Finite Element Model Updating of Complicated Beam-Type Structures Based on Reduced Super Beam Model
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摘要
A finite element model updating technique for complicated beam-type structures is presented in this study. Firstly, a complicated beam-type structure is reduced to a reduced super beam model with a much smaller degree of freedom by using the reduced super beam method, which is based on the classic plane cross-section assumption and displacement interpolation function of beam theory. Then based on the reduced super beam, the analysis of eigensolutions and eigensensitivities from the reduced eigenequation are processed for model updating, which will greatly reduce the computational effort when compared to the traditional model updating methods performed on the global model. Optimization techniques are adopted for updating the difference of modal dynamic properties, resulting in optimal values of the structural parameters. Finally, a complicated stiffened cylindrical shell model and a practical missile structure, served as the illustrative examples, are employed for model updating application, which demonstrate that the reduced super beam-based method is both effective and highly efficient.
A finite element model updating technique for complicated beam-type structures is presented in this study. Firstly, a complicated beam-type structure is reduced to a reduced super beam model with a much smaller degree of freedom by using the reduced super beam method, which is based on the classic plane cross-section assumption and displacement interpolation function of beam theory. Then based on the reduced super beam, the analysis of eigensolutions and eigensensitivities from the reduced eigenequation are processed for model updating, which will greatly reduce the computational effort when compared to the traditional model updating methods performed on the global model. Optimization techniques are adopted for updating the difference of modal dynamic properties, resulting in optimal values of the structural parameters. Finally, a complicated stiffened cylindrical shell model and a practical missile structure, served as the illustrative examples, are employed for model updating application, which demonstrate that the reduced super beam-based method is both effective and highly efficient.
A finite element model updating technique for complicated beam-type structures is presented in this study. Firstly, a complicated beam-type structure is reduced to a reduced super beam model with a much smaller degree of freedom by using the reduced super beam method, which is based on the classic plane cross-section assumption and displacement interpolation function of beam theory. Then based on the reduced super beam, the analysis of eigensolutions and eigensensitivities from the reduced eigenequation are processed for model updating, which will greatly reduce the computational effort when compared to the traditional model updating methods performed on the global model. Optimization techniques are adopted for updating the difference of modal dynamic properties, resulting in optimal values of the structural parameters. Finally, a complicated stiffened cylindrical shell model and a practical missile structure, served as the illustrative examples, are employed for model updating application, which demonstrate that the reduced super beam-based method is both effective and highly efficient.
引文
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[6]Xia Y,Lin R M.Improvement on the iterated IRS method for structural eigensolutions.Journal of Sound and Vibration,2004,270(4-5):713–727.DOI:10.1016/S0022-460X(03)00188-3.
[7]Weng S,Xia Y,Xu Y L,et al.Improved substructuring method for eigensolutions of large-scale structures.Journal of Sound and Vibration,2009,323(3-5):718-36.DOI:10.1016/j.jsv.2009.01.015.
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[10]Perera R,Ruiz A.A multistage FE updating procedure for damage identification in large-scale structures based on multi-objective evolutionary optimization.Mechanical Systems and Signal Processing,2008,22(4):970-991.DOI:10.1016/j.ymssp.2007.10.004.
[11]Ko J M,Sun Z G,Ni Y Q.Multi-stage identification scheme for detecting damage in cable-stayed Kap Shui Mun Bridge.Engineering Structures,2002,24(7):857-68.DOI:10.1016/S0141-0296(02)00024-X.
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[14]Papadimitriou C,Papadioti D C.Component mode synthesis techniques for finite element model updating.Computers and Structures,2013,126(15):15-28.DOI:10.1016/j.compstruc.2012.10.018.
[15]Wang W S,Cheng G D,Li Q H.Fast dynamic performance optimization of complicated beam-type structures based on two new reduced physical models.Engineering Optimization,2013,45(7):835-850.DOI:10.1080/0305215X.2012.709513.
[16]Cheng G D,Wang W S.Fast dynamic analysis of complicated beam-type structure based on reduced super beam model.AIAA Journal,2014,52(5):952-963.DOI:10.2514/1.J052312.
