Littérature scientifique sur le sujet « Component-mode synthesi »

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Articles de revues sur le sujet "Component-mode synthesi"

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FUNAMOTO, Kenichi, et Masayoshi MISAWA. « Component Mode Synthesis Using Component Test Results ». Proceedings of the JSME annual meeting 2002.1 (2002) : 297–98. http://dx.doi.org/10.1299/jsmemecjo.2002.1.0_297.

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Seshu, P. « Substructuring and Component Mode Synthesis ». Shock and Vibration 4, no 3 (1997) : 199–210. http://dx.doi.org/10.1155/1997/147513.

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Substructuring and component mode synthesis (CMS), is a very popular method of model reduction for large structural dynamics problems. Starting from the pioneering works on this technique in the early 1960s, many researchers have studied and used this technique in a variety of applications. Besides model reduction, CMS offers several other crucial advantages. The present work aims to provide a review of the available literature on this important technique.
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Greif, R. « Substructuring and Component Mode Synthesis ». Shock and Vibration Digest 18, no 7 (1 juillet 1986) : 3–8. http://dx.doi.org/10.1177/058310248601800703.

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Kim, Soo Min, Jin-Gyun Kim, Soo-Won Chae et K. C. Park. « Evaluating Mode Selection Methods for Component Mode Synthesis ». AIAA Journal 54, no 9 (septembre 2016) : 2852–63. http://dx.doi.org/10.2514/1.j054936.

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Kubomura, Kenji. « Component mode synthesis for damped structures ». AIAA Journal 25, no 5 (mai 1987) : 740–45. http://dx.doi.org/10.2514/3.9691.

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Engels, Remi C. « Convergence improvement for component mode synthesis ». AIAA Journal 30, no 2 (février 1992) : 490–95. http://dx.doi.org/10.2514/3.10943.

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Koutsovasilis, Panagiotis. « Improved component mode synthesis and variants ». Multibody System Dynamics 29, no 4 (1 août 2012) : 343–59. http://dx.doi.org/10.1007/s11044-012-9327-6.

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Suarez, L. E., et M. P. Singh. « An exact component mode synthesis approach ». Earthquake Engineering & ; Structural Dynamics 16, no 2 (février 1988) : 293–310. http://dx.doi.org/10.1002/eqe.4290160210.

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MORITA, Shigeru, et Shouhe KUMANO. « Amendment of Identified Mode Shape for Component Mode Synthesis ». Transactions of the Japan Society of Mechanical Engineers Series C 63, no 608 (1997) : 1153–58. http://dx.doi.org/10.1299/kikaic.63.1153.

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Cha, Hyun Joo, Jin Ho Kim et Shi Bok Lee. « Hybrid Component Mode Synthesis Considering Residual Dynamic Flexibility Attachment Mode ». Transactions of the Korean Society of Mechanical Engineers A 29, no 5 (1 mai 2005) : 716–25. http://dx.doi.org/10.3795/ksme-a.2005.29.5.716.

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Thèses sur le sujet "Component-mode synthesi"

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Soucy, Yvan. « Test-based hybrid component mode synthesis ». Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape17/PQDD_0014/NQ37056.pdf.

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Troeng, Tor. « Frequency Response Analysis using Component Mode Synthesis ». Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-37809.

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Solutions to physical problems described by Differential Equationson complex domains are in except for special cases almost impossibleto find. This turns our interest toward numerical approaches. Sincethe size of the numerical models tends to be very large when handlingcomplex problems, the area of model reduction is always a hot topic. Inthis report we look into a model reduction method called ComponentMode Synthesis. This can be described as dividing a large and complexdomain into smaller and more manageable ones. On each of thesesubdomains, we solve an eigenvalue problem and use the eigenvectorsas a reduced basis. Depending on the required accuracy we mightwant to use many or few modes in each subdomain, this opens for anadaptive selection of which subdomains that affects the solution most.We cover two numerical examples where we solve Helmholtz equationin a linear elastic problem. The first example is a truss and the othera gear wheel. In both examples we use an adaptive algorithm to refinethe reduced basis and compare the results with a uniform refinementand with a classic model reduction method called Modal Analysis. Wealso introduce a new approach when computing the coupling modesonly on the adjacent subdomains.
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Blackwood, Gary H. (Gary Howard). « Experimental component mode synthesis of structures with joint freeplay ». Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/37486.

