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Author: Grafiati

Published: 14 March 2023

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1

Wang, Gengxiang, Zepeng Niu, and Ying Feng. "Improved Craig–Bampton Method Implemented into Durability Analysis of Flexible Multibody Systems." Actuators 12, no. 2 (February 2, 2023): 65. http://dx.doi.org/10.3390/act12020065.

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The Craig–Bampton method is frequently applied in most commercial multibody dynamic software. Nevertheless, the Craig–Bampton modes only represent the free-free modes in flexible multibody systems. However, the free-free modes are incapable of all engineering applications. Hence, a rational set of reference conditions must be correctly chosen to define a unique displacement field. Firstly, a simple 2D beam with two revolute joints is taken as an example to prove that the free-free modes are not suitable for all engineering applications, and the results are validated by ANSYS and the analytical solution. Secondly, the Craig–Bampton method is improved by two different methods: (i) the reference conditions are added to the original Craig–Bampton matrix and (ii) the reference conditions are applied to the shape functions to redefine the mass and stiffness matrices before constructing the original Craig–Bampton matrix. This implementation illustrates that the improved Craig–Bampton matrix can not only generate the free-free modes but is also suitable for the non-free-free modes. Finally, two discrepant reference conditions are imposed to obtain the dynamic response of the flexible connecting rod based on the improved Craig–Bampton method, which is validated using the normal mode approach. Simulations show that the improved Craig–Bampton method can be used as a general-purpose method in durability analysis.

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2

Kluger, Jocelyn, Lynn Crevier, and Martin Udengaard. "Speed-Dependent Eigenmodes for Efficient Simulation of Transverse Rotor Vibration." Vibration 5, no. 4 (October 31, 2022): 732–54. http://dx.doi.org/10.3390/vibration5040043.

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Accurate, computationally efficient simulations enable engineers to design high-performing, cost-efficient, lightweight machines that can leverage models of predictive controls and digital twin predictive maintenance schedules. This study demonstrates a new speed-dependent eigenmode method for accurately and efficiently simulating shaft transverse vibrations. The method involves first independently computing shaft eigenmodes over a range of operating speeds, then correlating the eigenmodes across the different speeds during compilation, and finally adjusting modal properties gradually in accordance with a lookup method during simulation. The new method offers several distinct advantages over the traditional static eigenmodes and Craig-Bampton methods. The new method maintains accuracy over a large range of shaft rotation speeds whereas the static eigenmodes method does not. The new method typically requires fewer modal degrees of freedom than the Craig-Bampton method. Whereas the Craig-Bampton method is limited to modeling changes at the boundaries, the new method is suitable for modeling changing body properties as well as boundary-based changes. For this paper, a fluid-bearing-supported 10 MW direct-drive wind turbine drive shaft is tested virtually in a simulation model developed in Simscape™ Driveline™. Using the simulation statistics, this study compares the accuracy and computational efficiency of the speed-dependent eigenmode method to the traditional finite lumped element, static eigenmode, and Craig–Bampton methods. This paper shows that the new method simulates the chosen system 5 times faster than the traditional lumped mass method and 2.4 times faster than the Craig-Bampton method.

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3

Leoro, Jose, Vladislav Borisenko, Egor Degilevich, and Anton Didenko. "Application of the Craig-Bampton method to blade rotation." E3S Web of Conferences 258 (2021): 09075. http://dx.doi.org/10.1051/e3sconf/202125809075.

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The Craig-Bampton method has repeatedly shown its effectiveness in modelling the deformable solid body motion and in practical experience of implementing this approach in engineering software. It reduces the motion equations system which is obtained by approximating small elastic displacements of the body finite element model with a set of acceptable modes. The application of this method in engineering improves the computing time performance and requires less computational resources. In this article the effectiveness of using the Craig-Bampton method for the blade rotation is evaluated. The need to consider the inertial relationship between large body displacements and elastic deformations was investigated. As a result of the numerical solution, it was obtained that the method works correctly for the investigated task. It allows us to conclude that the Craig-Bampton method is applicable for the blade rotation process.

