Subcritical Large-Amplitude Vibrations of Imperfect Rotating Shafts

1989 ◽  
Vol 42 (11S) ◽  
pp. S157-S160
Author(s):  
C. E. N. Mazzilli
Keyword(s):  
Dry Friction ◽  
Large Amplitude ◽  
Critical Speed ◽  
Multiple Scales ◽  
Viscous Damping ◽  
Rotating Shaft ◽  
Geometrical Imperfection ◽  
Rotating Shafts ◽  
Large Amplitude Vibrations ◽  
Practical Implications

The effect of a geometrical imperfection, such as the axis flexural deformation, on the large-amplitude vibrations of a horizontal rotating shaft is analyzed with the aid of the Multiple Scales Method. Internal viscous damping and linear elasticity are assumed in the model. It is then seen that no matter how small the imperfection is, a “critical” speed of the order of half the classical critical speed arises, with relevant practical implications. A number of reported large-amplitude cases may eventually be explained this way. It is possible that events such as this will not appear in systems with high dry friction.

On the Dynamical Behavior of Rotating Shafts Driven by Universal (Hooke) Couplings

1958 ◽  
Vol 25 (1) ◽  
pp. 47-51
Author(s):  
R. M. Rosenberg
Keyword(s):  
Critical Speed ◽  
Dynamical Behavior ◽  
Rotating Shaft ◽  
Critical Speeds ◽  
Elastic Shaft ◽  
Rotating Shafts

Abstract The system considered here is a massless, uniform elastic shaft carrying at its mid-point a disk (having mass) and supported at the ends by universal (Hooke) joints. The purpose of this investigation is to examine the effect of Hooke-joint angularity (as obtained by design, or from faulty alignment) on the bending stability of the rotating shaft. It is found that separate investigations are required for shafts not transmitting axial torques and for those required to transmit torques. Each gives rise to instabilities which are absent when the Hooke joint is straight. In the absence of axial torques, the shaft develops unsuspected mild critical speeds at odd integer submultiples of the “familiar” critical speed found with a straight Hooke joint. When the shaft is required to transmit moderate axial torques, the joint angularity produces true instabilities near all integer submultiples of the familiar critical speed. Surprisingly, these instabilities vanish for sufficiently large axial torques.

Predicting critical speeds in various rotordynamics problems

2016 ◽  
Vol 231 (21) ◽  
pp. 3913-3922
Author(s):  
Raymond H Plaut ◽  
Lawrence N Virgin ◽  
Josiah D Knight
Keyword(s):  
Large Amplitude ◽  
Critical Speed ◽  
Experimental Results ◽  
Nondestructive Technique ◽  
New Approach ◽  
Practical Utility ◽  
Critical Speeds ◽  
Model Free ◽  
Measured Information ◽  
Rotating Shafts

Rotating shafts often experience undesirable large-amplitude whirling oscillations associated with resonance at critical speeds. This paper further develops a nondestructive technique in which measured information about the growing nature of the response is used to predict an incipient critical speed. A number of models of varying degrees of sophistication are developed and tested using the new approach, but the main advantage of the method is that it is model-free and thus possesses considerable practical utility. In addition, further experimental results are presented for the case of two disks mounted on a shaft, and the technique is successfully demonstrated in predicting a critical speed associated with a higher mode.

scholarly journals Thermally Induced Principal Parametric Resonance in Circular Plates

2002 ◽  
Vol 9 (3) ◽  
pp. 143-150 ◽  
Author(s):  
Ali H. Nayfeh ◽  
Waleed Faris
Keyword(s):  
Parametric Resonance ◽  
Large Amplitude ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Temperature Fields ◽  
Circular Plates ◽  
Thermally Induced ◽  
Principal Parametric Resonance ◽  
Large Amplitude Vibrations ◽  
External Heat Flux

We consider the problem of large-amplitude vibrations of a simply supported circular flat plate subjected to harmonically varying temperature fields arising from an external heat flux (aeroheating for example). The plate is modeled using the von Karman equations. We used the method of multiple scales to determine an approximate solution for the case in which the frequency of the thermal variations is approximately twice the fundamental natural frequency of the plate; that is, the case of principal parametric resonance. The results show that such thermal loads produce large-amplitude vibrations, with associated multi-valued responses and subcritical instabilities.

Combination Parametric Resonance of Nonlinear Unbalanced Rotating Shafts

2018 ◽  
Vol 13 (11) ◽  
Author(s):  
M. S. Qaderi ◽  
S. A. A. Hosseini ◽  
M. Zamanian
Keyword(s):  
Parametric Excitation ◽  
Multiple Scales ◽  
Nonlinear Differential Equations ◽  
Geometrical Nonlinearity ◽  
Primary Resonance ◽  
Rotating Shaft ◽  
Rotating Shafts ◽  
Slow Evolution ◽  
The Stability ◽  
Parametric And External Excitations

In this paper, dynamic response of a rotating shaft with geometrical nonlinearity under parametric and external excitations is investigated. Resonances, bifurcations, and stability of the response are analyzed. External excitation is due to shaft unbalance and parametric excitation is due to periodic axial force. For this purpose, combination resonances of parametric excitation and primary resonance of external force are assumed. Indeed, simultaneous effect of nonlinearity, parametric, and external excitations are investigated using analytical method. By applying the method of multiple scales, four ordinary nonlinear differential equations are obtained, which govern the slow evolution of amplitude and phase of forward and backward modes. Eigenvalues of Jacobian matrix are checked to find the stability of solutions. Both periodic and quasi-periodic motion were observed in the range of study. The influence of various parameters on the response of the system is studied. A main contribution is that the parametric excitation in the presence of nonlinearity can be used to suppress the forward synchronous vibration. Indeed, in the presence of combination parametric excitation, the energy is transferred from forward whirling mode to backward one. This property can be applied in control of rotor unbalance vibrations.

Bisynchronous Torsional Vibrations in Rotating Shafts

1987 ◽  
Vol 54 (4) ◽  
pp. 893-897 ◽  
Author(s):  
O. Bernasconi
Keyword(s):  
Angular Momentum ◽  
Nonlinear Term ◽  
Rotation Frequency ◽  
Longitudinal Component ◽  
Torsional Vibrations ◽  
Rotating Shaft ◽  
Rotating Shafts

In this study, the intrinsic behavior of rotating shafts with residual unbalance is considered. The longitudinal component of the angular momentum caused by synchronous precession (whirling) induces torsional vibrations with a frequency of twice the rotation frequency (bisynchronous). The nonlinear term which represents this coupling is characteristic of the asymmetrical aspect of rotating shaft kinematics. This result has been obtained analytically and confirmed experimentally.

A nonlinear model of thick shells for large-amplitude vibrations

2021 ◽  
Vol 130 ◽  
pp. 103668
Author(s):  
Hamid Reza Moghaddasi ◽  
Mojtaba Azhari ◽  
Mohammad Mehdi Saadatpour ◽  
Saeid Sarrami-Foroushani
Keyword(s):  
Nonlinear Model ◽  
Large Amplitude ◽  
Large Amplitude Vibrations ◽  
Thick Shells
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