热环境对功能梯度薄壁圆柱壳模态频率的影响  

Effects of Thermal Environments on Modal Frequencies of a Functionally Graded Thin-walled Cylindrical Shell

作　　者：吕志鹏[1] 刘文光[1] 刘超 丰霞瑶 张宇航 LYU Zhipeng;LIU Wenguang;LIU Chao;FENG Xiayao;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：《噪声与振动控制》2022年第1期28-33,共6页Noise and Vibration Control

基　　金：国家自然科学基金资助项目(51965042)。

摘　　要：以热环境对金属陶瓷功能梯度薄壁圆柱壳模态频率的影响为研究对象,首先在描述功能梯度薄壁圆柱壳模型和四种典型的热环境模型的基础上,通过Love薄壳理论得到了薄壁圆柱壳的应变能和动能,运用Rayleigh-Ritz法推导圆柱壳的模态频率方程。然后分别以镍金属圆柱壳和镍钢功能梯度材料圆柱壳为对象,验证模态频率方程的合理性。最后分析不同温度场对金属陶瓷功能梯度薄壁圆柱壳环向振动和轴向振动模态频率的影响。结果表明:随着温度的升高,金属陶瓷功能梯度薄壁圆柱壳的模态频率逐渐下降,均匀温度场下模态频率下降速率最快,其次是线性温度场和非线性温度场,热流温度场对模态频率的影响几乎可以忽略;热环境只影响模态频率的大小,不影响模态频率随波数的变化趋势。The effects of thermal environments on the modal frequencies of a metal-ceramic functionally graded thin-walled cylindrical shell are studied.First of all,the model of a functionally graded thin-walled cylindrical shell was established and four classical models of thermal environments were introduced.The strain energy and kinetic energy of the thin-walled cylindrical shell were obtained by using the first order shear deformation theory.The modal frequency equation was derived by using Rayleigh-Ritz method.Then,a nickel cylindrical shell and a functionally graded cylindrical shell composed of nickel and steel were analyzed to verify the feasibility of the modal frequency equation.Finally,the effects of different temperature fields on the modal frequencies of the cylindrical shell were analyzed.Results indicate that the modal frequencies of the functionally graded cylindrical shell decrease with the increasing of temperature.The modal frequencies decrease fastest in the uniform temperature field,followed by in the linear temperature field and nonlinear temperature field.The influence of heat flux temperature field on the modal frequencies is negligible.The thermal environments only affect the magnitudes of modal frequencies and have no effect on the variation tendency of modal frequencies with wave numbers.

关 键 词：振动与波 功能梯度材料 热环境 圆柱壳 模态频率 

分 类 号：V215.4[航空宇航科学与技术—航空宇航推进理论与工程]