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4

Kim, Jin-Gyun, and Phill-Seung Lee. "An enhanced Craig-Bampton method." International Journal for Numerical Methods in Engineering 103, no. 2 (March 26, 2015): 79–93. http://dx.doi.org/10.1002/nme.4880.

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5

Morgan, J. A., C. Pierre, and G. M. Hulbert. "Calculation of Component Mode Synthesis Matrices From Measured Frequency Response Functions, Part 2: Application." Journal of Vibration and Acoustics 120, no. 2 (April 1, 1998): 509–16. http://dx.doi.org/10.1115/1.2893859.

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This paper demonstrates how to calculate Craig-Bampton component mode synthesis matrices from measured frequency response functions. The procedure is based on a modified residual flexibility method, from which the Craig-Bampton CMS matrices are recovered, as presented in the companion paper, Part I (Morgan et al., 1998). A system of two coupled beams is analyzed using the experimentally-based method. The individual beams’ CMS matrices are calculated from measured frequency response functions. Then, the two beams are analytically coupled together using the test-derived matrices. Good agreement is obtained between the coupled system and the measured results.

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6

Morgan, J. A., C. Pierre, and G. M. Hulbert. "Calculation of Component Mode Synthesis Matrices From Measured Frequency Response Functions, Part 1: Theory." Journal of Vibration and Acoustics 120, no. 2 (April 1, 1998): 503–8. http://dx.doi.org/10.1115/1.2893858.

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This paper presents a new method to calculate the so-called Craig-Bampton component mode synthesis (CMS) matrices from measured frequency response functions. The procedure is based on a modified residual flexibility method, from which the Craig-Bampton CMS matrices are recovered. Experimental implementation of the method requires estimating the modal parameters corresponding to the measured free boundary modes and the Maclaurin series expansion coefficients corresponding to the omitted modes. Theoretical developments are presented in the present paper, Part 1. The performance of the new method is then demonstrated in Part 2 (Morgan et al., 1998) by comparison of experiment and analysis for a simple two-beam system.

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7

Boo, Seung-Hwan, Jeong-Ho Kim, and Phill-Seung Lee. "Towards improving the enhanced Craig-Bampton method." Computers & Structures 196 (February 2018): 63–75. http://dx.doi.org/10.1016/j.compstruc.2017.10.017.

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8

Borisenko, V., J. Leoro, and A. Didenko. "Main rotor blade modeling approaches comparison. Finite element and Craig-Bampton methods." Journal of Physics: Conference Series 2131, no. 3 (December 1, 2021): 032096. http://dx.doi.org/10.1088/1742-6596/2131/3/032096.

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Abstract The paper focuses on the helicopter main rotor blade FE model. And the main goal is to prove the feasibility of the helicopter main rotor MBD model in calculations of blade deformation as a result of applied aerodynamic forces. FE model is used as a basis for two different computational methods. A mathematical approach in the MBD based on the Craig-Bampton method on the one hand. And finite element model on the other hand. The results of high-frequency blade rotations are obtained. Calculations of these models are compared in order to determine the best method for modeling a linear-elastic blade. By the results, it is necessary to consider the preloaded state of the blade when using the Craig-Bampton method approach. The comparison of blade nodes displacements at various external conditions for both models are given. The influence of rotor MBS model damping parameters on the amplitude of blade oscillations under sinusoidal action is considered.

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9

Rixen, Daniel J. "A dual Craig–Bampton method for dynamic substructuring." Journal of Computational and Applied Mathematics 168, no. 1-2 (July 2004): 383–91. http://dx.doi.org/10.1016/j.cam.2003.12.014.

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10

Pařík, Petr, Jin-Gyun Kim, Martin Isoz, and Chang-uk Ahn. "A Parallel Approach of the Enhanced Craig–Bampton Method." Mathematics 9, no. 24 (December 16, 2021): 3278. http://dx.doi.org/10.3390/math9243278.