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Petersen, Lynn James. « Mast-antenna survivability : structural dynamic design analysis by component mode synthesis ». Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1994. http://handle.dtic.mil/100.2/ADA280669.

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Zoet, Petrus Gosse. « Component mode synthesis for ship structures : investigation into an alternative approach ». Thesis, University of Strathclyde, 2013. http://digitool.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=24881.

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The main aim of this work is to help the shipbuilder to effectively assess a ships' structural design for its vibratory behaviour. For that purpose state of the art structural modelling techniques are reviewed for the validity of their basic principles, accuracy, practicality and required computation time when applied on typical marine structures. Full finite element modelling has been applied on a part of the structure of an LNG carrier on board which the author has taken vibration and noise measurements. Also fixed interface (Craig-Bampton) and free interface (Rubin's method) component mode synthesis sub structuring techniques have been applied. The aim of the analysis is to evaluate the effectiveness of finite element modelling through evaluation with measurement results, evaluate the accuracy of the sub structuring modelling techniques and to identify short comings of any of the tested methods. Two alternative component synthesis modelling sub structuring techniques are proposed in order to reduce required computation time; Zoet's method and the Rubin Zoet method. The Zoet method is tested using a section of the LNG carrier's structural model. The method is evaluated for accuracy (comparing obtained results with the results obtained through the full harmonic finite element analysis) and required computation time through comparison with the required computation time for: - full harmonic analysis - the classical modal reduction and mode superposition technique - the classical Rubin free interface component mode synthesis - and Rubin's method with interface reduction according to the IRS method (see section 6.5.3) - the Rubin-Zoet technique.
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Abdallah, Ayman Ahmed. « Dynamic substructuring by the boundary flexibility vector method of component mode synthesis ». Case Western Reserve University School of Graduate Studies / OhioLINK, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=case1054567783.

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Ramani, Anand. « Two-step Component Mode Synthesis with convergence for the eigensolution of large-degree-of-freedom systems ». Diss., Virginia Tech, 1996. http://hdl.handle.net/10919/39162.

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Beck, Joseph A. « Stochastic Mistuning Simulation of Integrally Bladed Rotors using Nominal and Non-Nominal Component Mode Synthesis Methods ». Wright State University / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=wright1278600105.

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Covi, Patrick. « Multi-hazard analysis of steel structures subjected to fire following earthquake ». Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/313383.

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Fires following earthquake (FFE) have historically produced enormous post-earthquake damage and losses in terms of lives, buildings and economic costs, like the San Francisco earthquake (1906), the Kobe earthquake (1995), the Turkey earthquake (2011), the Tohoku earthquake (2011) and the Christchurch earthquakes (2011). The structural fire performance can worsen significantly because the fire acts on a structure damaged by the seismic event. On these premises, the purpose of this work is the investigation of the experimental and numerical response of structural and non-structural components of steel structures subjected to fire following earthquake (FFE) to increase the knowledge and provide a robust framework for hybrid fire testing and hybrid fire following earthquake testing. A partitioned algorithm to test a real case study with substructuring techniques was developed. The framework is developed in MATLAB and it is also based on the implementation of nonlinear finite elements to model the effects of earthquake forces and post-earthquake effects such as fire and thermal loads on structures. These elements should be able to capture geometrical and mechanical non-linearities to deal with large displacements. Two numerical validation procedures of the partitioned algorithm simulating two virtual hybrid fire testing and one virtual hybrid seismic testing were carried out. Two sets of experimental tests in two different laboratories were performed to provide valuable data for the calibration and comparison of numerical finite element case studies reproducing the conditions used in the tests. Another goal of this thesis is to develop a fire following earthquake numerical framework based on a modified version of the OpenSees software and several scripts developed in MATLAB to perform probabilistic analyses of structures subjected to FFE. A new material class, namely SteelFFEThermal, was implemented to simulate the steel behaviour subjected to FFE events.
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Zhou, Changwei. « Approche couplée propagative et modale pour l'analyse multi-échelle des structures périodiques ». Thesis, Ecully, Ecole centrale de Lyon, 2014. http://www.theses.fr/2014ECDL0040/document.

