The in-plane vibration problem of functionally graded (FG) sandwich circular arch made up of two layers of power law FGM face sheet and one layer of homogeneous core is investigated. A framework for the vibration analysis of FG sandwich circular arches is presented, and the quasi-3D theories for the arch structures compatible with this framework are established for the first time. The quasi-3D theories take into account the changes of displacement through the thickness of the arch, and satisfy the stress-free boundary conditions naturally. The Lagrange equation is employed to derive the equation of motion, and various boundary conditions are implemented by applying simple algebraic polynomials as admissible functions to discrete the displacement fields of the FG sandwich arches. The comparison study of various high-order shear deformation theories and quasi-3D deformation theories for the FG sandwich circular arches is carried out via different numerical examples. The influences of material distributions and geometric parameters on the vibration characteristics of the FG sandwich circular arches are also presented and discussed for the first time.

研究了由两层幂律 FGM 面板和一层均质芯组成的功能梯度 (FG) 夹心圆拱的面内振动问题。提出了FG夹芯圆拱的振动分析框架，并首次建立了与该框架兼容的拱结构准三维理论。准三维理论考虑了位移随拱厚度的变化，自然满足无应力边界条件。采用拉格朗日方程推导运动方程，并通过应用简单的代数多项式作为允许函数来离散FG夹层拱的位移场来实现各种边界条件。通过不同的数值算例，对FG夹芯圆拱的各种高阶剪切变形理论和准三维变形理论进行了对比研究。还首次介绍和讨论了材料分布和几何参数对 FG 夹层圆拱振动特性的影响。