[17]Wang W S,Cheng G D,Hao P.Frequency analysis of stiffened cylindrical shell based on reduced super beam model.Journal of Solid Rocket Technology,2015,38(3):401-406.(in Chinese)
[18]Zipfel P H.Modeling and Simulation of Aerospace Vehicle Dynamics.2nd ed.Reston,VA :American Institute of Aeronautics and Astronautics,Inc.2007.
[19]Li Bingwei,Dai Xianjin,Wang Liang.A modification technique of missile dynamic model based on multi-objective optimization algorithm.Structure and Environment Engineering,2012,39(6):30-35.(in Chinese)
[20]Zhao Ling,Liu Changchang,Liu Ziqiang.Dynamic model updating of missile based on the smallest mode shape area difference.Missile and Space Vehicles,2013,328(5):59-62.(in Chinese)
[21]Lyu Haibo,Li Ming,Guo Baisen,et al.An updating method for structural dynamic model applicable for transient rocket response computation.Noise and Vibration Control,2013,33(6):11-14.DOI:10.3969/j.issn.1006-1335.2013.06.003.(in Chinese)
[22]Bathe K J.Finite element procedures in engineering analysis.Englewood Chiffs:Prentice-Hall,Inc.,1982.
[23]Mottershead J E,Link M,Friswell M I.The sensitivity method in finite element model updating:A tutorial.Mechanical Systems and Signal Processing,2011,25(7),2275-2296.DOI:10.1016/j.ymssp.2010.10.012.
[24]Allemang R J,Brown D L.A correlation coefficient for modal vector analysis.Proceeding of the 1st International Modal Analysis Conference.Berlin:Springer,1982.110-116.
[25]Modak S V,Kundra T K,Nakra B C.Comparative study of model updating methods using simulated experimental data.Computers and Structures,2002,80(5-6):437-447.DOI:10.1016/S0045-7949(02) 00017-2.
[26]Svanber K.The method of moving asymptotes—a new method for structural optimization.International Journal for Numerical Methods in Engineering,1987,24(2):359-373.-DOI:10.1002/nme.1620240207.
[27]Louis K.The Lanczos Method:Evolution and Application.Society for Industrial and Applied Mathematics,1987.
[28]Wu K S,Simon H.Thick-restart Lanczos method for large symmetric eigenvalue problems.SIAM Journal on Matrix Analysis and Applications (SIAM),2000,22 (2):602-616.
[29]Choi K K,Kim N H.Structural Sensitivity Analysis and Optimization 1:Linear Systems.New York:Springer Science and Business Media,Inc.,2005.
[2]Ma S C,Zang CP,Lan H B.Dynamic model updating of an aero-engine casing.Journal of Aaerospace Power,2013,28(4):878-884.DOI:10.13224/j.cnki.jasp.2013.04.024.(in Chinese)
[3]Mottershead J,Friswell M I.Model updating in structural dynamics:A survey.Journal of Sound and Vibration,1993,167(2):347-375.DOI:10.1006/jsvi.1993.1340.
[4]Brownjohn J M W,Xia P Q,Hao H,et al.Civil structure condition assessment by FE model updating:Methodology and case studies.Finite Elements in Analysis and Design,2001,37(10):761-775.DOI:10.1016/S0168-874X(00)00071-8.
[5]Bakira P G,Reynders E,Roeck G D.Sensitivity-based finite element model updating using constrained optimization with a trust region algorithm.Journal of Sound and Vibration,2007,305(1-2):211-225.DOI:10.1016/j.jsv.2007.03.044.
[6]Xia Y,Lin R M.Improvement on the iterated IRS method for structural eigensolutions.Journal of Sound and Vibration,2004,270(4-5):713–727.DOI:10.1016/S0022-460X(03)00188-3.
[7]Weng S,Xia Y,Xu Y L,et al.Improved substructuring method for eigensolutions of large-scale structures.Journal of Sound and Vibration,2009,323(3-5):718-36.DOI:10.1016/j.jsv.2009.01.015.
[8]Xia Y,Weng S,Xu Y L.A substructuring method for calculation of eigenvalue derivatives and eigenvector derivatives.The 4th International Conference on Structural Health Monitoring of Intelligent Infrastructure.Zurich,2009.
[9]de Klerk D,Rixen D J,Voormeeren S N.General framework for dynamic substructuring:History,review,and classification of techniques.AIAA Journal,2008,46(5):1169-1181.DOI:10.2514/1.33274.
