中文摘要：

双曲壳被广泛应用于工程结构中,例如飞机机身,液化气船,土木建筑等,对双曲壳的动力学行为进行分析研究是国内外学者关注的热点之一.本文在Reddy高阶剪切变形理论的基础上,提出了一种考虑Zigzag函数影响的新位移场.针对FGM表层和均质芯层的夹层类型,假设材料特性沿厚度方向按幂律变化,利用所给出的新位移场以及Hamilton原理,推导出简支边界条件下功能梯度材料夹层双曲壳的偏微分运动控制方程.利用Navier法,根据简支边界条件假设振型函数,在自由振动情况下得出考虑不同长厚比,夹层厚比和体积分数的情况下系统的前五阶固有频率.此研究对深入研究其多模态共振具有重要意义.

英文摘要：

The double curved shell is widely used in practical engineering such as aircraft fuselage, liquefied gas ship, and civil construction. Study on the dynamics of these structures has become a focus of research around the world. In this paper, a new displacement field based on the Reddy＇s higher-order shear deformation theory is proposed in which the Zigzag function is included. Using the new displacement field and Hamilton principle, governing equations of motion in the form of partial differentiation for the simply supported FGM sandwich double curved shell with FGM face sheet and homogeneous core are obtained. The material properties of the FGM are graded according to the power-law variation along the thickness direction. Considering the simply supported boundary condition and using Navier method, the first five eigen frequencies of the system can be computed. The effects of the length-to-thickness ratio, thickness layer ratio and volume fractions on the natural frequencies are discussed in details. This study is of considerable importance for further analysis of multi modal resonance.