Reduced-order state-space models of structures with imposed displacements and accelerations

[en] Generating reduced state-space models of base-excited structures is of great help in control engineering but is not straightforward to implement in practice, and this problem is addressed in this work. Methods to impose non-homogeneous boundary displacements or accelerations are reviewed, and a novel relative acceleration method is proposed to treat the case of imposed displacements. Various construction approaches for state-space models having prescribed displacements or accelerations as input and including a static correction term are then developed. The theoretical developments are eventually illustrated with structures of increasing complexity, namely, a bar, a beam, and a multi-story building model.

Disciplines :

Mechanical engineering
Civil engineering

Author, co-author :

Raze, Ghislain ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux

Dumoulin, Cédric ; ULB - Université Libre de Bruxelles [BE] > Building Architecture and Town Planning (BATir)

Deraemaeker, Arnaud ; ULB - Université Libre de Bruxelles [BE] > Building Architecture and Town Planning (BATir)

Language :

English

Title :

Reduced-order state-space models of structures with imposed displacements and accelerations

Publication date :

May 2023

Journal title :

Mechanical Systems and Signal Processing

ISSN :

0888-3270

eISSN :

1096-1216

Publisher :

Elsevier BV

Volume :

191

Pages :

110156

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S0888327023000638?httpAccept=text/xml

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique

Funding text :

Ghislain Raze is a Postdoctoral Researcher of the Fonds de la Recherche Scientifique - FNRS which is gratefully acknowledged.

Available on ORBi :

since 02 February 2023

Statistics

Number of views

94 (10 by ULiège)

