates an increased natural-frequency sensitivity to variation in opening angles. Lastly, increasing the elastic layer coefficient of stiffness causes an increment in the second series natural frequency of the system.

当前研究的目标是确定双拱系统的动态行为：该系统由两个拱组成，由三种不同功能梯度的碳纳米管图案加固，并与弹簧床的弹性层连接。所考虑的碳纳米管功能梯度图案是均匀分布的FG-X和FG-O。针对加筋双拱，研究了可动简支和不可动简支（SS1和SS2）两种不同的边界条件，其中SS2拱的端部沿曲线的位移受到约束。利用哈密顿原理和力-力矩技术来制定耦合运动方程。然后使用级数展开技术来求解方程。进行了验证，并在所提出的方法和双架构系统的简化版本之间达成了一致的协议。这项研究产生的一个重要观察结果是，双拱系统的张角增加会导致 SS1 横向固有频率的两个系列下降。相反，具有 SS2 边界条件的系统随着张角的增加，两个系列的固有频率都呈现出初始上升，然后逐渐下降。较厚的碳纳米管增强功能梯度双拱系统表现出对张角变化的固有频率敏感性增加。最后，增加弹性层刚度系数会导致系统的第二级固有频率增加。