摄动力方法在模态扩展中的应用讨论
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摘要
摄动力方法是一种模态振型扩展方法。首先,从摄动方程出发重新推导了模态扩展矩阵。在测试模态频率与有限元模态频率相等时会有矩阵奇异问题,这可以通过一个较小的移轴量消除奇异,从而简化扩展矩阵的表达。其次,实际应用中为了避免计算满阵,可以展开伪逆,得到一个更实用的模态扩展矩阵。接着,根据伪逆展开结果,给出了这种方法和SEREP方法等效的条件。最后,针对有限元模态基选择问题,讨论了如何挑选低阶振型以及如何确定扩展基振型数目,并以一个具体的测试案例演示了整个分析流程。
The perturbed force approach is a modal shape expansion method,it can also be derived from the perturbed eigenvalue equation. Here,the simplification of this method was discussed when tested eigenvalues were very much close to FE model eigenvalues to cause a singularity problem of eigen-matrix. Again using perturbation analysis,an arbitrary small shift was introduced to eliminate the matrix singularity and simplify the modal expansion matrix expressing.To avoid computation of a full matrix in actual application,the expansion of the generalized inverse of a matrix could be used to obtain a more efficient modal expansion scheme. Through implementing the generalized inverse expansion,the necessary conditions for the perturbed force approach being equivalent to SEREP method were gained. Finally,some criteria for FE modal base selection were proposed to choose lower order modal shapes and determine the number of modal expansion bases,a notched beam modal test demo was conducted to validate the discussion.
The perturbed force approach is a modal shape expansion method,it can also be derived from the perturbed eigenvalue equation. Here,the simplification of this method was discussed when tested eigenvalues were very much close to FE model eigenvalues to cause a singularity problem of eigen-matrix. Again using perturbation analysis,an arbitrary small shift was introduced to eliminate the matrix singularity and simplify the modal expansion matrix expressing.To avoid computation of a full matrix in actual application,the expansion of the generalized inverse of a matrix could be used to obtain a more efficient modal expansion scheme. Through implementing the generalized inverse expansion,the necessary conditions for the perturbed force approach being equivalent to SEREP method were gained. Finally,some criteria for FE modal base selection were proposed to choose lower order modal shapes and determine the number of modal expansion bases,a notched beam modal test demo was conducted to validate the discussion.
引文
[1]FRISWELL M I,MOTTERSHEAD J E.Finite element model updating in structural dynamics[M].Dordrecht:Kluwer Academic Publishers,1995.
[2]曹宏瑞,何正嘉.机床主轴耦合系统动力学建模与模型修正[J].机械工程学报,2012,48(3):88-94.CAO Hongrui,HE Zhengjia.Dynamic modeling and model updating of coupled systems between machine tool and its spindle[J].Journal of Mechanical Engineering,2012,48(3):88-94.
[3]王柯,范忠华,党西军.基于模态实验与优化的静动力学模型转换[J].振动工程学报,2012,25(1):38-42.WANG Ke,FAN Zhonghua,DANG Xijun.The transformation of static structure models to dynamic models based on modal tests and optimization[J].Journal of Vibration Engineering,2012,25(1):38-42.
[4]冯慧华,左正兴,廖日东,等.内燃机复杂部件结构动力学模型修正技术研究[J].内燃机学报,2006,24(4):357-362.FENG Huihua,ZUO Zhengxing,LIAO Ridong,et al.Research on the modification technique on structural dynamic model of complex I.C.E components[J].Transactions of CSICE,2006,24(4):357-362.
[5]张纯,宋固全.去噪正则化模型修正方法在桥梁损伤识别中的应用[J].振动工程学报,2012,25(1):97-102.ZHANG Chun,SONG Guquan.Bridge damage identification by finite element model updating with Tikhonov regularization and wavelet denoising[J].Journal of Vibration Engineering,2012,25(1):97-102.
[6]夏品奇,BROWNJOHN J M W.斜拉桥有限元模型与模型修正[J].振动工程学报,2003,16(2):219-223.XIA Pinqi,BROWNJOHN J M W.Finite element modeling and model updating of a cable-stayed bridge[J].Journal of Vibration Engineering,2003,16(2):219-223.