Number of downloads

123 (1 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

Léger, P., Idé, I., Paultre, P., Multiple-support seismic analysis of large structures. Comput. Struct. 36:6 (1990), 1153–1158, 10.1016/0045-7949(90)90224-P URL https://linkinghub.elsevier.com/retrieve/pii/004579499090224P.
Zhao, G., Ding, B., Watchi, J., Deraemaeker, A., Collette, C., Experimental study on active seismic isolation using interferometric inertial sensors. Mech. Syst. Signal Process., 145, 2020, 106959, 10.1016/j.ymssp.2020.106959 URL https://linkinghub.elsevier.com/retrieve/pii/S0888327020303459.
Béliveau, J.-G., Vigneron, F., Soucy, Y., Draisey, S., Modal parameter estimation from base excitation. J. Sound Vib. 107:3 (1986), 435–449, 10.1016/S0022-460X(86)80117-1 URL https://linkinghub.elsevier.com/retrieve/pii/S0022460X86801171.
Müller, F., Woiwode, L., Gross, J., Scheel, M., Krack, M., Nonlinear damping quantification from phase-resonant tests under base excitation. Mech. Syst. Signal Process., 177(January), 2022, 109170, 10.1016/j.ymssp.2022.109170 URL https://linkinghub.elsevier.com/retrieve/pii/S0888327022003272.
Mindlin, R.D., Goodman, L.E., Beam vibrations with time-dependent boundary conditions. J. Appl. Mech. 17:4 (1950), 377–380, 10.1115/1.4010161 URL https://asmedigitalcollection.asme.org/appliedmechanics/article/17/4/377/1106510/Beam-Vibrations-With-Time-Dependent-Boundary.
Liu, Y., Lu, Z., Methods of enforcing earthquake base motions in seismic analysis of structures. Eng. Struct. 32:8 (2010), 2019–2033, 10.1016/j.engstruct.2010.02.035 URL https://linkinghub.elsevier.com/retrieve/pii/S014102961000088X.
Géradin, M., Rixen, D.J., Mechanical Vibrations: Theory and Application to Structural Dynamics. 2014, John Wiley & Sons URL https://www.wiley.com/en-us/Mechanical+Vibrations%3A+Theory+and+Application+to+Structural+Dynamics%2C+3rd+Edition-p-9781118900208.
Craig, R.R., Bampton, M.C.C., Coupling of substructures for dynamic analyses. AIAA J. 6:7 (1968), 1313–1319, 10.2514/3.4741 URL https://arc.aiaa.org/doi/10.2514/3.4741.
DebChaudhury, A., Gazis, G.D., Response of MDOF systems to multiple support seismic excitation. J. Eng. Mech. 114:4 (1988), 583–603, 10.1061/(ASCE)0733-9399(1988)114:4(583) URL https://ascelibrary.org/doi/10.1061/(ASCE)0733-9399(1988)114:4(583).
Ilanko, S., Monterrubio, L.E., Mochida, Y., The Rayleigh-Ritz Method for Structural Analysis. 2014, John Wiley & Sons, Inc., Hoboken, NJ, USA, 10.1002/9781118984444 URL http://doi.wiley.com/10.1002/9781118984444.
Paraskevopoulos, E.A., Panagiotopoulos, C.G., Manolis, G.D., Imposition of time-dependent boundary conditions in FEM formulations for elastodynamics: critical assessment of penalty-type methods. Comput. Mech. 45:2–3 (2010), 157–166, 10.1007/s00466-009-0428-x URL http://link.springer.com/10.1007/s00466-009-0428-x.
Qin, H., Li, L., Error caused by damping formulating in multiple support excitation problems. Appl. Sci., 10(22), 2020, 8180, 10.3390/app10228180 URL https://www.mdpi.com/2076-3417/10/22/8180.
Géradin, M., Cardona, A., Flexible Multibody Dynamics: A Finite Element Approach. 2001, Wiley URL https://www.wiley.com/en-us/Flexible+Multibody+Dynamics%3A+A+Finite+Element+Approach-p-9780471489900.
Deng, J., Xu, Y., Guasch, O., Gao, N., Tang, L., Nullspace technique for imposing constraints in the Rayleigh–Ritz method. J. Sound Vib., 527(February), 2022, 116812, 10.1016/j.jsv.2022.116812 URL https://linkinghub.elsevier.com/retrieve/pii/S0022460X22000633.
MacNeal, R.H., A hybrid method of component mode synthesis. Comput. Struct. 1:4 (1971), 581–601, 10.1016/0045-7949(71)90031-9 URL https://linkinghub.elsevier.com/retrieve/pii/0045794971900319.
Rubin, S., Improved component-mode representation for structural dynamic analysis. AIAA J. 13:8 (1975), 995–1006, 10.2514/3.60497 URL https://arc.aiaa.org/doi/10.2514/3.60497.
Rixen, D.J., A dual Craig–Bampton method for dynamic substructuring. J. Comput. Appl. Math. 168:1–2 (2004), 383–391, 10.1016/j.cam.2003.12.014 URL https://linkinghub.elsevier.com/retrieve/pii/S0377042703010045.
de Klerk, D., Rixen, D.J., Voormeeren, S.N., General framework for dynamic substructuring: History, review and classification of techniques. AIAA J. 46:5 (2008), 1169–1181, 10.2514/1.33274 URL https://arc.aiaa.org/doi/10.2514/1.33274.
Besselink, B., Tabak, U., Lutowska, A., van de Wouw, N., Nijmeijer, H., Rixen, D., Hochstenbach, M., Schilders, W., A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control. J. Sound Vib. 332:19 (2013), 4403–4422, 10.1016/j.jsv.2013.03.025 URL https://linkinghub.elsevier.com/retrieve/pii/S0022460X1300285X.
Krattiger, D., Wu, L., Zacharczuk, M., Buck, M., Kuether, R.J., Allen, M.S., Tiso, P., Brake, M.R., Interface reduction for Hurty/Craig–Bampton substructured models: Review and improvements. Mech. Syst. Signal Process. 114 (2019), 579–603, 10.1016/j.ymssp.2018.05.031 URL https://linkinghub.elsevier.com/retrieve/pii/S088832701830284X.
Kuhar, E.J., Stahle, C.V., Dynamic transformation method for modal synthesis. AIAA J. 12:5 (1974), 672–678, 10.2514/3.49318 URL https://arc.aiaa.org/doi/10.2514/3.49318.
