二维壁板颤振的本征正交分解降阶模型研究

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (23) : 144-151.

论文

二维壁板颤振的本征正交分解降阶模型研究

梅冠华 1 ，张家忠 2，康灿 1

作者信息 +

Reduced order model based on proper orthogonal decomposition for two-dimensional panel flutter

MEI Guan-hua 1, ZHANG Jia-zhong 2, KANG Can 1

Author information +

文章历史 +

摘要

针对二维壁板颤振问题，基于Galerkin方法和本征正交分解（POD）方法，发展了兼具高效性和全局性的降阶模型（ROM）。首先，简述了二维壁板颤振的经典Galerkin解法，及在物理空间上提取POD模态和建立ROM的传统方法。然后，为简化流程和提高效率，发展了一种在Galerkin基函数所张成的模态空间上进行POD模态提取与ROM建立的新方法，并证明了该方法与传统POD-ROM的等效性。随后，通过对系统典型响应的POD模态分析，表明POD模态可高效反映系统的最本质特征。最后，基于混沌响应下的POD模态建立了ROM，并用其详细研究了系统的分岔特性和稳定区域边界。计算表明该POD-ROM与Galerkin方法的计算精度非常接近，计算效率却有大幅提升。该方法可推广应用于其他复杂动力系统的ROM构建。

Abstract

Here, a reduced order model (ROM) was developed based on Galerkin method and the proper orthogonal decomposition (POD) with higher effectiveness and wholeness for two-dimensional panel flutter. Firstly, the classic Galerkin method, the traditional POD mode extraction method and the ROM construction method for two-dimensional panel flutter were introduced briefly. Then, in order to simplify the process and improve the efficiency, a new method was proposed to extract POD modes and construct ROM in the modal space spanned with Galerkin basis functions, the equivalence of this method to the traditional POD-ROM method was proved. Furthermore, through the POD modal analysis of typical responses of a panel, it was clarified that the POD modes can effectively reflect the most intrinsic characteristics of the system. Finally, a global ROM for the panel flutter was established based on POD modes in the case of a chaotic response of a panel, and it was employed to study the bifurcation behavior and boundaries of the stable region of the system in detail. The calculation results showed that the accuracy of this POD-ROM is very close to that of Galerkin method, its efficiency, however, is highly improved; the proposed method can be extended to construct ROMs for other complicated dynamic systems.

导出引用

梅冠华 1,张家忠 2，康灿 1. 二维壁板颤振的本征正交分解降阶模型研究[J]. 振动与冲击, 2017, 36(23): 144-151

MEI Guan-hua 1, ZHANG Jia-zhong 2, KANG Can 1. Reduced order model based on proper orthogonal decomposition for two-dimensional panel flutter[J]. Journal of Vibration and Shock, 2017, 36(23): 144-151