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The enhanced Craig–Bampton (ECB) method is a novel extension of the original Craig–Bampton (CB) method, which has been widely used for component mode synthesis (CMS). The ECB method, using residual modal compensation that is neglected in the CB method, provides dramatic accuracy improvement of reduced matrices without an increasing number of eigenbasis. However, it also needs additional computational requirements to treat the residual flexibility. In this paper, an efficient parallelization of the ECB method is presented to handle this issue and accelerate the applicability for large-scale structural vibration problems. A new ECB formulation within a substructuring strategy is derived to achieve better scalability. The parallel implementation is based on OpenMP parallel architecture. METIS graph partitioning and Linear Algebra Package (LAPACK) are used to automated algebraic partitioning and computational linear algebra, respectively. Numerical examples are presented to evaluate the accuracy, scalability, and capability of the proposed parallel ECB method. Consequently, based on this work, one can expect effective computation of the ECB method as well as accuracy improvement.

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11

Kammer, D. C., and M. J. Triller. "Selection of Component Modes for Craig-Bampton Substructure Representations." Journal of Vibration and Acoustics 118, no. 2 (April 1, 1996): 264–70. http://dx.doi.org/10.1115/1.2889657.

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Three measures of modal dynamic importance are studied for the purpose of ranking Craig-Bampton substructure fixed interface mode shapes based upon their contribution to forces at the substructure interface, modal velocity, or modal displacement. These measures can be employed to identify mode shapes which are dynamically important and thus should be retained in a reduced analytical representation, or identified during a modal survey of the substructure. The first method considered. Effective Interface Mass, has been studied previously. However, new results are presented showing the relation between Effective Interface Mass and a commonly used control dynamics measure of modal importance called approximate balanced singular values. In contrast to the general case of approximate balanced singular values, Effective Interface Mass always gives an absolute measure of the dynamic importance of mode shapes. The EIM method is extended to consider modal velocity and modal displacement outputs. All three measures are applied to a simple substructure called the General Purpose Spacecraft. It is shown that each of these measures provides an efficient method for ranking the dynamic importance of Craig-Bampton fixed interface modes such that a reduced representation will accurately reproduce the substructure’s response in the frequency range of interest.

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12

Triller, Michael J., and Daniel C. Kammer. "Controllability and observability measures for Craig-Bampton substructure representations." Journal of Guidance, Control, and Dynamics 17, no. 6 (November 1994): 1198–204. http://dx.doi.org/10.2514/3.21333.

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13

Kim, Jin-Gyun, Kang-Heon Lee, and Phill-Seung Lee. "Estimating relative eigenvalue errors in the Craig-Bampton method." Computers & Structures 139 (July 2014): 54–64. http://dx.doi.org/10.1016/j.compstruc.2014.04.008.

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14

Kim, Jeong-Ho, Jaemin Kim, and Phill-Seung Lee. "Improving the accuracy of the dual Craig-Bampton method." Computers & Structures 191 (October 2017): 22–32. http://dx.doi.org/10.1016/j.compstruc.2017.05.010.

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15

Yotov, V. V., M. Remedia, G. S. Aglietti, and G. Richardson. "Improved Craig–Bampton stochastic method for spacecraft vibroacoustic analysis." Acta Astronautica 178 (January 2021): 556–70. http://dx.doi.org/10.1016/j.actaastro.2020.07.011.

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16

Legrand, Mathias, Dongying Jiang, Christophe Pierre, and Steven W. Shaw. "Nonlinear Normal Modes of a Rotating Shaft Based on the Invariant Manifold Method." International Journal of Rotating Machinery 10, no. 4 (2004): 319–35. http://dx.doi.org/10.1155/s1023621x04000338.

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The nonlinear normal mode methodology is generalized to the study of a rotating shaft supported by two short journal bearings. For rotating shafts, nonlinearities are generated by forces arising from the supporting hydraulic bearings. In this study, the rotating shaft is represented by a linear beam, while a simplified bearing model is employed so that the nonlinear supporting forces can be expressed analytically. The equations of motion of the coupled shaft-bearings system are constructed using the Craig–Bampton method of component mode synthesis, producing a model with as few as six degrees of freedom (d.o.f.). Using an invariant manifold approach, the individual nonlinear normal modes of the shaft-bearings system are then constructed, yielding a single-d.o.f. reduced-order model for each nonlinear mode. This requires a generalized formulation for the manifolds, since the system features damping as well as gyroscopic and nonconservative circulatory terms. The nonlinear modes are calculated numerically using a nonlinear Galerkin method that is able to capture large amplitude motions. The shaft response from the nonlinear mode model is shown to match extremely well the simulations from the reference Craig–Bampton model.