Aumann, Q., Deckers, E., Jonckheere, S., Desmet, W., Müller, G., Automatic model order reduction for systems with frequency-dependent material properties. Comput. Methods Appl. Mech. Engrg., 397, 2022, 115076, 10.1016/j.cma.2022.115076 URL https://linkinghub.elsevier.com/retrieve/pii/S004578252200281X.
Franklin, G.F., Powell, J.D., Emami-Naeini, A., Feedback Control of Dynamic Systems. 2015, Pearson London URL https://www.pearson.com/uk/educators/higher-education-educators/program/Franklin-Feedback-Control-of-Dynamic-Systems-Global-Edition-8th-Edition/PGM2639960.html.
Balmès, E., New results on the identification of normal modes from experimental complex modes. Mech. Syst. Signal Process. 11:2 (1997), 229–243, 10.1006/mssp.1996.0058 URL https://linkinghub.elsevier.com/retrieve/pii/S0888327096900588.
Gruber, F.M., Rixen, D.J., Dual Craig–Bampton component mode synthesis method for model order reduction of nonclassically damped linear systems. Mech. Syst. Signal Process. 111 (2018), 678–698, 10.1016/j.ymssp.2018.04.019 URL https://linkinghub.elsevier.com/retrieve/pii/S0888327018302218.
McKelvey, T., Akcay, H., Ljung, L., Subspace-based multivariable system identification from frequency response data. IEEE Trans. Automat. Control 41:7 (1996), 960–979, 10.1109/9.508900 URL http://ieeexplore.ieee.org/document/508900/.
Alvin, K.F., Park, K.C., Second-order structural identification procedure via state-space-based system identification. AIAA J. 32:2 (1994), 397–406, 10.2514/3.11997 URL https://arc.aiaa.org/doi/10.2514/3.11997.
De Angelis, M., Luş, H., Betti, R., Longman, R.W., Extracting physical parameters of mechanical models from identified state-space representations. J. Appl. Mech. 69:5 (2002), 617–625, 10.1115/1.1483836 URL https://asmedigitalcollection.asme.org/appliedmechanics/article/69/5/617/445202/Extracting-Physical-Parameters-of-Mechanical.
Luş, H., De Angelis, M., Betti, R., Longman, R.W., Constructing second-order models of mechanical systems from identified state space realizations. Part I: Theoretical discussions. J. Eng. Mech. 129:5 (2003), 477–488, 10.1061/(ASCE)0733-9399(2003)129:5(477) URL http://ascelibrary.org/doi/10.1061/(ASCE)0733-9399(2003)129:5(477).
Gibanica, M., Abrahamsson, T.J., Identification of physically realistic state-space models for accurate component synthesis. Mech. Syst. Signal Process., 145, 2020, 106906, 10.1016/j.ymssp.2020.106906.
Gibanica, M., Abrahamsson, T.J., McKelvey, T., State-space system identification with physically motivated residual states and throughput rank constraint. Mech. Syst. Signal Process., 142, 2020, 106579, 10.1016/j.ymssp.2019.106579.
Sjövall, P., Abrahamsson, T., Component system identification and state-space model synthesis. Mech. Syst. Signal Process. 21:7 (2007), 2697–2714, 10.1016/j.ymssp.2007.03.002 URL https://linkinghub.elsevier.com/retrieve/pii/S088832700700043X.
Scheel, M., Gibanica, M., Nord, A., State-space dynamic substructuring with the transmission simulator method. Exp. Tech. 43:3 (2019), 325–340, 10.1007/s40799-019-00317-z URL http://link.springer.com/10.1007/s40799-019-00317-z.
Bernstein, D.S., Matrix Mathematics. 2009, Princeton University Press, 10.1515/9781400833344.
Ghosh, T., Improved method of generating control system model using modal synthesis. Modeling and Simulation Technologies Conference, 1997, American Institute of Aeronautics and Astronautics, Reston, Virigina, 231–239, 10.2514/6.1997-3673 URL https://arc.aiaa.org/doi/10.2514/6.1997-3673.
Monjaraz Tec, C., Gross, J., Krack, M., A massless boundary component mode synthesis method for elastodynamic contact problems. Comput. Struct., 260, 2022, 106698, 10.1016/j.compstruc.2021.106698 URL https://linkinghub.elsevier.com/retrieve/pii/S0045794921002200.
Craig, R. Jr., Coupling of substructures for dynamic analyses - An overview. 41st Struct. Struct. Dyn. Mater. Conf. Exhib., 2000, American Institute of Aeronautics and Astronautics, Reston, Virigina, 10.2514/6.2000-1573 URL https://arc.aiaa.org/doi/10.2514/6.2000-1573.
De Angelis, M., Imbimbo, M., A procedure to identify the modal and physical parameters of a classically damped system under seismic motions. Adv. Acoust. Vib. 2012 (2012), 1–11, 10.1155/2012/975125 URL https://www.hindawi.com/journals/aav/2012/975125/.
J.C. O'Callahan, System equivalent reduction expansion process, in: Proceedings of the 7th International Modal Analysis Conference, 1989.
Balmes, E., Vermot des Roches, G., Martin, G., Bianchi, J.-P., Structural dynamics toolbox & FEMLink. 2019 URL https://www.sdtools.com/help/sdt.pdf.
Raze, G., Dietrich, J., Paknejad, A., Lossouarn, B., Zhao, G., Deraemaeker, A., Collette, C., Kerschen, G., Passive control of a periodic structure using a network of periodically-coupled piezoelectric shunt circuits. Desmet, W., Pluymers, B., Moens, D., Vandemaele, S., (eds.) Proceedings of ISMA 2020-International Conference on Noise and Vibration Engineering and USD 2020-International Conference on Uncertainty in Structural Dynamics, 2020, KU Leuven, Leuven, 145–160 URL https://orbi.uliege.be/handle/2268/252957.