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La dynamique d’une structure peut être vue aussi bien en termes de modes (ondes stationnaires) qu’en termes d’ondes élastiques libres. Les approches modales sont largement utilisées en mécanique et de nombreuses techniques de réduction de modèles (Model Order Reduction - MOR) ont été développées dans ce cadre. Quant à la dynamique des structures périodiques, les approches propagatives sont majoritairement utilisées, où la périodicité est exploitée en utilisant la théorie de Bloch. Pour les structures périodiques complexes, plusieurs techniques MOR sur la base d’onde ont été proposées dans la littérature. Dans ce travail, une approche couplée propagative et modale a été développée pour étudier la propagation des ondes dans les structures périodiques. Cette approche commence par la description modale d’une cellule unitaire (échelle mésoscopique) en utilisant la synthèse modale (Component Mode Synthesis - CMS). Par la suite, la méthode propagative - Wave Finite Element Method (WFEM) est appliquée sur la structure (échelle macroscopique). Cette méthode est nommée “CWFEM” pour CondensedWave Finite Element Method. Elle combine les avantages de la CMS et WFEM. La CMS permet d’analyser le comportement local d’en extraire une base réduite. La WFEM exploite la périodicité de la structure d’en extraire les paramètres de propagation. Ainsi, l’analyse de la propagation des ondes dans la structure à l’échelle macroscopique peut être réalisée en prenant en compte l’échelle mésoscopique. L’efficacité de la CWFEM est illustrée par de nombreuse applications aux structures périodiques monodimensionnelle (1D) et bidimensionnelle (2D). Le critère de réduction optimale assurant la convergence est discuté. Les caractéristiques de propagation dans les structures périodiques sont identifiées: bande passante, bande interdite, la directivité marquée (wave beaming effects), courbe de dispersion, band structure, surface des lenteurs... Ces propriétés peuvent répondre au besoin de conception des barrières vibroacoustiques, pièges à ondes. La CWFEM est ensuite appliquée pour étudier la propagation des ondes dans des plaques perforées et plaques raidies. Une méthode d’homogénéisation pour déterminer le modèle équivalent de la plaque perforée est proposée. Les comportements à haute fréquence tels que la directivité marquée sont également prédits par CWFEM. Trois modèles de plaques avec perforations différentes sont étudiées dans ce travail. Une validation expérimentale est effectuée sur deux plaques. Pour la plaque raidie, l’influence des modes internes sur la propagation globale est discutée. La densité modale est estimée, en moyenne et haute fréquences, pour une plaque raidie finie, où une bonne corrélation est obtenue en comparant les résultats à l’issue des analyses modales
Structural dynamics can be described in terms of structural modes as well as elastic wave motions. The mode-based methods are widely applied in mechanical engineering and numerous model order reduction (MOR) techniques have been developed. When it comes to the study of periodic structures, wave description is mostly adopted where periodicity is fully exploited based on the Bloch theory. For complex periodic structures, several MOR techniques conducted on wave basis have been proposed in the literature. In this work, a wave and modal coupled approach is developed to study the wave propagation in periodic structures. The approach begins with the modal description of a unit cell (mesoscopic scale) using Component Mode Synthesis (CMS). Subsequently, the wave-based method -Wave Finite Element Method (WFEM) is applied to the structure (macroscopic scale). The method is referred as “CWFEM” for Condensed Wave Finite Element Method. It combines the advantages of CMS and WFEM. CMS enables to analyse the local behaviour of the unit cell using a reduced modal basis. On the other hand, WFEM exploits fully the periodic propriety of the structure and extracts directly the propagation parameters. Thus the analysis of the wave propagation in the macroscopic scale waveguides can be carried out considering the mesoscopic scale behaviour. The effectiveness of CWFEM is illustrated via several one-dimensional (1D) periodic structures and two-dimensional (2D) periodic structures. The criterion of the optimal reduction to ensure the convergence is discussed. Typical wave propagation characteristics in periodic structures are identified, such as pass bands, stop bands, wave beaming effects, dispersion relation, band structure and slowness surfaces...Their proprieties can be applied as vibroacoustics barriers, wave filters. CWFEM is subsequently applied to study wave propagation characteristics in perforated plates and stiffened plate. A homogenization method to find the equivalent model of perforated plate is proposed. The high frequency behaviours such as wave beaming effect are also predicted by CWFEM. Three plate models with different perforations are studied. Experimental validation is conducted on two plates. For the stiffened plate, the influence of internal modes on propagation is discussed. The modal density in the mid- and high- frequency range is estimated for a finite stiffened plate, where good correlation is obtained compared to the mode count from modal analysis
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Livres sur le sujet "Component-mode synthesi"