[10]Perera R,Ruiz A.A multistage FE updating procedure for damage identification in large-scale structures based on multi-objective evolutionary optimization.Mechanical Systems and Signal Processing,2008,22(4):970-991.DOI:10.1016/j.ymssp.2007.10.004.
[11]Ko J M,Sun Z G,Ni Y Q.Multi-stage identification scheme for detecting damage in cable-stayed Kap Shui Mun Bridge.Engineering Structures,2002,24(7):857-68.DOI:10.1016/S0141-0296(02)00024-X.
[12]Weng S,Xia Y,Xu Y L,et al.Substructure based approach to finite element model updating.Computers and Structures,2011,89(9-10):772-782.DOI:10.1016/j.compstruc.2011.02.004.
[13]Zhu D P,Dong X J,Wang Y.Substructure model updating through modal dynamic residual approach.Proceedings of the 9th International Workshop on Structural Health Monitoring.Stanford,CA.2013.1047-1054
[14]Papadimitriou C,Papadioti D C.Component mode synthesis techniques for finite element model updating.Computers and Structures,2013,126(15):15-28.DOI:10.1016/j.compstruc.2012.10.018.
[15]Wang W S,Cheng G D,Li Q H.Fast dynamic performance optimization of complicated beam-type structures based on two new reduced physical models.Engineering Optimization,2013,45(7):835-850.DOI:10.1080/0305215X.2012.709513.
[16]Cheng G D,Wang W S.Fast dynamic analysis of complicated beam-type structure based on reduced super beam model.AIAA Journal,2014,52(5):952-963.DOI:10.2514/1.J052312.
[17]Wang W S,Cheng G D,Hao P.Frequency analysis of stiffened cylindrical shell based on reduced super beam model.Journal of Solid Rocket Technology,2015,38(3):401-406.(in Chinese)
[18]Zipfel P H.Modeling and Simulation of Aerospace Vehicle Dynamics.2nd ed.Reston,VA :American Institute of Aeronautics and Astronautics,Inc.2007.
[19]Li Bingwei,Dai Xianjin,Wang Liang.A modification technique of missile dynamic model based on multi-objective optimization algorithm.Structure and Environment Engineering,2012,39(6):30-35.(in Chinese)
[20]Zhao Ling,Liu Changchang,Liu Ziqiang.Dynamic model updating of missile based on the smallest mode shape area difference.Missile and Space Vehicles,2013,328(5):59-62.(in Chinese)
[21]Lyu Haibo,Li Ming,Guo Baisen,et al.An updating method for structural dynamic model applicable for transient rocket response computation.Noise and Vibration Control,2013,33(6):11-14.DOI:10.3969/j.issn.1006-1335.2013.06.003.(in Chinese)
[22]Bathe K J.Finite element procedures in engineering analysis.Englewood Chiffs:Prentice-Hall,Inc.,1982.
[23]Mottershead J E,Link M,Friswell M I.The sensitivity method in finite element model updating:A tutorial.Mechanical Systems and Signal Processing,2011,25(7),2275-2296.DOI:10.1016/j.ymssp.2010.10.012.
[24]Allemang R J,Brown D L.A correlation coefficient for modal vector analysis.Proceeding of the 1st International Modal Analysis Conference.Berlin:Springer,1982.110-116.
[25]Modak S V,Kundra T K,Nakra B C.Comparative study of model updating methods using simulated experimental data.Computers and Structures,2002,80(5-6):437-447.DOI:10.1016/S0045-7949(02) 00017-2.
[26]Svanber K.The method of moving asymptotes—a new method for structural optimization.International Journal for Numerical Methods in Engineering,1987,24(2):359-373.-DOI:10.1002/nme.1620240207.
[27]Louis K.The Lanczos Method:Evolution and Application.Society for Industrial and Applied Mathematics,1987.
[28]Wu K S,Simon H.Thick-restart Lanczos method for large symmetric eigenvalue problems.SIAM Journal on Matrix Analysis and Applications (SIAM),2000,22 (2):602-616.
[29]Choi K K,Kim N H.Structural Sensitivity Analysis and Optimization 1:Linear Systems.New York:Springer Science and Business Media,Inc.,2005.