A method is proposed to obtain the exact solution for the dynamic analysis of functionally graded porous (FGP) curved beams with general boundary conditions and variable curvatures. First, the model of a curved beam of variable curvature is constructed, and then the beam is divided into a number of free beam segments via a multi-segment segmentation (MSS) strategy. Second, the first-order shear deformation theory (FSDT) is adopted to obtain the displacement fields of each segment, and then the kinetic energy and potential energy of the structure are expressed by the displacement field. Finally, the exact solution is obtained by the Hamilton principle. Using the springs to simulate various boundary conditions, the frequency parameters, modal shapes and forced vibration responses of the structure with elastic boundary conditions are calculated, with the convergence and correctness verified. Finally, effects of the FGP curved beams, such as porosity distribution types, porosity ratios, boundary condition types, geometry parameters and load types, are investigated in detail.

提出了一种方法来获得具有一般边界条件和可变曲率的功能梯度多孔 (FGP) 弯曲梁的动力学分析的精确解。首先，构建了变曲率弯曲梁的模型，然后通过多段分割（MSS）策略将梁分成多个自由梁段。其次，采用一阶剪切变形理论（FSDT）求得各节段的位移场，然后用位移场表示结构的动能和势能。最后通过哈密顿原理得到精确解。利用弹簧模拟各种边界条件，计算具有弹性边界条件的结构的频率参数、模态形状和受迫振动响应，并验证了收敛性和正确性。最后，详细研究了 FGP 曲线梁的影响，例如孔隙率分布类型、孔隙率比、边界条件类型、几何参数和载荷类型。