On the numerical damping of time integrators for coupled mechatronic systems

Bruls, Olivier; Golinval, Jean-Claude

doi:10.1016/j.cma.2007.08.007

Request a copy

Article (Scientific journals)

On the numerical damping of time integrators for coupled mechatronic systems

Bruls, Olivier; Golinval, Jean-Claude

2008 • In Computer Methods in Applied Mechanics and Engineering, 197 (6-8), p. 577-588

Peer Reviewed verified by ORBi

Permalink
https://hdl.handle.net/2268/19989

DOI
10.1016/j.cma.2007.08.007

Files (1)Send to Details Statistics Bibliography Similar publications

Files

Full Text

B07_postEd_2008_BrulsGolinval_OnTheNumericalDampingOfTimeIntegratorsForCoupledMechatronicSystems.pdf

Publisher postprint (338.89 kB)

Request a copy

All documents in ORBi are protected by a user license.

Send to

RIS BibTex APA Chicago Permalink X Linkedin

Details

Keywords :

generalized-alpha scheme; coupled problems; flexible multibody dynamics; mechatronics; numerical damping

Abstract :

[en] The generalized-alpha time integrator is considered for the simulation of mechatronic systems. In this context, the fundamental concept of numerical damping is analysed for coupled sets of first and second-order differential-algebraic equations. First, it appears that the algebraic variables do not influence the spectral properties of the dynamic variables. Second, we demonstrate that the coupling between the dynamic variables does not influence the high-frequency spectral response, so that the numerical damping can be determined as usual from elementary characteristic polynomials. Those results are exploited to assess the stability properties of the scheme and to select an algorithm with optimal damping properties.

Disciplines :

Engineering, computing & technology: Multidisciplinary, general & others
Mechanical engineering
Mathematics

Author, co-author :

Bruls, Olivier ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS - Vibrations et identification des structures

Golinval, Jean-Claude ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS - Vibrations et identification des structures

Language :

English

Title :

On the numerical damping of time integrators for coupled mechatronic systems

Publication date :

2008

Journal title :

Computer Methods in Applied Mechanics and Engineering

ISSN :

0045-7825

eISSN :

1879-2138

Publisher :

Elsevier Science, Lausanne, Switzerland

Volume :

197

Issue :

6-8

Pages :

577-588

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 26 August 2009

Statistics

Number of views

157 (9 by ULiège)

Number of downloads

7 (3 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

Newmark, N., A method of computation for structural dynamics (1959) ASCE J. Engrg. Mech. Div., 85, pp. 67-94
Hilber, H., Hughes, T., Taylor, R., Improved numerical dissipation for time integration algorithms in structural dynamics (1977) Earthquake Engrg. Struct. Dyn., 5, pp. 283-292
Chung, J., Hulbert, G., A time integration algorithm for structural dynamics with improved numerical dissipation: The generalized-α method (1993) ASME J. Appl. Mech., 60, pp. 371-375
Hughes, T., (1987) The Finite Element Method, Linear Static and Dynamics Finite Element Analysis, , Prentice Hall
Géradin, M., Rixen, D., (1997) Mechanical Vibrations: Theory and Application to Structural Dynamics. second ed., , John Wiley & Sons, New York
Erlicher, S., Bonaventura, L., Bursi, O., The analysis of the generalized-α method for non-linear dynamic problems (2002) Comput. Mech., 28, pp. 83-104
Cardona, A., Géradin, M., Time integration of the equations of motion in mechanism analysis (1989) Comput. Struct., 33, pp. 801-820
Géradin, M., Cardona, A., (2001) Flexible Multibody Dynamics: A Finite Element Approach, , John Wiley and Sons, New York
Lunk, C., Simeon, B., Solving constrained mechanical systems by the family of Newmark and α-methods (2006) Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 86, pp. 772-784
Jay, L., Negrut, D., Extensions of the HHT-method to differential-algebraic equations in mechanics (2007) Electron. Trans. Numer. Anal., 26, pp. 190-208
Arnold, M., Brüls, O., Convergence of the generalized-α scheme for constrained mechanical systems (2007) Multibody Syst. Dyn., 18 (2), pp. 185-202
Van Brussel, H., Mechatronics - a powerful concurrent engineering framework (1996) IEEE/ASME Trans. Mechatron., 1 (2), pp. 127-136
Negrut, D., Rampalli, R., Ottarsson, G., Sajdak, A., On an implementation of the Hilber-Hughes-Taylor method in the context of index 3 differential-algebraic equations of multibody dynamics (2007) ASME J. Comput. Nonlinear Dyn., 2 (1), pp. 73-85
Brüls, O., Golinval, J.-C., The generalized-α method in mechatronic applications (2006) Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 86, pp. 748-758
Lötsted, P., Petzold, L., Numerical solution of differential equations with algebraic constraints I: Convergence results for backward differentiation formulas (1986) Math. Comput., 46, pp. 491-516
Brenan, K., Engquist, B., Backward differentiation approximations of nonlinear differential/algebraic systems (1988) Math. Comput., 51, pp. 659-676
Brenan, K., Campbell, S., Petzold, L., (1996) Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. second ed., , SIAM, Philadelphia
Hairer, E., Wanner, G., (1996) Solving Ordinary Differential Equations II - Stiff and differential-algebraic Problems. second ed., , Springer-Verlag
Jansen, K., Whiting, C., Hulbert, G., A generalized-α method for integrating the filtered Navier-Stokes equations with a stabilized finite element method (2000) Comput. Methods Appl. Mech. Engrg., 190, pp. 305-319
Preumont, A., (1997) Vibration Control of Active Structures, An Introduction, , Kluwer