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17

Berthillier, M., C. Dupont, R. Mondal, and J. J. Barrau. "Blades Forced Response Analysis With Friction Dampers." Journal of Vibration and Acoustics 120, no. 2 (April 1, 1998): 468–74. http://dx.doi.org/10.1115/1.2893853.

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A multiharmonic frequency domain analysis combined with a Craig-Bampton component mode synthesis is presented to compute the dry friction damped forced response of blades. The accuracy of the analysis is established, for a cantilever beam with a dry friction damper attached, by comparison with experimental results and time domain analysis. The method has then been applied to a model fan blade damped by a blade to ground damper.

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18

Wandinger, Johannes. "A symmetric Craig‐Bampton method of coupled fluid‐structure systems." Engineering Computations 15, no. 4 (June 1998): 450–61. http://dx.doi.org/10.1108/02644409810219811.

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19

Go, Myeong-Seok, Jae Hyuk Lim, Jin-Gyun Kim, and Ki-ryoung Hwang. "A family of Craig–Bampton methods considering residual mode compensation." Applied Mathematics and Computation 369 (March 2020): 124822. http://dx.doi.org/10.1016/j.amc.2019.124822.

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20

Eberhard, Peter, and Philip Holzwarth. "Coupling Elastic Bodies with an Enhanced Craig-Bampton-like Scheme." PAMM 15, no. 1 (October 2015): 51–52. http://dx.doi.org/10.1002/pamm.201510016.

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21

Akçay Perdahcıoğlu, D., M. H. M. Ellenbroek, H. J. M. Geijselaers, and A. de Boer. "Updating the Craig-Bampton reduction basis for efficient structural reanalysis." International Journal for Numerical Methods in Engineering 85, no. 5 (December 29, 2010): 607–24. http://dx.doi.org/10.1002/nme.2983.

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22

Pradeepkumar, S., and P. Nagaraj. "Tactile Response Characterization of a Dynamic System Using Craig-Bampton Method." Sound&Vibration 56, no. 3 (2022): 221–33. http://dx.doi.org/10.32604/sv.2022.014889.

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23

Wu, Long, Paolo Tiso, and Fred van Keulen. "Interface Reduction with Multilevel Craig–Bampton Substructuring for Component Mode Synthesis." AIAA Journal 56, no. 5 (May 2018): 2030–44. http://dx.doi.org/10.2514/1.j056196.

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24

Krattiger, Dimitri, Long Wu, Martin Zacharczuk, Martin Buck, Robert J. Kuether, Matthew S. Allen, Paolo Tiso, and Matthew R. W. Brake. "Interface reduction for Hurty/Craig-Bampton substructured models: Review and improvements." Mechanical Systems and Signal Processing 114 (January 2019): 579–603. http://dx.doi.org/10.1016/j.ymssp.2018.05.031.

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25

Lei, Zhen, Frederic Gillot, and Louis Jezequel. "Modal Synthesis with the Isogeometric Kirchhoff–Love Shell Elements." International Journal of Applied Mechanics 09, no. 02 (March 2017): 1750017. http://dx.doi.org/10.1142/s175882511750017x.

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The modal synthesis method is frequently used for the analysis of large structures composed of multiple parts concerning dynamic aspects. In this paper, we extended the modal synthesis method under the isogeometric analysis framework. The isogeometric Kirchhoff–Love shell elements are used for the analysis of the substructures, the Craig–Bampton method is used for the modal synthesis and the bending-strip method is used for the substructures coupling. We give examples on the modal analysis and the harmonic response analysis. The results show the effectiveness of the method.

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26

Feng, Hui-hua, Xiao-long Mou, and Khaled Teffah. "Stabilized Solution to Spurious Mode Problem and Ill-Conditioning in Interface Force Based Substructure Coupling Method." Shock and Vibration 2018 (July 17, 2018): 1–12. http://dx.doi.org/10.1155/2018/1589794.

