On the Critical Speed of Continuous Shaft-Disk Systems

1984 ◽  
Vol 106 (1) ◽  
pp. 59-61 ◽  
Author(s):  
H. Nevzat O¨zgu¨ven
Keyword(s):  
Critical Speed ◽  
Degree Of Freedom ◽  
Mass Ratio ◽  
Disk System ◽  
Single Degree Of Freedom ◽  
Single Degree

The critical speed of a shaft-disk system can be approximately determined from a single degree-of-freedom model. The errors in the critical speed predictions obtained from such a model are investigated. The percentage errors are plotted against disk to shaft mass ratio for different bearings and various disk locations.

The Acceleration of a Single Degree of Freedom System Through its Resonant Frequency

1958 ◽  
Vol 62 (574) ◽  
pp. 752-757 ◽  
Author(s):  
S. Hother-Lushington ◽  
D. C. Johnson
Keyword(s):  
Resonant Frequency ◽  
Critical Speed ◽  
Bessel Functions ◽  
Degree Of Freedom ◽  
Series Solutions ◽  
Mechanical Vibrations ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Method Of Solution ◽  
Simple Integration

It is Sometimes required to find the maximum amplitudes of vibration attained and the speeds at which they occur when a machine is run through its critical speed with different accelerations. The solution of this problem for single degree of freedom systems has been obtained by Lewis and by Ellington and McCallion for mechanical vibrations and by Hok for the equivalent electrical case. These solutions require higher mathematics (contour integration, Fresnel's integrals or series solutions leading to Bessel functions). The purpose of this note is to show how, by using simple integration only, an alternative method of solution can be obtained for both zero and small values of damping.

Deceleration of an Unbalanced Rotor Through a Critical Speed

1967 ◽  
Vol 89 (4) ◽  
pp. 582-585
Author(s):  
W. K. Bodger
Keyword(s):  
Critical Speed ◽  
Degree Of Freedom ◽  
Bending Stress ◽  
Rotor Speed ◽  
Single Degree Of Freedom ◽  
Closed Solution ◽  
Rotor Shaft ◽  
Single Degree ◽  
Unbalanced Rotor ◽  
Maximum Increment

The problem of a single-degree-of-freedom rotor decelerating slowly through its critica speed is solved by an energy approach; a closed solution is obtained. A small discontinuous downward jump of rotor speed across the critical speed is shown to be required, either with or without damping in the system. The maximum increment of deflection, hence bending stress, in the rotor shaft is shown to be small, provided the rotor is carefully balanced and/or the system is sufficiently damped.

Study on Applicability of Equivalent Single Degree of Freedom Methods for Single Column Pier with Uniform Cross Section

2011 ◽  
Vol 255-260 ◽  
pp. 1716-1720
Author(s):  
Liang Chen
Keyword(s):  
Cross Section ◽  
Fundamental Mode ◽  
Degree Of Freedom ◽  
Mass Ratio ◽  
Shape Functions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Single Column ◽  
Simplified Method ◽  
Uniform Cross Section

Applicability of the simplified method based on equivalent single-degree-of-freedom (ESDOF) for single-column pier with uniform cross-section is investigated in this paper. The modal participating mass ratio of pier’s fundamental mode is taken as an index to evaluate the applicability of the simplified method. Based on the fundamental mode shape functions selected deliberately in the first step, equations to evaluate the modal participating mass ratio of pier fundamental mode is obtained. Using the proposed equations, it is convenient to evaluate applicability of the simplified method with the height of the pier and the ratio of the linear mass along the column to the dumped mass at the top of the pier. Finally, the index is verified in the different nonlinear range of piers.

Vibration of Satellite Subsystem During Orbiter Lift-Off

1993 ◽  
Vol 8 (3) ◽  
pp. 167-176 ◽  
Author(s):  
Gina Lee-Glauser ◽  
Goodarz Ahmadi
Keyword(s):  
Response Spectra ◽  
Degree Of Freedom ◽  
Mass Ratio ◽  
Acceleration Response ◽  
Single Degree Of Freedom ◽  
Lump Parameter Model ◽  
Single Degree ◽  
Acceleration Response Spectra ◽  
Lift Off ◽  
Sinusoidal Excitation

Vibrations of a satellite and one of its sensitive subsystems during orbiter lift-off are studied. A single degree-of-freedom representation of the subsystem and a five degree-of-freedom lump parameter model of the satellite are considered. Deflection and acceleration response spectra of the satellite and its subsystem subject to sinusoidal excitation and the STS - 41 lift-off accelerations are evaluated. The significance of the subsystem and primary satellite interaction is investigated. The effect of mass ratio and damping coeficient of the subsystem on the peak deflection and acceleration response spectra of the satellite and its subsystem are examined.

Active Stiffness Control of Cable Vibration

1993 ◽  
Vol 60 (4) ◽  
pp. 948-953 ◽  
Author(s):  
Yozo Fujino ◽  
Pennung Warnitchai ◽  
B. M. Pacheco
Keyword(s):  
Energy Analysis ◽  
Optimal Algorithm ◽  
Degree Of Freedom ◽  
Scale Model ◽  
Mass Ratio ◽  
Combined System ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stiffness Control ◽  
Cable Vibrations

To suppress cable vibrations, active stiffness control, which changes the tension as a positive use of parametric excitation, is studied. An optimal algorithm is obtained from energy analysis and verified by experiment on a scale model. Numerical investigation is then made on the control of a combined system of cable and single-degree- of-freedom structure; the degree-of-freedom of the latter is along the cable axis. It is found by numerical simulation that instability occurs when the mass ratio of cable to structure is large, or when the frequency ratio of structure to cable is close to 2.0.

Kinematic comparison of single degree-of-freedom robotic gait trainers

2021 ◽  
Vol 159 ◽  
pp. 104258
Author(s):  
Jeonghwan Lee ◽  
Lailu Li ◽  
Sung Yul Shin ◽  
Ashish D. Deshpande ◽  
James Sulzer
Keyword(s):  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Robotic Gait
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