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Brown, Andrew M. Probabilistic component mode synthesis of nondeterministic substructures. Washington, DC : [National Aeronautics and Space Administration, 1997.

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Hucklebridge, Arthur A. Identification of structural interface characteristics using component mode synthesis. [Washington, DC : National Aeronautics and Space Administration, 1987.

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Gordis, Joshua H. Mast-antenna survivability : Structural dynamic design analysis by component mode synthesis. Monterey, Calif : Naval Postgraduate School, 1994.

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Petersen, Lynn James. Mast-antenna survivability : Structural dynamic design analysis by component mode synthesis. Monterey, Calif : Naval Postgraduate School, 1994.

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United States. National Aeronautics and Space Administration. et Case Western Reserve University. Dept. of Civil Engineering., dir. Dynamic substructuring by the boundary flexibility vector method of component mode synthesis. [Cleveland, Ohio] : Dept. of Civil Engineering, Case Western Reserve University, 1990.

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Brown, Andrew M. Development of a probabilistic component mode synthesis method for the analysis of non-deterministic substructures. Washington, DC : [National Aeronautics and Space Administration, 1995.

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Mei, C. Component mode synthesis and large deflection vibration of complex structures : Final report for the period ended January 31, 1987. [Washington, DC : National Aeronautics and Space Administration, 1987.

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Chapitres de livres sur le sujet "Component-mode synthesi"

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Wijker, Jaap. « Component Mode Synthesis ». Dans Mechanical Vibrations in Spacecraft Design, 369–98. Berlin, Heidelberg : Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-08587-5_18.

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Rixen, Daniel. « Substructuring Concepts and Component Mode Synthesis ». Dans Handbook of Experimental Structural Dynamics, 833–56. New York, NY : Springer New York, 2022. http://dx.doi.org/10.1007/978-1-4614-4547-0_16.

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Rixen, Daniel. « Substructruring Concepts and Component Mode Synthesis ». Dans Handbook of Experimental Structural Dynamics, 1–24. New York, NY : Springer New York, 2020. http://dx.doi.org/10.1007/978-1-4939-6503-8_16-1.

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Hou, Gene J. W., et Venkateshwarlu Maroju. « Component-Mode-Synthesis-Based Method for Structural Synthesis ». Dans Computational Mechanics ’95, 189–92. Berlin, Heidelberg : Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-79654-8_31.

