Response of Non-Linear Shock Absorbers-Boundary Value Problem Analysis
More details
Hide details
Department of Mechanical Engineering Bangladesh University of Engineering and Technology (BUET), Dhaka-1000, BANGLADESH
Online publication date: 2013-09-06
Publication date: 2013-08-01
International Journal of Applied Mechanics and Engineering 2013;18(3):793-814
A nonlinear boundary value problem of two degrees-of-freedom (DOF) untuned vibration damper systems using nonlinear springs and dampers has been numerically studied. As far as untuned damper is concerned, sixteen different combinations of linear and nonlinear springs and dampers have been comprehensively analyzed taking into account transient terms. For different cases, a comparative study is made for response versus time for different spring and damper types at three important frequency ratios: one at r = 1, one at r > 1 and one at r <1. The response of the system is changed because of the spring and damper nonlinearities; the change is different for different cases. Accordingly, an initially stable absorber may become unstable with time and vice versa. The analysis also shows that higher nonlinearity terms make the system more unstable. Numerical simulation includes transient vibrations. Although problems are much more complicated compared to those for a tuned absorber, a comparison of the results generated by the present numerical scheme with the exact one shows quite a reasonable agreement
Ahmed A.U. (2009): Stability analysis of vibration absorbers. - M. Sc. Engg. Thesis, Department of Mechanical Engineering, BUET, Bangladesh.
Alexander N.A. and Schilder F. (2009): Exploring the performance of a nonlinear tuned mass damper. - Journal of Sound and Vibration vol.319, pp.445-462.
Asfar K.R. and Akour S.N. (2005): Optimization analysis of impact viscous damper for controlling self-excited vibrations. - Journal of Vibration and Control, vol.11, no.1, pp.103-120.
Chatterjee S. (2007): Non-linear control of friction-induced self-excited vibration. - International Journal of Non-Linear Mechanics, vol.42, No.3, pp.459-469.
Dohnal F. (2007): Suppressing self-excited vibrations by synchronous and time-periodic stiffness and damping variation. - Journal of Sound and Vibration, vol.306, No.1-2, pp.136-152.
Jordanov I.N. and Cheshankov B.I. (1988): Optimal design of linear and non-linear dynamic vibration absorbers - Journal of Sound and Vibration 123(1), pp.157-170.
Kalnins A. and Dym C. L. (1976): Vibration of Beams, Plates, and Shells. - Dowden, Hutchinson and Ross, Inc.
Kalnins A. and Lestingi, J.E. (1967): On nonlinear analysis of elastic shells of revolution. - J. Appl. Mech., vol.34, pp.59-64.
Manevitch L.I., Gendelman O., Musienko A.I., Vakakis A.F. and Bergman L. (2003): Dynamic interaction of a semiinfinite linear chain of coupled oscillators with a strongly nonlinear end attachment. - Physica D. Nonlinear Phenomena, vol.178(1-2), pp.1-18.
McFarland D.M., Bergman L.A., Vakakis A.F., Manevitch L.I. and Gendelman O. (2002 ): Energy pumping into passive nonlinear energy sinks attached to forced linear substructures: analytical and experimental results. - 9th Conference on Nonlinear Vibrations, Stability, and Dynamics of Structures, Virginia Polytechnic Institute and State University.
Mikhlin Y.V. and Reshetnikova S.N. (2005): Dynamical interaction of an elastic system and essentially nonlinear absorber. - Journal of Sound and Vibration, vol.283 (1-2), pp.91-120.
Nakhaie G., Narimani A., Golnaraghi M.F. and Swanson D.A. (2003): Practical frequency and time optimal design of passive linear vibration isolation mounts. - Vehicle System Dynamics 39, pp.437-466.
Natsiavas S. (1992): Steady state oscillations and stability of non-linear dynamic vibration absorbers. - Journal of Sound and Vibration 156 (2), pp.227-245.
Oueini S.S., Nayfeh A.H. and Pratt J.R. (1998): A nonlinear vibration absorber for flexible structures. - Nonlinear Dynamics 15, pp.259-282.
Plaut R.H and Limam W. (1991): Oscillations of weakly non-linear, self-excited systems under multi-frequency parametric excitation. - Journal of Sound and Vibration, vol.144, No.2, pp.197-214.
Rahman M.A. and Ahmed A.U. (2009): Boundary value problem analysis of a tuned vibration absorber having nonlinear springs. - Int. J. Structural Engineering (Inderscience Enterprises Ltd., Switzerland) - In press.
Rice H.J. (1986): Combinational instability of the non-linear vibration absorbe. - Journal of Sound and Vibration, 108(4), pp.526-532.
Shaw J., Shaw S.W. and Haddow A.G. (1989): On the response of the non-linear vibration absorber. - Journal of Non- Linear Mechanics 24, pp.281-293.
Shekhar N.C., Hatwal H. and Mallik A.K. (1998): Response of non-linear dissipative shock isolators. - Journal of Sound and Vibration 214, pp.589-603.
Shekhar N.C., Hatwal H. and Mallik A.K. (1999): Performance of nonlinear isolators and absorbers to shock excitation. - Journal of Sound and Vibration 227, pp.293-307.
Soom A. and Lee M. (1983): Optimal design of linear and non-linear vibration absorbers for damped system. - Journal of Vibration, Acoustic Stress, and Reliability in Design 105, pp.112-119.
Thomson W. (2004): Theory of Vibrations with Applications (4th Edition). - Publisher Taylor and Francis (ISBN 0748743804, 9780748743803).
Vakakis A.F. and Paipetis S.A. (1986): The effect of a viscously damped dynamic absorber on a linear multi degree of freedom system. - Journal of Sound and Vibration 105(1) pp.45-60.
Zhu S.J., Zheng Y.F. and Fu Y.M. (2004): Analysis of non-linear dynamics of a two degree of freedom vibration system with non-linear damping and nonlinear spring. - Journal of Sound and Vibration 271, pp.15-24.
Journals System - logo
Scroll to top