Imposed displacement; Imposed acceleration; Base excitation; Reduced-order model; Craig–Bampton method; State-space model
Abstract :
[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
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
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.
Similar publications
Sorry the service is unavailable at the moment. Please try again later.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.