Abstract
The chapter introduces orthogonal rotor equations of the Cauchy form into rotor dynamics where the integration time is substituted by a rotation angle. This has the advantage that the periodic rotations and vibrations of Sommerfeld rotors are calculable using Fourier expansions, which leads to a new moment speed characteristic of the rotor where the classical result is massively corrected by the unbalanced mass moment of inertia.
The chapter extends these investigations to two unbalanced visco-elastically supported rotors. New forms of limit cycles are calculated when the applied driving moments lead to mean values of the rotation speeds with the ratios 1:1 and 1:3, resulting in single and triple periodic limit cycles, respectively. For more general driving moments, the periodicity conditions are violated and the stationary rotor vibrations become pseudo-stochastic.
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
Sommerfeld, A.: Beiträge zum dynamischen Ausbau der Festigkeitslehre. Zeitschrift des Vereins Deutscher Ingenieure. 46, 391–394. (in German) (1902)
Smith, D.M.: The motion of a rotor carried by a flexible shaft in flexible bearings. Proc. R. Soc. Lond. Ser. A. 142(846), 92–118 (1933)
Brosens, P.J., Crandall, S.H.: Whirling of unsymmetrical rotors. Tran. ASME J. Appl. Mech. 28(3), 355–362 (1961)
Dimentberg, M., McGovern, L., Norton, R., Chapdelaine, J., Harrison, R.: Dynamics of an unbalanced shaft interacting with a limited power supply. Nonlin. Dynam. 13, 171–187 (1997)
Bisoi, A., Samantaray, A.K., Bhattacharyya, R.: Sommerfeld effect in a two-disk rotor dynamic system at various unbalanced conditions. Meccanica. 53(4–5), 681–701 (2018)
Bharti, S.K., Bisoi, A., Sinha, A., Samantaray, A.K., Bhattacharyya, R.: Sommerfeld effect at forward and backward critical speeds in a rigid rotor shaft system with anisotropic supports. J. Sound Vib. 442, 330–349 (2019)
Wedig, W.V.: Multiple Sommerfeld effects in vehicle dynamics. In: Lacorbonara, W., Balachandra, B., Lamey, M.J., Ma, J., Machado, J.A.T., Stepan, G. (eds.) Advances in Nonlinear Dynamics, Proceedings of the Second International Nonlinear Dynamics Conference, vol. 2, pp. 538–550 (2022)
Wedig, W.V.: Speed oscillations of a vehicle rolling on a wavy road. In special issue “Performance and safety enhancement strategies in vehicle dynamics and ground contact”. Appl. Sci. 11(21), 10431 (2021)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Wedig, W.V. (2024). Multiple Periodic Symmetric Limit Cycles of Two Coupled Sommerfeld Rotors. In: Lacarbonara, W. (eds) Advances in Nonlinear Dynamics, Volume I. ICNDA 2023. NODYCON Conference Proceedings Series. Springer, Cham. https://doi.org/10.1007/978-3-031-50631-4_9
Download citation
DOI: https://doi.org/10.1007/978-3-031-50631-4_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-50630-7
Online ISBN: 978-3-031-50631-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)