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There are two major types of substructure mode synthesis methods, i.e., the fixed-interface component mode synthesis and free-interface component mode synthesis. There are two coupling methods, the interface degrees of freedom based coupling method and the interface force based coupling method, the former one is referred to as the primary assembly method, and the latter is referred to as the dual assembly method. However, the dual assembly method is theoretically shown to be unstable in this research, such reduced stiffness matrix is indefinite, this fatal weakness can be conquered by further interface reduction, and the interface compatibility is therefore rigorously enforced. Unfortunately, Craig’s method leads to another numerical instability when inverting a submatrix of residual flexibility on the interface degrees of freedom, this problem is neglectable in small dimensional matrix problems, but it is prominent in large models when the number of interface degrees of freedom is large, this ill-conditioning problem may be circumvented by truncated singular value decomposition technique; here, a more efficient strategy is proposed, the substructure reduction is modified, this modification proves to be numerically stable, and it can be even more accurate than the prevailing Craig-Bampton method; the numerical examples validate the suggestion.

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27

Kammer, Daniel C., and Mary Baker. "Comparison of the Craig-Bampton and residual flexibility methods of substructure representation." Journal of Aircraft 24, no. 4 (April 1987): 262–67. http://dx.doi.org/10.2514/3.45435.

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28

Vizzini, Simone, Magnus Olsson, and Alessandro Scattina. "Component mode synthesis methods for a body-in-white noise and vibration analysis." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 231, no. 2 (August 5, 2016): 279–88. http://dx.doi.org/10.1177/0954407016656542.

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In this work the dynamic substructuring approach was applied to a noise, vibration and harshness problem within the automotive engineering field. In particular, a noise, vibration and harshness analysis was carried out on the body-in-white structure of a passenger car. The work focuses on the theory of component mode synthesis. Two component mode synthesis reduction methods, namely the Craig–Bampton method and the Craig–Chang method, were applied to the body-in-white structure of the Volvo V40. The influences of various parameters were investigated. In particular, the effect of the reduction basis on the response accuracy and on the reduction time was studied. Moreover, the effects of the connection properties between different parts of the model were examined. The simulation times of the reduced models and of the full finite element model were compared. The results showed that the Craig–Chang method performs better when the modes are retained for up to one and a half times the maximum frequency response studied. Additionally, the Craig–Chang method gives a very accurate representation of the system dynamics even when connections with a low stiffness are used. Finally, it is possible to reduce the simulation time by up to 90% if component mode synthesis methods are used instead of the full finite element model.

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29

Kim, Jaemin, Seung-Hwan Boo, and Phill-Seung Lee. "Considering the Higher-Order Effect of Residual Modes in the Craig–Bampton Method." AIAA Journal 56, no. 1 (January 2018): 403–12. http://dx.doi.org/10.2514/1.j055666.

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30

Kammer, Daniel C., Mathew S. Allen, and Randy L. Mayes. "Formulation of an experimental substructure model using a Craig–Bampton based transmission simulator." Journal of Sound and Vibration 359 (December 2015): 179–94. http://dx.doi.org/10.1016/j.jsv.2015.09.002.

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31

Wang, Gengxiang, and Liang Wang. "Coupling relationship of the non-ideal parallel mechanism using modified Craig-Bampton method." Mechanical Systems and Signal Processing 141 (July 2020): 106471. http://dx.doi.org/10.1016/j.ymssp.2019.106471.

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32

De Lellis, Salvatore, Alessandro Stabile, Guglielmo S. Aglietti, and Guy Richardson. "Structural uncertainty estimation through a Craig-Bampton Stochastic Method optimisation in satellites structures." Journal of Sound and Vibration 469 (March 2020): 115123. http://dx.doi.org/10.1016/j.jsv.2019.115123.

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33

Lim, Jae Hyuk, Do-Soon Hwang, Kyoung-Won Kim, Geun Ho Lee, and Jin-Gyun Kim. "A coupled dynamic loads analysis of satellites with an enhanced Craig–Bampton approach." Aerospace Science and Technology 69 (October 2017): 114–22. http://dx.doi.org/10.1016/j.ast.2017.06.023.