参考文献

[1] McNamara J J, Friedmann P P, Powell K G, et al. Aeroelastic and aerothermoelastic behavior in hypersonic flow [J]. AIAA Journal, 2008, 46(10): 2591-2610.
[2] Lamorte N, Friedmann P P. Hypersonic aeroelastic and aerothermoelastic studies using computational fluid dynamics [J]. AIAA Journal, 2014, 52(9): 2062-2078.
[3] Ashley H, Zartarian G. Piston theory-a new aerodynamic tool for the aeroelastician [J]. Journal of the Aeronautical Science, 1956, 23(12): 1109-1118.
[4] 梅冠华, 杨树华, 张家忠, 等. 用于跨/超声速壁板颤振精确分析的流-固耦合有限元算法 [J]. 西安交通大学学报, 2014, 48(1): 73-83.
MEI Guan-hua, YANG Shu-hua, ZHANG Jia-zhong. A fluid-structure coupling algorithm based on finite element method for precise analysis of transonic and supersonic panel flutter [J]. Journal of Xi’an Jiaotong University, 2014, 48(1): 73-83.
[5] MEI Guan-hua, ZHANG Jia-zhong, XI Guang, et al. Analysis of supersonic and transonic panel flutter using a fluid-structure coupling algorithm. Journal of Vibration and Acoustics-Transactions of ASME, 2014, 136(3): 031013 (11 pages).
[6] 安效民, 胥伟, 徐敏. 非线性壁板颤振分析 [J]. 航空学报, 2015, 36(4): 1119-1127.
AN Xiao-min, XU Wei, XU Min. Analysis of nonlinear panel flutter [J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(4): 1119-1127.
[7] Dowell E H. Nonlinear oscillations of a fluttering plate [J]. AIAA Journal, 1966, 4(7): 1267-1275.
[8] Ye W L, Dowell E H. Limit cycle oscillation of a fluttering cantilever plate [J]. AIAA Journal, 1991, 29(11): 1929-1936.
[9] Olson M D. Finite element approach to panel flutter [J]. AIAA Journal, 1967, 5(12): 226-227.
[10] Olson M D. Some flutter solutions using finite element [J]. AIAA Journal, 1970, 8(4): 747-752.
[11] Marzocca P, Fazelzadeh S A, Hosseini M. A review of nonlinear aero-thermo-elasticity of functionally graded panels [J]. Journal of Thermal Stresses, 2011, 34(5-6): 536-568.
[12] 梅冠华, 张家忠, 席光. 基于时滞惯性流形的二维平面壁板非线性气动弹性分析 [J]. 振动与冲击, 2012, 31(10): 141-146.
MEI Guan-hua, ZHANG Jia-zhong, Xi Guang. Nonlinear aeroelastic analysis of a two-dimensional panel based on inertial manifolds with delay [J]. Journal of Vibration and Shock, 2012, 31(10): 141-146.
[13] MEI Guan-hua, ZHANG Jia-zhong, WANG Zhuo-pu. Numerical analysis of panel flutter on inertial manifolds with delay [J]. Journal of Computational and Nonlinear Dynamics-Transactions of ASME, 2013, 8(2): 021009 (11 pages).
[14] Epureanu B I, Tang L S, Paidoussis M P. Exploiting chaotic dynamics for detecting parametric variations in aeroelastic systems [J]. AIAA Journal, 2004, 42(4): 728-735.
[15] Vetrano F, Le Garrec C, Moerchwlewicz G D, Ohayon R. Assessment of strategies for interpolating POD based reduced order models and application to aeroelasticity [J]. Journal of Aeroelasticity and Structural Dynamics, 2012, 2(2): 85-104.
[16] 谢丹, 徐敏. 基于特征正交分解的三维壁板非线性颤振分析 [J]. 工程力学, 2015, 32(1): 1-9.
XIE Dan, XU Min. Three-dimensional panel nonlinear flutter analysis based on proper orthogonal decomposition method [J]. Engineering Mechanics, 2015, 32(1): 1-9.
[17] XIE Dan, XU Min, Dowell E H. Proper orthogonal decomposition reduced-order model for nonlinear aeroelastic oscillations [J]. AIAA Journal, 2014, 52(2): 229-241.
[18] 谢丹. 基于降阶模型的超音速气流中壁板非线性颤振研究 [D]. 中国西安: 西北工业大学, 2014.
XIE Dan. Analysis of nonlinear panel flutter in supersonic flow based on reduced-order model [D]. China Xi'an: Northwestern Polytechnical University, 2014.
[19] Amabili M, Sarkar A, Paidoussis M P. Reduced-order models for nonlinear vibrations of cylindrical shells via the proper orthogonal decomposition method [J]. Journal of Fluid and Structures, 2003, 18(2): 227-250.
[20] Epureanu B I, Tang L S, Paidoussis M P. Coherent structures and their influence on the dynamics of aeroelastic panels [J]. International Journal of Non-Linear Mechanics, 2004, 39(6): 977-991.
[21] Wolf A, Swift J B, Swinney H L, et al. Determining Lyapunov exponents from a time series [J]. Physica D: Nonlinear Phenomena, 1985, 16(3): 285-317.