旋转FGMs层合圆柱壳行波模态频率分析  

Analysis on traveling wave modal frequency of a rotating FGMs laminated cylindrical shell

作　　者：刘超 刘文光[1] 吕志鹏[1] 张宇航 LIU Chao;LIU Wenguang;Lü Zhipeng;ZHANG Yuhang(School of Aeronautical Manufacturing Engineering,Nanchang Hangkong University,Nanchang 330063,China)

机构地区：[1]南昌航空大学航空制造工程学院,南昌330063

出　　处：《航空动力学报》2022年第4期721-733,共13页Journal of Aerospace Power

基　　金：国家自然科学基金(51965042)。

摘　　要：为推进功能梯度(FGMs)材料在发动机、导弹和火箭等领域的应用,旨在研究旋转FGMs层合圆柱壳的行波模态频率。采用Voigt模型和Sigmoid体积分数描述FGMs层合圆柱壳的材料属性,考虑科里奥利力、离心惯性力、环向初应力以及热内力推导了FGMs层合圆柱壳的能量表达式。采用切比雪夫正交多项式构造位移容许函数,建立了任意边界旋转FGMs层合圆柱壳的模态频率方程,并探讨了组分含量、夹层厚度、温度梯度和弹簧刚度系数等对FGMs层合圆柱壳模态频率的影响。结果表明:夹层厚度相比Sigmoid体积分数对模态频率的变化更为敏感;高旋转短薄壁圆柱壳相比长薄壁圆柱壳对边界条件和失稳现象的影响更为敏感;轴向弹簧相比其他弹簧对模态频率的影响更大。For prompting the application of functionally graded materials(FGMs)in the fields of engines,missiles and rockets,the traveling wave modal frequencies of rotating FGMs laminated cylindrical shell were studied.The Voigt model and Sigmoid volume fraction were employed to describe the material properties of the FGMs laminated cylindrical shell.The energy expression of the rotating FGMs laminated cylindrical shell was derived with the Coriolis force,centrifugal inertial force,hoop initial tension and thermal internal force involved.The modal frequency equation of the FGMs laminated cylindrical shell with arbitrary boundary conditions was derived by using the Chebyshev orthogonal polynomial as the admissible displacement function.And the effects of material components,sandwich thickness,temperature gradient and spring stiffness coefficients on the modal frequency of the FGMs laminated cylindrical shell were discussed.Results indicate that the sandwich thickness is more sensitive to the traveling wave mode than the Sigmoid volume fraction index;the short thin-walled cylindrical shell is more sensitive to boundary conditions and instability than the long thin-walled structures at high rotation speeds;the axial spring stiffness has a greater effect on the traveling wave mode than other spring stiffness.

关 键 词：FGMs层合圆柱壳 旋转速度 模态频率 任意边界 切比雪夫多项式 

分 类 号：V214.33[航空宇航科学与技术—航空宇航推进理论与工程]