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34

Gruber, Fabian M., and Daniel J. Rixen. "A Dual Craig-Bampton State-Space Approach for Model Reduction of Damped Systems." PAMM 17, no. 1 (December 2017): 303–4. http://dx.doi.org/10.1002/pamm.201710121.

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35

Ciurezu-Gherghe, Leonard Marius, Gabriel Cătălin Marinescu, Andra Raluca Constantin, and Nicolae Dumitru. "Dynamic Modal Analysis of a Mechanical System with Deformable Elements." Applied Mechanics and Materials 896 (February 2020): 75–82. http://dx.doi.org/10.4028/www.scientific.net/amm.896.75.

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This paper addresses to a dynamic modal analysis of a crank-type mechanism. The proposed mechanism will have all the components considered as deformable bodies. Thus, the proposed research consists on two methods, namely an analytical and a numerical one. The analytical method allows to identify the static and dynamic components of the matrices that from the equation of motion based on the Kane formalism and the finite element modeling. The numerical method is based on the virtual prototyping of the whole assembly with the ADAMS software. In this case, for the deformable bodies analysis, will be used the method of superposition which have on its base the modal analysis and the RR Craig and MCC Bampton procedure.

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36

Pölöskei, Tamás, and András Szekrényes. "Dynamic stability analysis of reduced delaminated planar beam structures using extended Craig-Bampton method." Applied Mathematical Modelling 102 (February 2022): 153–69. http://dx.doi.org/10.1016/j.apm.2021.09.024.

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37

Yin, Xiao-chun, Peng-bo Qian, and Lin-fang Qian. "Improved Craig-Bampton method for transient analysis of structures with large-scale plastic deformation." Journal of Vibroengineering 19, no. 2 (March 31, 2017): 812–30. http://dx.doi.org/10.21595/jve.2016.17288.

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38

Hughes, Patrick J., and Robert J. Kuether. "Nonlinear Interface Reduction for Time-Domain Analysis of Hurty/Craig-Bampton Superelements with Frictional Contact." Journal of Sound and Vibration 507 (September 2021): 116154. http://dx.doi.org/10.1016/j.jsv.2021.116154.

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39

Zucca, Stefano. "On the dual Craig–Bampton method for the forced response of structures with contact interfaces." Nonlinear Dynamics 87, no. 4 (November 16, 2016): 2445–55. http://dx.doi.org/10.1007/s11071-016-3202-6.

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40

Song, Shun Guang, Chun Jie Wang, Han Wang, and Qiu Hong Lin. "Dynamic Analysis of Extendible Support Structure Deployment." Applied Mechanics and Materials 163 (April 2012): 91–94. http://dx.doi.org/10.4028/www.scientific.net/amm.163.91.

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To study the dynamic behavior of the extendible support structure deployment, a digital simulation using the multibody system dynamics methodology is conducted. Floating frame of reference formulations are used to establish the flexible dynamics model, in which the deformation vector of each flexible part is modeled with the component mode synthesis technique based on the Craig-Bampton method. Modal truncation is implemented through modal participation factors to reduce the computational burden. Angular displacements results of antenna panels as well as those of truss rods are then obtained and show that all parts of the structure have reached accurate positions and keep stable after deployment as expected. Start torque of the driving motor is also acquired and proved acceptable according to the design requirements. Impact forces acting on the hinges at locking moment are finally extracted to evaluate performances of locking processes.

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41

Schmidt, Henry, David Kriebel, and Jan Mehner. "Reduced Order Component & System Level Modelling for Fluid-Solid Interactions in Complex MEMS Devices." Proceedings 2, no. 13 (January 11, 2019): 937. http://dx.doi.org/10.3390/proceedings2130937.