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Crandall, S. H., et N. A. Yeh. « Component Mode Synthesis of Multi-Rotor Systems ». Dans Lecture Notes in Engineering, 44–55. Berlin, Heidelberg : Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-83040-2_5.

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Brink, A. R., D. G. Tipton, J. E. Freymiller et B. L. Stevens. « Methods for Component Mode Synthesis Model Generation for Uncertainty Quantification ». Dans Model Validation and Uncertainty Quantification, Volume 3, 177–88. Cham : Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-54858-6_19.

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Owens, Brian C., et Randall L. Mayes. « Verification of Experimental Component Mode Synthesis in the Sierra Analysis Framework ». Dans Dynamics of Coupled Structures, Volume 4, 1–5. Cham : Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-29763-7_1.

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De Fonseca, P., H. Van Brussel et P. Sas. « Component Mode Synthesis in the Design and Optimisation of Mechatronic Systems ». Dans Integrated Design and Manufacturing in Mechanical Engineering ’98, 217–24. Dordrecht : Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-015-9198-0_27.

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Carassale, Luigi, Andrea Bessone et Andrea Cavicchi. « Interface Reduction in Component Mode Synthesis of Bladed Disks by Orthogonal-Polynomial Series ». Dans Dynamics of Coupled Structures, Volume 4, 201–4. Cham : Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74654-8_17.

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Wolf, Walter L., Alan E. Duncan et Arthur R. Solomon. « Normal Modes Analysis of Structures Using an Out-of-Core Component Mode Synthesis Technique ». Dans CAD/CAM Robotics and Factories of the Future, 255–59. Berlin, Heidelberg : Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-52320-5_43.

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Actes de conférences sur le sujet "Component-mode synthesi"

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Bah, Mamadou, Prasanth Nair, Atul Bhaskar et Andy Keane. « Stochastic Component Mode Synthesis ». Dans 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Reston, Virigina : American Institute of Aeronautics and Astronautics, 2003. http://dx.doi.org/10.2514/6.2003-1750.

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Masarati, Pierangelo, Fanny Darbas et Israël Wander. « Compliant Interface in Component Mode Synthesis ». Dans ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/detc2020-22255.

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Abstract Substructuring, or component mode synthesis, requires components to share interface regions. When components modeled with rather different, often incompatible levels of refinement need to be connected, correctly defining the interfaces may be important. This work proposes the definition of the reduction of interface regions to the equivalent rigid-body motion which minimizes the strain energy in the structural component. The proposed formulation provides a natural and physically sound solution for the connection of detailed structural components within coarse, multi-rigid-body and 1D flexible models.
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Apiwattanalunggarn, Polarit, Steven W. Shaw et Christophe Pierre. « Component Mode Synthesis Using Nonlinear Normal Modes ». Dans ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48441.

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This paper describes a methodology for developing reduced-order dynamic models of nonlinear structural systems that are composed of an assembly of component structures. The approach is a nonlinear extension of the fixed-interface component mode synthesis technique developed for linear structures by Hurty and modified by Craig and Bampton. Specifically, the case of nonlinear substructures is handled by using fixed-interface nonlinear normal modes. These normal modes are constructed for the various substructures using an invariant manifold approach, and are then coupled through the traditional linear constraint modes (i.e., the static deformation shapes produced by unit interface motions). A simple system is used to demonstrate the proof of concept and show the effectiveness of the proposed procedure. Simulations are performed to show that the reduced-order model obtained from the proposed procedure outperforms the reduced-order model obtained from the classical fixed-interface linear component mode synthesis approach. Moreover, the proposed method is readily applicable to large-scale nonlinear structural systems.
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Castanier, Matthew P., Yung-Chang Tan et Christophe Pierre. « Characteristic Constraint Modes for Component Mode Synthesis ». Dans ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8187.

