Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-15T17:14:04.781Z Has data issue: false hasContentIssue false
  • English
  • Français

Vibration Calculation of Spatial Multibody Systems Based on Constraint-Topology Transformation

Published online by Cambridge University Press:  07 December 2011

W. Jiang ,
X. D. Chen ,
X. Luo ,
Y. T. Hu  and
H. P. Hu
W. Jiang
Affiliation:
State Key Laboratory of Digital Manufacturing Equipment & Technology, Huazhong University of Science and Technology, Wuhan 430074, China
X. D. Chen*
Affiliation:
State Key Laboratory of Digital Manufacturing Equipment & Technology, Huazhong University of Science and Technology, Wuhan 430074, China
X. Luo
Affiliation:
State Key Laboratory of Digital Manufacturing Equipment & Technology, Huazhong University of Science and Technology, Wuhan 430074, China
Y. T. Hu
Affiliation:
Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China
H. P. Hu
Affiliation:
Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China
*
**Professor, corresponding author
Get access

Abstract

Many kinds of mechanical systems can be modeled as spatial rigid multibody systems (SR-MBS), which consist of a set of rigid bodies interconnected by joints, springs and dampers. Vibration calculation of SR-MBS is conventionally conducted by approximately linearizing the nonlinear equations of motion and constraint, which is very complicated and inconvenient for sensitivity analysis. A new algorithm based on constraint-topology transformation is presented to derive the oscillatory differential equations in three steps, that is, vibration equations for free SR-MBS are derived using Lagrangian method at first; then, an open-loop constraint matrix is derived to obtain the vibration equations for open-loop SR-MBS via quadric transformation; finally, a cut-joint constraint matrix is derived to obtain the vibration equations for closed-loop SR-MBS via quadric transformation. Through mentioned above, the vibration calculation can be significantly simplified and the sensitivity analysis can be conducted conveniently. The correctness of the proposed method has been verified by numerical experiments in comparison with the traditional approaches.

