Abstract
The paper concerns analysis of nonlinear vibration of the rotating systems consisted of rigid disks mounted on the elastic massless shaft. The investigations are focused on their behaviour under the resonance conditions. The analytical method of multiple scales in time domain is applied to the analysis of dynamics of the system near main resonance. The transition phenomenon depending on the value of the nonlinearity parameter is discussed.
Highlights
Torsional vibration belongs to major problems in design of the power transmission systems
The Multiple Scales Method (MSM) in time domain, belonging to the asymptotic methods, allows obtain the approximate solutions, and gives the possibility to exact investigate the influence of the particular parameters on the motion
Associating the MSM with an interesting approach proposed by Manevich [3] known as Limiting Phase Trajectory (LPT) Method allows to predict the sudden change of the shape of the amplitude modulation which appears in resonance at a certain value of the nonlinearity parameter
Summary
Torsional vibration belongs to major problems in design of the power transmission systems. The dynamic stresses caused by torsional oscillations, especially near resonance when the amplitudes grow significantly, may be very large and can lead to failure of the whole system Both discrete and continuous models are commonly used in order to investigate the torsional vibration of the power transmission systems [1,4,6]. The Multiple Scales Method (MSM) in time domain, belonging to the asymptotic methods, allows obtain the approximate solutions, and gives the possibility to exact investigate the influence of the particular parameters on the motion This method is applied in the paper to solve the problem of torsional vibration of the shaft on which the rigid disks are mounted. A similar approach, but based completely on the proposed by Manevich formulation in the field of complex functions, was applied to investigate the torsional vibration in the system with one degree of freedom [5]
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