[7]PAZ M.Dynamic condensation[J].AIAA Journal,1984,22(5):724-727.
[8]O’CALLAHAN J,AVITABILE P,RIEMER R.System equivalent reduction expansion process(SEREP)[C]//Proceedings of the 7th IMAC.Las Vegas,NV,1989.
[9]KAMMER D C.Test-analysis-model development using an exact modal reduction[J].The International Journal of Analytical and Experimental Modal Analysis,1987,2(4):174-179.
[10]李伟明,洪嘉振,张以帅.新的模型修正与模态扩展迭代方法[J].振动与冲击,2010,29(6):4-7.LI Weiming,HONG Jiazhen,ZHANG Yishuai.New iterative method for model updating and modal expansion[J].Journal of Vibration and Shock,2010,29(6):4-7.
[11]CHEN Huapeng.Mode shape expansion using perturbed force approach[J].Journal of Sound and Vibration,2010,329:1177-1190.
[12]CHEN H P,MAUNG T S.Regularised finite element model updating using measured incomplete modal data[J].Journal of Sound and Vibration,2014,333:5566-5582.
[2]曹宏瑞,何正嘉.机床主轴耦合系统动力学建模与模型修正[J].机械工程学报,2012,48(3):88-94.CAO Hongrui,HE Zhengjia.Dynamic modeling and model updating of coupled systems between machine tool and its spindle[J].Journal of Mechanical Engineering,2012,48(3):88-94.
[3]王柯,范忠华,党西军.基于模态实验与优化的静动力学模型转换[J].振动工程学报,2012,25(1):38-42.WANG Ke,FAN Zhonghua,DANG Xijun.The transformation of static structure models to dynamic models based on modal tests and optimization[J].Journal of Vibration Engineering,2012,25(1):38-42.
[4]冯慧华,左正兴,廖日东,等.内燃机复杂部件结构动力学模型修正技术研究[J].内燃机学报,2006,24(4):357-362.FENG Huihua,ZUO Zhengxing,LIAO Ridong,et al.Research on the modification technique on structural dynamic model of complex I.C.E components[J].Transactions of CSICE,2006,24(4):357-362.
[5]张纯,宋固全.去噪正则化模型修正方法在桥梁损伤识别中的应用[J].振动工程学报,2012,25(1):97-102.ZHANG Chun,SONG Guquan.Bridge damage identification by finite element model updating with Tikhonov regularization and wavelet denoising[J].Journal of Vibration Engineering,2012,25(1):97-102.
[6]夏品奇,BROWNJOHN J M W.斜拉桥有限元模型与模型修正[J].振动工程学报,2003,16(2):219-223.XIA Pinqi,BROWNJOHN J M W.Finite element modeling and model updating of a cable-stayed bridge[J].Journal of Vibration Engineering,2003,16(2):219-223.
[7]PAZ M.Dynamic condensation[J].AIAA Journal,1984,22(5):724-727.
[8]O’CALLAHAN J,AVITABILE P,RIEMER R.System equivalent reduction expansion process(SEREP)[C]//Proceedings of the 7th IMAC.Las Vegas,NV,1989.
[9]KAMMER D C.Test-analysis-model development using an exact modal reduction[J].The International Journal of Analytical and Experimental Modal Analysis,1987,2(4):174-179.
[10]李伟明,洪嘉振,张以帅.新的模型修正与模态扩展迭代方法[J].振动与冲击,2010,29(6):4-7.LI Weiming,HONG Jiazhen,ZHANG Yishuai.New iterative method for model updating and modal expansion[J].Journal of Vibration and Shock,2010,29(6):4-7.
[11]CHEN Huapeng.Mode shape expansion using perturbed force approach[J].Journal of Sound and Vibration,2010,329:1177-1190.
[12]CHEN H P,MAUNG T S.Regularised finite element model updating using measured incomplete modal data[J].Journal of Sound and Vibration,2014,333:5566-5582.
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