热环境下功能梯度夹层双曲壳三维自由振动分析

功能梯度夹层双曲壳结构广泛应用在航空航天、海洋工程等领域中，对于该类结构的动力学特性研究非常重要。本文以热环境下功能梯度夹层双曲壳为研究对象，在三阶剪切变形理论的基础上，考虑横向拉伸作用的影响提出了一种新的位移场，假设材料的物性参数与温度有关，且沿厚度方向表示为幂律函数。利用Hamilton原理得到简支边界条件下功能梯度夹层双曲壳三维振动系统动力学方程，利用Navier法求得两种不同夹层类型的系统固有频率。研究了几何物理参数和温度场对功能梯度夹层双曲壳自由振动固有频率的影响。

Three-dimensional free vibration of functionally graded sandwich doubly curved shell in thermal environment

Functionally graded doubly-curved sandwich shell structure has vast application prospect in aircraft, aerospace, marine, transportation, and so on. It is very important to study its dynamic characteristics. Free vibration analysis of functionally graded doubly-curved sandwich shell in thermal environment is carried out by using the Navier method in this paper. Two types of functionally graded doubly-curved sandwich shell are considered. Of the first type, the sandwich core is made of functionally graded material (FGM), and the face sheets are made of pure ceramic and pure metal, respectively. Of the second type, the sandwich core is made of homogeneous metal, and the top and bottom face sheets are made of functionally graded material. The doubly-curved sandwich shell is in thermal environment with nonlinear temperature varying along the thickness direction. It is assumed that the material properties of functionally graded material are temperature-dependent. A new displacement field based on the three-order shear deformation theory is presented considering the effect of transverse stretch. The governing equations of the system are derived using the Hamilton principle. In the present investigation, the effects of volume fraction index, radius, temperature distribution, length-to-width ratio, length-to-thickness ratio, and core thickness are investigated in detail. In order to evaluate the accuracy of the present formulation, the obtained results are compared with those available in the literature. The results are more accurate for plate and shell structures with moderate thickness when the effect of transverse stretch is considered. The non-dimensional frequency of the sandwich shell with FGM core decreases with the increase of volume fraction index. However, the non-dimensional frequency of the sandwich shell with homogeneous core increases with the increase of volume fraction index. It is also observed that the non-dimensional frequency decreases with the increase of temperature gradient for a particular volume fraction index and sandwich type, but increases with the increases of length-to-width ratio and length-to-thickness ratio.