Keywords

Multibody systemVibration calculationConstraint-topology transformation
Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 4 , December 2011 , pp. 479 - 491
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Flores, P., Ambrósio, J., Claro, P. and Lankarani, H. M., “Kinematics and Dynamics of Multibody Systems with Imperfect Joints: Models and Case Studies, Springer-Verlag,” Berlin, Germany, pp. 24–25 (2008).Google Scholar
2.Wittbrodt, E., Adamiec-Wójcik, I. and Wojciech, S., “Dynamics of Flexible Multibody Systems: Rigid Finite Element Method, Springer-Verlag,” Berlin, Germany, pp. 37–45 (2006).Google Scholar
3.Wittenburg, J., “Dynamics of Multibody Systems, Springer-Verlag,” Berlin, Germany, pp. 162–192 (2008).Google Scholar
4.Schiehlen, W., Guse, N. and Seifried, R., “Multibody Dynamics in Computational Mechanics and Engineering Applications,” Computer Methods in Applied Mechanics and Engineering, 195, pp. 5509–5522 (2006).CrossRefGoogle Scholar
5.Laulusa, A. and Bauchau, O. A., “Review of Classical Approaches for Constraint Enforcement in Multibody Systems,” Journal of Computational and Nonlinear Dynamics, 3, pp. 011004 (2008).CrossRefGoogle Scholar
6.Pott, A., Kecskeméthy, A. and Hiller, M., “A Simplified Force-based Method for the Linearization and Sensitivity Analysis of Complex Manipulation Systems,” Mechanism and Machine Theory, 42, pp. 1445–1461 (2007).CrossRefGoogle Scholar
7.Cruz, H. D., Biscay, R. J., Carbonell, F., Ozaki, T. and Jimenez, J. C., “A Higher Order Local Linearization Method for Solving Ordinary Differential Equations,” Applied Mathematics and Computation, 185, pp. 197–212 (2007).CrossRefGoogle Scholar
8.Negrut, D. and Ortiz, J. L., “A Practical Approach for the Lnearization of the Constrained Multibody Dynamics Equations,” Journal of Computational and Nonlinear Dynamics, 1, pp. 230–239 (2006).CrossRefGoogle Scholar
9.Minaker, B. and Frise, P., “Linearizing the Equations of Motion for Multibody Systems Using an Orthogonal Complement Method,” Journal of Vibration and Control, 11, pp. 51–66 (2005).CrossRefGoogle Scholar
10.Roy, D. and Kumar, R., “A Multi-step Transversal Linearization (MTL) Method in Non-linear Structural Dynamics,” Journal of Sound and Vibration, 287, pp. 203–226 (2005).CrossRefGoogle Scholar
11.Wasfy, T. M. and Noor, A. K., “Computational Strategies for Flexible Multibody Systems,” Applied Mechanics Review, 56, pp. 553–613 (2003).CrossRefGoogle Scholar
12.McPhee, J. J. and Redmond, S. M., “Modelling Multibody Systems with Indirect Coordinates,” Computer Methods in Applied Mechanics and Engineering, 195, pp. 6942–6957 (2006).CrossRefGoogle Scholar
13.Liu, J. Y., Hong, J. Z. and Cui, L., “An Exact Nonlinear Hybrid-coordinate Formulation for Flexible Multibody Systems,” Acta Mechanica Sinica, 23, pp. 699–706 (2007).CrossRefGoogle Scholar
14.Valasek, M., Sika, Z. and Vaculin, O., “Multibody Formalism for Real-time Application Using Natural Coordinates and Modified State Space,” Multibody System Dynamics, 17, pp. 209–227 (2007).CrossRefGoogle Scholar
15.Attia, H. A., “Modelling of Three-dimensional Mechanical Systems Using Point Coordinates with a Recursive Approach,” Applied Mathematical Modelling, 32, pp. 315–326 (2008).CrossRefGoogle Scholar
16.Amirouche, F., Fundamentals of Multibody Dynamics: Theory and Applications, Boston: Birkhauser, pp. 225–316 (2006).Google Scholar
17.Eberhard, P. and Schiehlen, W., “Computational Dynamics of Multibody Systems: History, Formalisms, and Applications,” Journal of Computational and Nonlinear Dynamics, 1, pp. 3–12 (2006).CrossRefGoogle Scholar
18.Richard, M. J., McPhee, J. J. and Anderson, R. J., “Computerized Generation of Motion Equations Using Variational Graph-theoretic Methods,” Applied Mathematics and Computation, 192, pp. 135–156 (2007).CrossRefGoogle Scholar
19.Rui, X. T., Wang, G. P., Lu, Y. Q. and Yun, L. F., “Transfer Matrix Method for Linear Multibody System,” Multibody System Dynamics, 19, pp. 179–207 (2008).CrossRefGoogle Scholar
20.Van Keulen, F., Haftk, R. T. and Kim, N. H., “Review of Options for Structural Design Sensitivity Analysis. Part 1: Linear Systems,” Computer Methods in Applied Mechanics and Engineering, 194, pp. 3213–3243 (2005).CrossRefGoogle Scholar
21.Ding, J. Y., Pan, Z. K. and Chen, L. Q., “Second Order Adjoint Sensitivity Analysis of Multibody Systems Described by Differential-algebraic Equations,” Multibody System Dynamics, 18, pp. 599–617 (2007).CrossRefGoogle Scholar
22.Choi, K. M., Jo, H. K., Kim, W. H. and Lee, I. W., “Sensitivity Analysis of Non-conservative Eigen-systems,” Journal of Sound and Vibration, 274, pp. 997–1011 (2004).CrossRefGoogle Scholar
23.Xu, Z. H., Zhong, H. X., Zhu, X. W. and Wu, B. S., “An Efficient Algebraic Method for Computing Eigensolution Sensitivity of Asymmetric Damped Systems,” Journal of Sound and Vibration, 327, pp. 584–592 (2009).CrossRefGoogle Scholar
24.Sliva, G., Brezillon, A., Cadou, J. M. and Duigou, L., “A Study of the Eigenvalue Sensitivity by Homotopy and Perturbation Methods,” Journal of Computational and Applied Mathematics, 234, pp. 2297–2302 (2010).CrossRefGoogle Scholar
25.Jiang, W., Chen, X. D. and Yan, T. H., “Symbolic Formulation of Rigid Multibody Systems for Vibration Analysis based on Matrix Transformation,” Chinese Journal of Mechanical Engineering, Chinese, Ed., 44, pp. 54–60 (2008).CrossRefGoogle Scholar
26.Jiang, W., Chen, X. D., Luo, X. and Huang, Q. J., “Symbolic Formulation of Large-scale Open-loop Multibody Systems for Vibration Analysis Using Absolute Joint Coordinates,” Journal of System Design and Dynamics, 2, pp. 1015–1026 (2008).CrossRefGoogle Scholar
27.Lee, I. W., Kim, D. O. and Jung, G. H., “Natural Frequency and Mode Shape Sensitivities of Damped Systems: Part I, Distinct Natural Frequencies,” Journal of Sound and Vibration, 223, pp. 399–412 (1999).CrossRefGoogle Scholar
28.Lee, I. W., Kim, D. O. and Jung, G. H., “Natural Frequency and Mode Shape Sensitivities of Damped Systems: Part II, Multiple Natural Frequencies,” Journal of Sound and Vibration, 223, pp. 413–424 (1999).CrossRefGoogle Scholar
29.Müller, A., “Elimination of Redundant Cut Joint Constraints for Multibody System Models,” Journal of Mechanical Design, 126, pp. 488–494 (2004).CrossRefGoogle Scholar
30.Kang, J. S., Bae, S., Lee, J. M. and Tak, T. O., “Force Equilibrium Approach for Linearization of Constrained Mechanical System Dynamics,” Journal of Mechanical Design, ASME, 125, PP. 143–149 (2003).CrossRefGoogle Scholar