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高阶谐波平衡方法中非物理解来源分析及改进方法研究

刘南 白俊强 华俊 刘艳

刘南, 白俊强, 华俊, 刘艳. 高阶谐波平衡方法中非物理解来源分析及改进方法研究[J]. 力学学报, 2016, 48(4): 897-906. doi: 10.6052/0459-1879-15-157
引用本文: 刘南, 白俊强, 华俊, 刘艳. 高阶谐波平衡方法中非物理解来源分析及改进方法研究[J]. 力学学报, 2016, 48(4): 897-906. doi: 10.6052/0459-1879-15-157
Liu Nan, Bai Junqiang, Hua Jun, Liu Yan. INVESTIGATION OF THE SOURCE AND IMPROVEMENT OF NON-PHYSICAL SOLUTIONS IN HIGH-ORDER HARMONIC BALANCE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(4): 897-906. doi: 10.6052/0459-1879-15-157
Citation: Liu Nan, Bai Junqiang, Hua Jun, Liu Yan. INVESTIGATION OF THE SOURCE AND IMPROVEMENT OF NON-PHYSICAL SOLUTIONS IN HIGH-ORDER HARMONIC BALANCE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(4): 897-906. doi: 10.6052/0459-1879-15-157

高阶谐波平衡方法中非物理解来源分析及改进方法研究

doi: 10.6052/0459-1879-15-157
详细信息
    通讯作者:

    白俊强,教授,主要研究方向:飞行器设计、计算流体力学、气动弹性力学.E-mail:junqiang@nwpu.edu.cn

  • 中图分类号: O322

INVESTIGATION OF THE SOURCE AND IMPROVEMENT OF NON-PHYSICAL SOLUTIONS IN HIGH-ORDER HARMONIC BALANCE

  • 摘要: 对于周期性非定常问题,高阶谐波平衡(High-order Harmonic Balance, HOHB)方法将非定常方程的解用Fourier 级数展开至一定阶次,从而消除其中的时间导数项,大大降低了计算消耗. 本文以达芬振子方程为例,探讨了HOHB 方法中非物理解的来源,分析结果表明:非物理解出现的原因是在推导过程中非线性项的简化处理导致方程左右两边并不严格相等. 根据非线性项的特点,在其处理过程中扩充子时间层上的时域解,并将非线性项中出现的更高阶谐波截断,使方程左右两边严格相等. 通过对达芬振子方程进行数值模拟发现:改进方法在消除非物理解的同时,也显著减少了计算所需谐波数. 对比参考文献发现,同阶改进方法的精度和原始谐波平衡方法基本相当,证明了本方法的可行性. 最后将本方法应用于具有立方刚度非线性的气动弹性系统中,验证本方法的工程适用性. 但是,当方程中非线性项较多时,本方法所需要的计算消耗会有所增加.

     

