On the Stability of Periodic Systems in Connection with Rotating Shafts

1975 ◽  
pp. 546-564 ◽  
Author(s):  
Ch. Wehrli
Keyword(s):  
Periodic Systems ◽  
Rotating Shafts ◽  
The Stability

The whirling of a spinning top

1950 ◽  
Vol 2 (1) ◽  
pp. 9-14
Author(s):  
J. Morris
Keyword(s):  
High Speed ◽  
Moments Of Inertia ◽  
Prime Movers ◽  
Rotating Shafts ◽  
The Common ◽  
The Stability ◽  
Spinning Top

SummaryThis paper has been compiled because of the applicability of the treatment of the stability of the motion of the common spinning top to the problem of the whirling of rotating shafts, carrying loads of appreciable moments of inertia. This problem is assuming renewed interest and importance, especially in the drives of contra-propeller systems and the more recent high speed prime movers.

Free Vibration and Stability Analysis of Internally Damped Rotating Shafts With General Boundary Conditions

1998 ◽  
Vol 120 (3) ◽  
pp. 776-783 ◽  
Author(s):  
J. Melanson ◽  
J. W. Zu
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Beam Theory ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Rotating Shaft ◽  
Classical Boundary ◽  
Rotating Shafts ◽  
The Stability

Vibration analysis of an internally damped rotating shaft, modeled using Timoshenko beam theory, with general boundary conditions is performed analytically. The equations of motion including the effects of internal viscous and hysteretic damping are derived. Exact solutions for the complex natural frequencies and complex normal modes are provided for each of the six classical boundary conditions. Numerical simulations show the effect of the internal damping on the stability of the rotor system.

scholarly journals The Stability of Rotating Shafts

1911 ◽  
Vol s2-9 (1) ◽  
pp. 352-359
Author(s):  
F. B. Pidduck
Keyword(s):  
Rotating Shafts ◽  
The Stability

An Approximate Analysis of Quasi-Periodic Systems Via Floquét Theory

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Ashu Sharma ◽  
S. C. Sinha
Keyword(s):  
Parametric Excitation ◽  
Periodic System ◽  
Floquet Theory ◽  
Picard Iteration ◽  
Periodic Systems ◽  
Transition Matrices ◽  
Frequency Spectra ◽  
Periodic Coefficients ◽  
Stability Diagrams ◽  
The Stability

Parametrically excited linear systems with oscillatory coefficients have been generally modeled by Mathieu or Hill equations (periodic coefficients) because their stability and response can be determined by Floquét theory. However, in many cases, the parametric excitation is not periodic but consists of frequencies that are incommensurate, making them quasi-periodic. Unfortunately, there is no complete theory for linear dynamic systems with quasi-periodic coefficients. Motivated by this fact, in this work, an approximate approach has been proposed to determine the stability and response of quasi-periodic systems. It is suggested here that a quasi-periodic system may be replaced by a periodic system with an appropriate large principal period and thus making it suitable for an application of the Floquét theory. Based on this premise, a systematic approach has been developed and applied to three typical quasi-periodic systems. The approximate boundaries in stability charts obtained from the proposed method are very close to the exact boundaries of original quasi-periodic equations computed numerically using maximal Lyapunov exponents. Further, the frequency spectra of solutions generated near approximate and exact boundaries are found to be almost identical ensuring a high degree of accuracy. In addition, state transition matrices (STMs) are also computed symbolically in terms of system parameters using Chebyshev polynomials and Picard iteration method. Stability diagrams based on this approach are found to be in excellent agreement with those obtained from numerical methods. The coefficients of parametric excitation terms are not necessarily small in all cases.

Dynamic Stability of the Rotating Shaft Made of Boltzmann Viscoelastic Solid

1986 ◽  
Vol 53 (2) ◽  
pp. 424-429 ◽  
Author(s):  
W. Zhang ◽  
F. H. Ling
Keyword(s):  
Dynamic Stability ◽  
High Speed ◽  
Static Load ◽  
Viscoelastic Solid ◽  
Rotating Shaft ◽  
Special Cases ◽  
Analytical Formulas ◽  
Rotating Shafts ◽  
The Stability ◽  
Inclined Angle

A general theory is developed in this paper for studying the dynamic stability of high-speed nonuniform rotating shafts made of a Boltzmann viscoelastic solid. The equation of motion of the shaft is deduced. The stability criteria are derived by using this equation. The unstable regions for a nonhomogeneous viscoelastic shaft are worked out numerically. Analytical formulas are also given in this paper for determining the planar deflection of the shaft and its inclined angle due to a planar static load. The conclusions for special cases given in the literature known to the authors are all covered by the results in this paper.

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