Abstract
With regard to the problems of the dynamics of machines and mechanisms, the dynamic stability conditions are derived for the joint account of parametric and forced vibrations and the impact of nonlinear elastic and dissipative characteristics. It also proposes a new modification of the method of conditional oscillator by which it is possible to analytically study the oscillating systems with rheonomic and nonlinear constraints. For typical vibrational regimes, computer simulation results are presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Vulfson II (1990) Vibrations in machines with cyclic action mechanisms. Mashinostroenie, Leningrad (in Russian)
Vulfson I (2015) Dynamics of cyclic machines. Springer, London (Trans. from Russian, Politechnika, 2013)
Vulfson II (2013) Vibrations excitation in cyclic mechanisms due to energy generated in nonstationary constraints. Adv Mech Eng (Ed. A. Evgrafov). Springer, New York, pp 117–128
Bogoliubov NN, Mitropol’sky JA (1958) Asymptotic methods in the theory of nonlinear oscillations. Gordon & Breach, New York
Mitropol’sky JA (1964) Problems of the asymptotic theory of nonstationary vibrations. Nauka, Moscow (in Russian)
Bolotin VV (1956) Dynamic stability of elastic systems. Gostekhteoretizdat, Moscow (in Russian)
Schmidt G (1978) Parametric oscillations. Mir, Moscow (in Russian)
Vulfson II (1969) Oscillations of systems with parameters depending on the time. Prikladnaya matematika i mechanika 33(2):331–337 (in Russian)
Freman N, Freman P (1967) JWKB-approximation. North Holland Publ. Comp, Amsterdam
Vulfson II (2015) Quasistationarity of dynamic modes in cyclic mechanisms forming rheonomic oscillating systems with lattice structure. J Mach Manuf Reliab 44(4):312–318
Vulfson II (2015). To the problem of quasi-stationary dynamic characteristics of cyclic mechanisms. Theory Mech Mach (1):6–15 (in Russian)
Vulfson II (2008) Some nonlinear effects of machine dynamics. J Vibroeng 10(4):442–450
Kolovsky MZ (1963) On the effect of high-frequency of perturbations on resonant oscillations in a nonlinear system. In: Dynamics and strength of machines. Proceedings of the LPI. No 226. Mashgiz, Leningrad, pp 7–17 (in Russian)
Vulfson II (2005) Nonlinear resonant oscillations of a drive at the amplitude-modulation frequency of high-frequency excitation. J Mach Manuf Reliab (6):13–17
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Vulfson, I.I. (2017). Parametric Vibrations Excitation in Cyclic Mechanisms. In: Evgrafov, A. (eds) Advances in Mechanical Engineering. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-53363-6_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-53363-6_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-53362-9
Online ISBN: 978-3-319-53363-6
eBook Packages: EngineeringEngineering (R0)