  • 1 Silva WA. Reduced-order models based on linear and nonlinear aerodynamic impulse responses. AIAA-99-1262
    2 Raveh DE. Reduced-order models for nonlinear unsteady aerodynamics. AIAA Journal, 2001, 39(8): 1417-1429  
    3 Thomas JP, Dowell EH, Hall KC. Three-dimensional transonic aeroelasticity using proper orthogonal decomposition based reduced order models. AIAA-2001-1526
    4 Thomas JP, Dowell EH, Hall KC. Modeling viscous transonic limitcycle oscillation behavior using a harmonic balance approach. Journal of Aircraft, 2004, 41(6): 1266-1274  
    5 Lucia DJ, Beran PS, Silva WA. Reduced-order modeling: new approaches for computational physics. Progress in Aerospace Sciences, 2004, 40: 51-117  
    6 Krylo N, Bogoliubo N. Introduction to Nonlinear Mechanics. Princeton University Press, Princeton, NJ, 1947
    7 Liu L, Thomas JP, Dowell EH, et al. A comparison of classical and high dimensional harmonic balance approaches for a Duffing oscillator. Journal of Computational Physics, 2006, 215: 298-320  
    8 Liu L, Dowell EH, Hall KC. A novel harmonic balance analysis for the Van Der Pol oscillator. International Journal of Non-Linear Mechanics, 2007, 42: 2-12  
    9 Lau SL, Cheung YK. Amplitude incremental variational principle for nonlinear vibration of elastic systems. ASME Journal of Applied Mechanics, 1981, 48: 959-964  
    10 Shen JH, Lin KC, Chen SH, et al. Bifurcation and route-to-chaos analyses for Mathieu-Duffing oscillator by the incremental harmonic balance method. Nonlinear Dynamics, 2008, 52: 403-414  
    11 Liu JK, Chen FX, Chen YM. Bifurcation analysis of aeroelastic systems with hysteresis by incremental harmonic balance method. Applied Mathematics and Computation, 2012, 219: 2398-2411  
    12 Hall KC, Thomas JP, Clark WS. Computation of unsteady nonlinear flows in cascades using a harmonic balance technique. International Symposium on Unsteady Aerodynamics, Aeroacoustics and Aeroelasiticity of Turbomachines, 2000
    13 陈琦, 陈坚强, 谢昱飞等. 谐波平衡法在非定常流场中的应用. 航空学报, 2014, 35(3): 736-743 (Chen Qi, Chen Jianqiang, Xie Yufei, et al. Application of harmonic balance method to unsteady flow field. Acta Aeronautica et Astronautica Sinica, 2014, 35(3): 736-743 (in Chinese))
    14 Woodgate MA, Badcock KJ. Implicit harmonic balance solver for transonic flow with forced motions. AIAA Journal, 2009, 47(4): 893-901  
    15 Rouch AD, McCracken AJ, Badcock KJ, et al. Linear frequency domain and harmonic balance predictions of dynamic derivatives. Journal of Aircraft, 2013, 50(3): 694-707  
    16 陈琦, 陈坚强, 袁先旭, 等. 谐波平衡法在动导数快速预测中的应用研究. 力学学报, 2014, 46(2): 183-190 (Chen Qi, Chen Jianqiang, Yuan Xianxu, et al. Application of a harmonic balance method in rapid predictions of dynamic stability derivatives. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(2): 183-190 (in Chinese))
    17 Thomas JP, Dowell EH, Hall KC. Nonlinear inviscid aerodynamic effects on transonic divergence, flutter, and limit-cycle oscillations. AIAA Journal, 2002, 40(4): 638-646  
    18 Yao W, Marques S. Prediction of transonic limit cycle oscillations using an aeroelastic harmonic balance method. AIAA 2014-2310
    19 Ekici K, Beran PS. Adjoint sensitivity analysis of low-speed flows using an efficient harmonic balance technique. AIAA Journal, 2014, 52(6): 1330-1336  
    20 Huang H, Ekici K. A discrete adjoint harmonic balance method for turbomachinery shape optimization. Aerospace Science and Technology, 2014, 39: 481-490  
    21 Sicot F, Gomar A, Dufour G, et al. Time-domain harmonic balance method for turbomachinery aeroelasticity. AIAA Journal, 2014, 52(1): 62-71  
    22 Weiss JM, Subramanian V, Hall KC. Simulation of unsteady turbomachinery flows using an implicitly coupled nonlinear harmonic balance method. GT 2011-46367
    23 Thomas JP, Custer CH, Dowell EH, et al. Unsteady flow computation using a harmonic balance approach implemented about the OVERFLOW 2 flow solver. AIAA 2009-4270
    24 Blanc F, Roux F, Jouhaud J. Harmonic-balance-based code-coupling algorithm for aeroelastic systems subjected to forced excitation. AIAA Journal, 2010, 48(11): 2472-2481  
    25 McMullen M, Jameson A, Alonso J. Demonstration of nonlinear frequency domain methods. AIAA Journal, 2006, 44(7): 1428-1435  
    26 McMullen M, Jameson A. The computational efficiency of nonlinear frequency domain methods. Journal of Computational Physics, 2006, 212: 637-661  
    27 Dai H, Schnoor M, Atluri SN. A simple collocation scheme for obtaining the periodic solutions of the Duffing equation, and its equivalence to the high dimensional harmonic balance method: subharmonic oscillations. CMES, 2012, 84(5): 459-497
    28 Liu L, Kalmar-Nagy T, Dowell EH. The high dimensional harmonic balance analysis for second-order delay-differential equations. DETC 2007-34396
    29 Liu L, Dowell EH. The secondary bifurcation of an aeroelastic airfoil motion: effect of high harmonics. Nonlinear Dynamics, 2004, 37: 31-49  
    30 Liu L, Dowell EH, Thomas JP. A high dimensional harmonic balance approach for an aeroelastic airfoil with cubic restoring forces. Journal of Fluids and Structures, 2007, 23: 351-363  
    31 Dai H, Yue X, Yuan J, et al. A time domain collocation method for studying the aeroelasticity of a two dimensional airfoil with a structural nonlinearity. Journal of Computational Physics, 2014, 270: 214-237  
    32 Jones RT. The unsteady lift of a wing of finite aspect ratio. NACA Report 681, 1940
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出版历程
  • 收稿日期:  2015-05-05
  • 修回日期:  2016-04-21
  • 刊出日期:  2016-07-18

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