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Abstract In this paper, a technique is presented for improving the efficiency of the Craig-Bampton method of Component Mode Synthesis (CMS). An eigenanalysis is performed on the partitions of the CMS mass and stiffness matrices that correspond to the so-called constraint modes. The resultant eigenvectors are referred to as “characteristic constraint modes,” since they represent the characteristic motion of the interface between the component structures. By truncating the characteristic constraint modes, a CMS model with a highly-reduced number of degrees of freedom may be obtained. An example of a cantilever plate is considered. It is shown that relatively few characteristic constraint modes are needed to yield accurate approximations of the lower natural frequencies. This method also provides physical insight into the mechanisms of vibration transmission in complex structures.
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HUSTON, D., J. G. BELIVEAU et W. GRAVES. « Experimental verification of complex component mode synthesis ». Dans 32nd Structures, Structural Dynamics, and Materials Conference. Reston, Virigina : American Institute of Aeronautics and Astronautics, 1991. http://dx.doi.org/10.2514/6.1991-944.

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Taiping, Huang. « The Transfer Matrix–Component Mode Synthesis for Rotordynamic Analysis ». Dans ASME 1996 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-gt-079.

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The transfer matrix–component mode synthesis has been developed for the analysis of critical speed, response to imbalance and rotordynamic optimal design of multi–spool rotor system. This method adopted the advantages of the transfer matrix method for the train structure and the component mode synthesis for reducing degrees of freedom. In this method, the whole system is divided into several subsystems at the boundary coordinates. The constrained vibration modes and the static deflection curves of the constrained rotor subsystems are analysed by the improved transfer matrix method. The whole system is connected together by the component mode synthesis in accordance with the coordinate transformation. Numerical examples show that this method is superior to the traditional transfer matrix method and the component mode synthesis by FEM. This method has been successfully used for the rotordynamic analysis and optimal design of the compressors and the gas turbine aeroengines.
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SPANOS, J., et D. MINGORI. « Multibody model reduction by component mode synthesis and component cost analysis ». Dans 31st Structures, Structural Dynamics and Materials Conference. Reston, Virigina : American Institute of Aeronautics and Astronautics, 1990. http://dx.doi.org/10.2514/6.1990-1037.

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Zheng, Ji-zhou, et Yan Zhang. « Principle and Application of Component Mode Synthesis Method ». Dans 2010 International Conference on Measuring Technology and Mechatronics Automation (ICMTMA 2010). IEEE, 2010. http://dx.doi.org/10.1109/icmtma.2010.728.

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Kim, Jin-Gyun, Phill-Seung Lee et Kwang-Chun Park. « A MODE SELECTION ALGORITHM FOR THE FLEXIBILITY-BASED COMPONENT MODE SYNTHESIS ». Dans 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering Methods in Structural Dynamics and Earthquake Engineering. Athens : Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2015. http://dx.doi.org/10.7712/120115.3610.510.

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Ramani, Anand, et Charles E. Knight. « Application of Two-Step Component Mode Synthesis for System Eigensolutions ». Dans ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/cie-1627.

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Abstract Component Mode Synthesis (CMS) is a dynamic substructuring technique for approximate eigensolutions of large degree-of-freedom systems divisible into two or more components. System synthesis using component modes results in approximate eigenparameters. The approximation is improved by using more component modes in synthesis. Typically, all component modes up to x times the frequency range of interest are required to assure reasonable accuracy, where x varies from 2 to 10. This paper demonstrates the two-step CMS approach, wherein, the first step involves system synthesis using the minimum number of component modes (x∼1) required to obtain approximate eigenvalues up to a preselected frequency and the second step uses additional component modes in a convergence scheme operating on the system eigenparameters calculated in the first step. Results of studies on spring-mass systems, beam and plate models, and a refrigeration compressor assembly show that the two-step method provides the analyst some insight into the convergence and accuracy of the eigenparameters without resolving the system over and over with more component modes. The method is also efficient in terms of solution time, when compared to conventional CMS using the Jacobi method and the subspace-iteration method.
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