Vibration of Multifrequency Systems During Acceleration Through Critical Speeds

1949 ◽  
Vol 16 (4) ◽  
pp. 375-382
Author(s):  
G. D. McCann ◽  
R. R. Bennett
Keyword(s):  
Analog Computer ◽  
Degree Of Freedom ◽  
Generalized Solutions ◽  
Critical Speeds ◽  
Constant Magnitude ◽  
Electric Analog ◽  
Two Degree Of Freedom ◽  
Single Constant

Abstract This paper presents generalized solutions for the response of a linear two-degree-of-freedom system excited by a single constant-magnitude sinusoidal force whose frequency varies uniformly with time. These solutions were obtained with the Cal Tech “electric-analog computer” which is described briefly since it has wide application to problems of this type.

Rails on Elastic Foundations Under the Influence of High-Speed Traveling Loads

1953 ◽  
Vol 20 (1) ◽  
pp. 13-22
Author(s):  
H. E. Criner ◽  
G. D. McCann
Keyword(s):  
High Speed ◽  
Narrow Range ◽  
Analog Computer ◽  
Point Load ◽  
Specific Design ◽  
Computer Technique ◽  
Elastic Foundations ◽  
Constant Magnitude ◽  
Electric Analog ◽  
Track Beam

Abstract This paper presents an electric-analog-computer technique for the analysis of beams on elastic foundations that are subjected to traveling loads. This method is applicable to the study of such conditions as nonuniform beams, load magnitude and velocity variations, and such nonlinear conditions as the beam leaving contact with the foundation for upward deflections. A general set of dimensionless solutions is presented for the specific case of a point load of constant magnitude and velocity traveling over an infinite uniform linear track beam. These show high values of deflection and moment for a rather narrow range of velocity above and below the critical velocities producing peak disturbances. It was found that quite high accelerations are required to produce significantly less disturbance than in the constant velocity case. A range of nonlinear track-bouncing conditions was studied in connection with a specific design problem. For none of these cases could more severe conditions be produced than indicated by the linear solutions.

A Note on a New Stability Method for the Linear Modes of Nonlinear Two-Degree-of-Freedom Systems

1962 ◽  
Vol 29 (2) ◽  
pp. 258-262 ◽  
Author(s):  
Jack Porter ◽  
C. P. Atkinson
Keyword(s):  
Equations Of Motion ◽  
Analog Computer ◽  
Degree Of Freedom ◽  
Oscillatory Systems ◽  
Coupled Equations ◽  
Theoretical Predictions ◽  
Stability Method ◽  
The Stability ◽  
Two Degree Of Freedom

This paper presents a method for analyzing the stability of the linearly related modes of nonlinear two-degree-of-freedom oscillatory systems. For systems described by the coupled equations x¨1 = f(x1, x2) and x¨2 = g(x1, x2) there exist solutions related by the linear modal restraint x1 = cx2 where c is a constant. Such oscillations are not always stable. The method of this paper allows the prediction of the stability of the modes in terms of the amplitudes of the oscillations and the parameters of the equations of motion. Analog-computer results are presented which confirm the theoretical predictions.

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