CHEN Kui-fu, JIAO Qun-ying. On the Redundancy of Complex Modal Parameters[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1292-1298.
Citation: CHEN Kui-fu, JIAO Qun-ying. On the Redundancy of Complex Modal Parameters[J]. Applied Mathematics and Mechanics, 2004, 25(12): 1292-1298.

On the Redundancy of Complex Modal Parameters

  • Received Date: 2003-01-15
  • Rev Recd Date: 2004-07-06
  • Publish Date: 2004-12-15
  • Generating the simulation transfer function(TF)is indispensable to modal analysis,such as examining modal parameters identification algorithm,and assessing modal analysis software.Comparing 3 feasible algorithms to simulate TF shows that,one of them is preperable,which is expressing the TF as the function of the complex modal parameters(CMPs),because the deliberate behaviors of CMPs can be implemented easily,such as,dense modals,large damping,and complex modal shape, etc.Nonetheless,even this preferable algorithms is elected,the complex modal shapes cannot be specified arbitrarily,because the number of CMPs far more exceeds that in physical coordinate'so for physical realizable system,there are redundant constraints in CMPs.By analyzing the eigenvalue problem of a complex modal system,and the inversion equations from CMPs to physical parameters,the explicit redundancy constraints were presented.For the special cases,such as the real modal,the damping free modal,and non-complete identification,the specific forms of the redundancy constraints were discussed,along with the number of independent parameters.It is worthy of noting that,redundancy constraints are automatically satisfied for the real modal case.Their equivalent forms on the transfer matrix and a column of transfer matrix were also provided.These results are applicable to generate TF,to implement identification by optimization and appreciate the identification results,to evaluate residual modal,and to verify the complementary of identified modal orders.
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  • [1]
    He J M,Fu Z F.Modal Analysis[M].Oxford,England:Butterworth-Heinemann, 2001.
    [2]
    Ewins D J.Modal Testing: Theory, Practice and Application[M].Hertfordshire England:Research Studies Press Limited,1999.
    [3]
    Silva J M,Maia N M.Theoretical and Experimental Modal Analysis[M].Hertfordshire England:Research Studies Press Limited,1998.
    [4]
    许本文,焦群英.机械震动与模态分析基础[M].北京:机械工业出版社,1998.
    [5]
    陆秋海,李德葆.模态理论的进展[J].力学进展,1996,26(4):464—472.
    [6]
    Hasselman T K, Chrostowski J D, Pappa R.Estimation of full modal damping matrices from complex test modes[A].In:The 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference[C].La Jolla, CA, USA,1993,3388—3394.
    [7]
    Gladwell G M L.On the reconstruction of a damped vibrating system from two complex spectra—Part 1: Theory[J].J Sound Vibration,2001,240(2):203—217. doi: 10.1006/jsvi.2000.3213
    [8]
    Foltete E, Gladwell G M L. On the reconstruction of a damped vibrating system from two complex spectra—Part 2:Experiment[J].J Sound Vibration,2001,240(2):219—240. doi: 10.1006/jsvi.2000.3214
    [9]
    Rosa L F L,Magluta C,Roitman N.Modal parameters estimation using an optimization technique[A].In:A L Wicks Ed.Proceedings of the 15th International Modal Analysis Conference[C].IMAC. Part 1 (of 2).Orlando,FL,USA.Bethel:Society of Experimental Mechanics,1997,540—544.
    [10]
    Rosa L F L,Magluta C, Roitman N. Estimation of modal parameters through a non-linear optimisation technique[J].Mechanical Systems and Signal Processing,1999,13(4):593—607. doi: 10.1006/mssp.1998.1207
    [11]
    Garvey S D, Friswell M I, Penny J E.Efficient component mode synthesis with non-classically damped (sub-) structures[A].In:A L Wicks Ed.Proceedings of the 1998 16th International Modal Analysis Conference[C].Part 2 (of 2).Santa Barbara, CA,USA.Bethel:Society of Experimental Mechanics,1998,1602—1608.
    [12]
    Garvey S D, Penny J E, Friswell M I. The relationship between the real and imaginary parts of complex modes[J].J Sound Vibration,1998,212(1):75—83. doi: 10.1006/jsvi.1997.1377
    [13]
    李德葆,陆秋海.实验模态分析及其应用[M].北京:科学出版社,2001,78—87.
    [14]
    Zwillinger D.Standard Mathematical Tables and Formulae[M].Florida,USA:CRC Press,1996,130—134.
    [15]
    杨路,张景中,侯晓荣.非线性代数方程与定理机器证明[M].上海:上海科技教育出版社,1996.
    [16]
    Caughey T K,O'kelly M J.Classical normal modes in damped linear dynamics systems[J].ASME Journal of Applied Mechanics,1965,32(2):583—588. doi: 10.1115/1.3627262
    [17]
    Liu K F, Kujath M R. Zheng W P. Quantification of non-proportionality of damping in discrete vibratory systems[J].Computers and Structures,2000,77(5):557—569. doi: 10.1016/S0045-7949(99)00230-8
    [18]
    Levy E C. Complex-curve fitting[J].IEEE Transactions on Automatic Control,1959,4(1):37—44. doi: 10.1109/TAC.1959.1104874
    [19]
    Fahey S O F, Pratt J. Frequency domain modal estimation techniques[J].Experimental Techniques,1998,22(5):33—37. doi: 10.1111/j.1747-1567.1998.tb02320.x
    [20]
    Ruotolo R, Storer D M.Global smoothing technique for FRF data fitting[J].J Sound Vibration,2001,239(1):41—56. doi: 10.1006/jsvi.2000.3155
    [21]
    Formenti D, Richardson M.Parameter estimation from frequency response measurements using rational fraction polynomials (twenty years of progress)[A].In:A L Wicks Ed.Proceedings of the 20th International Modal Analysis Conference: A Conference on Structural Dynamics[C].Los Angeles, CA,USA.Bethel:Society of Experimental Mechanics,2002,373—382.
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