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The time-efficient and accurate implementation of physics-based fluidic damping effects is still one of the biggest challenges in the simulation of complex MEMS devices. Two modelling approaches utilizing the CRAIG/BAMPTON component mode synthesis method are discussed and compared in context of a highly automated model generation procedure. The first approach uses a modal projection technique with pressure profiles obtained from REYNOLDS flow simulations using the thermal-fluidic analogy. The second approach is based on the representation of the fluidic domain in form of a generalized KIRCHHOFFian lumped flow resistance network model. Both methods are generally suited for the simulation of structures like gyroscopes or accelerometers, but show different behaviors in terms of scaling and complexity during the model generation step and in the final ROM. The methods are demonstrated on examples and are compared to optical measurements of an out-of-plane teeter-totter type accelerometer.

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42

Gruber, Fabian M., and Daniel J. Rixen. "Dual Craig-Bampton component mode synthesis method for model order reduction of nonclassically damped linear systems." Mechanical Systems and Signal Processing 111 (October 2018): 678–98. http://dx.doi.org/10.1016/j.ymssp.2018.04.019.

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43

Xian Bin, Teng, and Zhang Jun Dong. "Marine Four-Stroke Diesel Engine Crankshaft Main Bearing Oil Film Lubrication Characteristic Analysis." Polish Maritime Research 25, s2 (August 1, 2018): 30–34. http://dx.doi.org/10.2478/pomr-2018-0070.

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Abstract The Craig-Bampton modal synthesis method was used to establish the dynamic model of marine four-stroke diesel engine body and crankshaft. Based on the Greenwood/Tripp microlong contact theory considering the surface roughness and the generalized Reynolds equation considering the oil filling rate, the elastohydrodynamic lubrication model of the main bearing of the four - stroke diesel engine is found. At the rated speed, the lubrication performance of the main bearing is simulated and analyzed by the maximum dynamic pressure, the minimum oil film thickness and the friction power. The results show that the oil pressure of 4 # main bearing is the largest and the maximum oil film pressure is in the 4 # main bearing position. The friction load of 4 # main bearing is the largest. The average oil film thickness of 4 # main bearing is the smallest and the minimum oil film The thickness also occurred in the 4 # main bearing position; it can be seen 4 # bearing the most bad lubrication conditions.

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44

Rapo, Marja Liisa, Jukka Aho, Hannu Koivurova, and Tero Frondelius. "Implementing model reduction to the JuliaFEM platform." Rakenteiden Mekaniikka 51, no. 1 (August 16, 2018): 36–54. http://dx.doi.org/10.23998/rm.69026.

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JuliaFEM is an open source finite element method solver written in the Julia language. This paper presents an implementation of two common model reduction methods: the Guyan reduction and the Craig-Bampton method. The goal was to implement these algorithms to the JuliaFEM platform and demonstrate that the code works correctly. This paper first describes the JuliaFEM concept briefly after which it presents the theory of model reduction, and finally, it demonstrates the implemented functions in an example model. This paper includes instructions for using the implemented algorithms, and reference the code itself in GitHub. The reduced stiness and mass matrices give the same results in both static and dynamic analyses as the original matrices, which proves that the code works correctly. The code runs smoothly on relatively large model of 12.6 million degrees of freedom. In future, damping could be included in the dynamic condensation now that it has been shown to work.

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Vrána, Tomáš, Josef Bradáč, and Jan Kovanda. "ELASTO-KINEMATIC COMPUTATIONAL MODEL OF SUSPENSION WITH FLEXIBLE SUPPORTING ELEMENTS." Acta Polytechnica 56, no. 2 (April 30, 2016): 147. http://dx.doi.org/10.14311/ap.2016.56.0147.

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This paper analyzes the impact of flexibility of individual supporting elements of independent suspension on its elasto-kinematic characteristics. The toe and camber angle are the geometric parameters of the suspension, which waveforms and their changes under the action of vertical, longitudinal and transverse forces affect the stability of the vehicle. To study these dependencies, the computational multibody system (MBS) model of axle suspension in the system HyperWorks is created. There are implemented Finite-Element-Method (FEM) models reflecting the flexibility of the main supporting elements. These are subframe, the longitudinal arms, transverse arms and knuckle. Flexible models are developed using Component Mode Synthesis (CMS) by Craig-Bampton. The model further comprises force elements, such as helical springs, shock absorbers with a stop of the wheel and the anti-roll bar. Rubber-metal bushings are modeled flexibly, using nonlinear deformation characteristics. Simulation results are validated by experimental measurements of geometric parameters of real suspension.

