Due to the excellent mechanical properties of doubly curved structure and functionally graded porous (FGP) material, the study of their vibration characteristics has attracted wide attention. The main aim of this research is to establish a formulation for free and forced vibration analysis of a new Sandwich FGP doubly curved structure. Four models of Sandwich materials are considered. The potential energy and kinetic energy functions are obtained on the foundation of the first-order shear deformation theory (FSDT). The idea of domain energy decomposition is applied to the theoretical modeling, where the structure is segmented along the generatrix direction. The continuity conditions for the interfaces between adjacent segments are balanced by the weighted parameters. For each segment, the displacement functions are selected as the Jacobi orthogonal polynomials and trigonometric series. The boundary conditions of the structure are obtained by the boundary spring simulation technique. The solution is obtained by the variational operation of the structural functional. The convergence performance and correctness of the theoretical model are examined by several numerical examples. Finally, some novel results are given, where free and forced vibration characteristics of Sandwich FGP doubly curved structures are examined in detail.

中文翻译：

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任意边界条件夹心FGP双曲面壳振动分析的半解析方法

由于双曲面结构和功能梯度多孔（FGP）材料优异的机械性能，对其振动特性的研究引起了广泛关注。本研究的主要目的是建立一种新的三明治 FGP 双弯曲结构的自由和受迫振动分析公式。考虑了三明治材料的四种模型。势能和动能函数是在一级剪切变形理论（FSDT）的基础上获得的。域能量分解的思想应用于理论建模，其中结构沿母线方向分割。相邻段之间界面的连续性条件通过加权参数进行平衡。对于每个细分市场，位移函数被选为雅可比正交多项式和三角级数。结构的边界条件是通过边界弹簧模拟技术获得的。解是通过结构泛函的变分运算得到的。通过几个数值例子检验了理论模型的收敛性能和正确性。最后，给出了一些新的结果，详细研究了三明治 FGP 双弯曲结构的自由和受迫振动特性。通过几个数值例子检验了理论模型的收敛性能和正确性。最后，给出了一些新的结果，详细研究了三明治 FGP 双弯曲结构的自由和受迫振动特性。通过几个数值例子检验了理论模型的收敛性能和正确性。最后，给出了一些新的结果，详细研究了三明治 FGP 双弯曲结构的自由和受迫振动特性。