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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.
Hyperbolic shells are widely used in engineering structures, such as aircraft fuselage, liquefied gas carrier, civil engineering, etc. The analysis of dynamic behavior of hyperbolic shells is one of the hot topics at home and abroad. Based on the shear deformation theory, a new displacement field considering the influence of Zigzag function is proposed. According to the sandwich type of FGM surface layer and homogeneous core layer, assuming that material properties change according to the power law along the thickness direction, Displacement field and Hamilton principle, the governing equations of partial differential motion for a functionally graded material sandwich hyperbolic shell under simple boundary conditions are deduced.Using the Navier method, the mode shape function is assumed under the condition of free vibration with respect to the simplified boundary conditions, Length-to-thickness ratio, interlayer thickness ratio and volume fraction of the first five natural frequencies of the system.This study is of great significance for further study of its multi-mode resonance.