Abstract
The paper deals with the application of the Runge–Kutta method for calculating steady-state periodic vibrations of the parametric vibration systems governed by linearized differential equations. The numerical calculation is also demonstrated by two models of multibody systems and measurements on real objects. Good agreement is obtained between the numerical and experimental results. Consequently, the obtained results can also be applicable to investigate other complicated models of multibody systems which perform the steady-state motions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Schiehlen, W., Eberhard, P.: Technische Dynamik, 2 Auflage. Teubner, Stuttgart (2004)
Shabana, A.A.: Dynamics of Multibody Systems, 3 edn. Cambridge University Press, Cambridge (2005)
Josephs, H., Huston, R.L.: Dynamics of Mechanical Systems. CRS Press, Boca Raton (2002)
Amirouche, F.: Fundamentals of Multibody Dynamics. Birkhäuser, Boston (2006)
Flores, P., Ambrosio, J., Claro, J.C.P., Lankarami, H.M.: Kinematics and Dynamics of Multibody Systems with Imperfect Joints. Springer, Berlin (2008)
Wittenburg, J.: Dynamics of Multibody Systems, 2 edn. Springer, Berlin (2008)
Schiehlen, W. (ed.): Multibody Systems Handbook. Springer, Berlin (1990)
Stoer, J., Bulirsch, R.: Numerische Mathematik 2, 4 Auflage. Springer, Berlin (2000)
Seydel, R.: Practical Bifurcation and Stability Analysis. Springer, New York (1994)
Nayfeh, A.H., Balachandran, B.: Applied Nonlinear Dynamics. Wiley, New York (1995)
Eich-Soellner, E., Fuehrer, C.: Numerical Methods in Multibody Dynamics. Teubner, Stuttgart (1998)
Kortüm, W., Lugner, P.: Systemdynamik und Regelung von Fahrzeugen. Springer, Berlin (1994)
Heimann, B., Gerth, W., Popp, K.: Mechantronik, 3 Auflage. Fachbuchverlag Leipzig in Carl Hanser, München (2007)
Dresig, H., Vulfson, I.I.: Dynamik der Mechanismen. Deutscher Verlag der Wissenschaften, Berlin (1989)
Müller, P.C., Schiehlen, W.: Lineare Schwingungen. Akademische Verlagsgesellschaft, Wiesbaden (1976)
Nguyen, V.K.: Dynamische Stabilität und periodische Schwingungen in Mechanismen. Diss. B, TH Karl-Marx-Stadt (1986)
Nguyen, V.K.: Numerische Bestimmung der dynamischen Stabilitätsparameter und periodischen Schwingungen ebener Mechanismen. Rev. Roum. Sci. Tech.-Mec. Appl. 27(4), 495–507 (1982)
Malkin, J.G.: Theorie der Stabilät einer Bewegung. Akademie, Berlin (1959)
Troger, H., Steindl, A.: Nonlinear Stability and Bifurcation Theory. Springer, Wien (1991)
Roessler, J.: Dynamik von Mechanismen—Antriebssystemen im Textil—und Verarbeitungsmaschinenbau. Diss. B, TH Karl-Marx-Stadt (1985)
Cleghorn, W.L., Fenton, R.G., Tabarrok, B.: Steady-state vibrational response of high-speed flexible mechanisms. Mech. Mach. Theory 19(4–5), 417–423 (1984)
Nguyen, P.D.: Beitrag zur Diagnostik der Verzahnungen in Getrieben mittels Zeit- Frequenz- Analyse. Fortschritt-Berichte VDI, Reihe 11, Nr. 135. VDI-Verlag GmbH, Düsseldorf (2003)
Nguyen, V.K., Thai, M.C., Nguyen, P.D.: Modelling parametric vibration of gear-pair systems as a tool for aiding gear-fault diagnosis. Tech. Mech. 24(3–4), 198–205 (2004)
Padmanabhan, C., Singh, R.: Analysis of periodically forced nonlinear Hill’s oscillator with application to a geared system. J. Acoust. Soc. Am. 99(1), 324–334 (1996)
Boerner, J.: Rechenprogramm LVR: Beanspruchungsverteilung an evolventischen Verzahnungen. Foschungsberichte, TU Dresden, Institut für Maschinenelemente und Maschinen-konstruktion (1999)
Dalpiaz, G., Rivola, A., Rubini, R.: Effectiveness and sensitivity of vibration processing techniques for local fault detection in gears. Mech. Syst. Signal Process. 14(3), 387–412 (2000)
Howard, I., Shengxiang, J., Wang, J.: The dynamic modelling of a spur gear in mesh including friction and a crack. Mech. Syst. Signal Process. 15(5), 831–853 (2001)
Parker, G.R., Vijayakar, S.M., Imajo, T.: Non-linear dynamic response of a spur gear-pair: modelling and experimental comparisons. J. Sound Vib. 237(3), 435–455 (2000)
Theodossiades, S., Natsiavas, S.: Non-linear dynamics of gear-pair systems with periodic stiffness and backlash. J. Sound Vib. 229(2), 287–310 (2000)
Nguyen, P.D.: Damping identification using the wavelet-based demodulation method: application to gearbox signals. Tech. Mech. 3–4, 324–333 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Nguyen, V.K., Nguyen, P.D. & Hoang, M.C. Linearization and parametric vibration analysis of some applied problems in multibody systems. Multibody Syst Dyn 22, 163–180 (2009). https://doi.org/10.1007/s11044-009-9156-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11044-009-9156-4