超音速流中纤维增强FGM梁的气动弹性动力学特性研究
Study on Aeroelastic Dynamic Characteristics of Fiber-Reinforced FGM Beams in Supersonic Flow
摘要: 本文基于经典梁理论(CBT)，研究了在高超音速作用下，活塞气动力理论的非线性效应对纤维增强功能梯度材料(FGM)的颤振特性的影响。首先通过混合率模型来表征纤维增强FGM梁的材料属性，然后通过Hamilton原理推导出只考虑横向振动的纤维增强FGM梁的非线性气动弹性偏微分方程，利用Galerkin方法，把该方程转化为非线性常微分方程，再利用Hurwitz行列式，把该方程的求根问题用以判定Hopf分叉，得到不同温度应力下梁的无量纲临界流速和无量纲临界频率。最后通过Runge-Kutta法得到纤维体积分数和无量纲温升对无量纲临界动压的影响。
Abstract: Based on the classical beam theory (CBT), the influence of the nonlinear effects of piston aerodynamic theory on the flutter characteristics of fiber-reinforced functionally graded materials (FGM) at hypersonic speeds is studied in this paper. First, the material properties of fiber-reinforced FGM beams are characterized by the mixing rate model. Then, the nonlinear aeroelastic partial differen-tial equation of fiber-reinforced FGM beams that only consider the transverse vibration is derived from Hamilton’s principle. The Galerkin method is used to convert the equation into a nonlinear ordinary differential equation, and the Hurwitz determinant is used to determine the Hopf bifurcation, the dimensionless critical velocity and the dimensionless critical frequency of the beam under different temperature stresses are obtained. Finally, fiber volume fraction and dimensionless tem-perature rise on dimensionless critical dynamic pressure are obtained by the Runge-Kutta method.
文章引用：韩明君, 张煜凯, 张浩晨. 超音速流中纤维增强FGM梁的气动弹性动力学特性研究[J]. 力学研究, 2023, 12(2): 79-90. https://doi.org/10.12677/IJM.2023.122008

参考文献

[1] 张鹏. 纤维增强功能梯度材料梁静态力学行为分析[D]: [硕士学位论文]. 扬州: 扬州大学, 2012.
[2] Lai, S.K., Harrington, J., Xiang, Y. and Chow, K.W. (2012) Accurate Analytical Perturbation Approach for Large Amplitude Vi-bration of Functionally Graded Beams. International Journal of Non-Linear Mechanics, 47, 473-480. [Google Scholar] [CrossRef] 
[3] 蹇越傲, 马连生. 热变形功能梯度梁的非线性振动[J]. 应用力学学报, 2021, 38(3): 1264-1271.
[4] 滕兆春, 昌博, 付小华. 弹性地基上转动功能梯度材料Timoshenko梁自由振动的微分变换法求解[J]. 中国机械工程, 2018, 29(10): 1147-1152.
[5] Liew, K.M., Lei, Z.X. and Zhang, L.W. (2015) Mechanical Analysis of Functionally Graded Carbon Nanotube Reinforced Composites: A Review. Com-posite Structures, 120, 90-97. [Google Scholar] [CrossRef] 
[6] 柏冬军, 石广玉. 压电功能梯度层合梁的力-电-热耦合梁单元及最优振动控制[J]. 工程力学, 2023, 40(3): 14-26.
[7] 吴振强, 刘宝瑞, 贾洲侠, 等. 强噪声激励下C/SiC复合材料壁板动态响应与失效分析[J]. 复合材料学报, 2019, 36(5): 198-206.
[8] Mehri, M., Asadi, H. and Kouchakzadeh, M.A. (2017) Computationally Efficient Model for Flow-Induced Instability of CNT Reinforced Functionally Graded Truncated Conical Curved Panels Subjected to Axial Compression. Computer Methods in Applied Mechanics and Engineering, 318, 957-980. [Google Scholar] [CrossRef] 
[9] Mehri, M., Asadi, H. and Wang, Q. (2016) On Dynamic Instability of a Pressurized Functionally Graded Carbon Nanotube Reinforced Truncated Conical Shell Subjected to Yawed Super-sonic Airflow. Composite Structures, 153, 938-951. [Google Scholar] [CrossRef] 
[10] Zhang, Y.W., Chen, W.J., Ni, Z.Y., Zang, J. and Hou, S. (2020) Supersonic Aerodynamic Piezoelectric Energy Harvesting Performance of Functionally Graded Beams. Compo-site Structures, 233, Article ID: 111537. [Google Scholar] [CrossRef] 
[11] Song, Z.G., Chen, Y., Li, Z.Y., Sha, J.C. and Li, F.M. (2019) Axially Functionally Graded Beams and Panels in Supersonic Airflow and Their Excellent Capability for Passive Flutter Suppression. Aerospace Science and Technology, 92, 668-675. [Google Scholar] [CrossRef] 
[12] Mahmoudkhani, S., Haddadpour, H. and Navazi, H.M. (2010) Su-personic Flutter Prediction of Functionally Graded Conical Shells. Composite Structures, 92, 377-386. [Google Scholar] [CrossRef] 
[13] Fazelzadeh, S.A., Hosseini, M. and Madani, H. (2011) Thermal Divergence of Supersonic Functionally Graded Plates. Journal of Thermal Stresses, 34, 759-777. [Google Scholar] [CrossRef] 
[14] Sohn, K.J. and Kim, J.H. (2008) Structural Stability of Func-tionally Graded Panels Subjected to Aero-Thermal Loads. Composite Structures, 82, 317-325. [Google Scholar] [CrossRef] 
[15] Clyne, T.W. and Hull, D. (2019) An Introduction to Com-posite Materials. 3rd Edition, Cambridge University Press, New York.
[16] Bouamama, M., Elmeiche, A., Elhennani, A., Kebir, T. and El Abidine Harchouche, Z. (2020) Exact Solution for Free Vibration Analysis of FGM Beams. Journal of Composite and Advanced Materials, 30, 55-60. [Google Scholar] [CrossRef] 

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