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46

Palomba, Ilaria, Dario Richiedei, and Alberto Trevisani. "Energy-Based Optimal Ranking of the Interior Modes for Reduced-Order Models under Periodic Excitation." Shock and Vibration 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/348106.

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This paper introduces a novel method for ranking and selecting the interior modes to be retained in the Craig-Bampton model reduction, in the case of linear vibrating systems under periodic excitation. The aim of the method is to provide an effective ranking of such modes and hence an optimal sequence according to which the interior modes should be progressively included to achieve a desired accuracy of the reduced-order model at the frequencies of interest, while keeping model dimensions to a minimum. An energy-based ranking (EBR) method is proposed, which exploits analytical coefficients to evaluate the contribution of each interior mode to the forced response of the full-order system. The application of the method to two representative systems is discussed: an ultrasonic horn and a vibratory feeder. The results show that the EBR method provides a very effective ranking of the most important interior modes and that it outperforms other state-of-the-art benchmark techniques.

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Sommariva, Alessandro, and Stefano Zucca. "A Comparison between Two Reduction Strategies for Shrouded Bladed Disks." Applied Sciences 8, no. 10 (September 26, 2018): 1736. http://dx.doi.org/10.3390/app8101736.

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Shrouded bladed disks exhibit a nonlinear dynamic behavior due to the contact interfaces at shrouds between neighboring blades. As a result, reduced order models (ROMs) are mandatory to compute the response levels during the design phase for high cycle fatigue (HCF) life assessment. In this paper, two reduction strategies for shrouded bladed disk reduction are presented. Both approaches rely on: (i) the cyclic symmetry of the linear bladed disk with open shrouds to perform only single sector calculations, (ii) the Craig–Bampton (CB) method to reduce the number of physical degrees of freedom (dofs). The two approaches are applied to a set of test cases in order to evaluate and compare their accuracy and the associated computational effort. Although both approaches allow for generating accurate ROMs, it is found that the numerical efficiency of the two methods depends on the ratio of the number of nodes at the inter-sector interfaces over the number of inner nodes of the elementary sector model.

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Liu, D. S., and Y. W. Chen. "Application of Craig-Bampton Reduction Technique and 2D Dynamic Infinite Element Modeling Approach to Membrane Vibration Problems." Journal of Mechanics 35, no. 4 (December 26, 2018): 513–25. http://dx.doi.org/10.1017/jmech.2018.45.

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ABSTRACTAn approach is presented for solving membrane vibration problems using an integrated scheme consisting of the Craig-Bampton (CB) reduction technique and a 2D dynamic infinite element modeling (DIEM) method. In the proposed CB-DIEM scheme, the substructure domain is partitioned into multiple layers of geometrically-similar infinite elements (IEs) which use only the data of the boundary nodes. A convergence criterion based on the first invariant of the DIEM mass matrix is used to determine the optimal parameters of the CB-DIEM scheme, namely the proportionality ratio and number of layers in the DIEM partitioning process and the number of retained frequency modes in the CB reduction method. Furthermore, in implementing the CB method, the inversion of the global stiffness matrix is calculated using only the stiffness matrix of the first element layer. Having reduced the DIEM model, a coupled DIE-FE algorithm is employed to model the dynamic problems of the full structure, which removes the respective methods disadvantages while keeping their advantages. The validity and performance of the proposed CB-DIEM method are investigated by means of three illustrative problems.

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Kim, Jin-Gyun, Jaho Seo, and Jae Hyuk Lim. "Novel modal methods for transient analysis with a reduced order model based on enhanced Craig–Bampton formulation." Applied Mathematics and Computation 344-345 (March 2019): 30–45. http://dx.doi.org/10.1016/j.amc.2018.09.070.

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Fang, Ming, Jian Wang, and Hui Li. "An adaptive numerical scheme based on the Craig-Bampton method for the dynamic analysis of tall buildings." Structural Design of Tall and Special Buildings 27, no. 1 (August 8, 2017): e1410. http://dx.doi.org/10.1002/tal.1410.

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