The Solution of Elastic Stability Problems With the Electric Analog Computer

1959 ◽  
Vol 26 (4) ◽  
pp. 635-642
Author(s):  
J. H. Shields ◽  
R. H. MacNeal
Keyword(s):  
Differential Equation ◽  
Elastic Stability ◽  
Analog Computer ◽  
Computing Methods ◽  
Electrical Circuit ◽  
Stability Problems ◽  
Analog Computing ◽  
General Differential Equation ◽  
Plate Stability ◽  
Electric Analog

Abstract An application of electric analog computing methods to the analysis of elastic stability problems is described. An electrical circuit is first devised which satisfies a general differential equation that is frequently encountered in the literature of elastic stability. This circuit, composed of inductors, capacitors, transformers, and current generators, is then used to obtain solutions for several classical column, framework, and plate-stability problems.

Beam-Vibration Analysis With the Electric-Analog Computer

1950 ◽  
Vol 17 (1) ◽  
pp. 13-26
Author(s):  
G. D. McCann ◽  
R. H. MacNeal
Keyword(s):  
Steady State ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Analog Computer ◽  
Accurate Solution ◽  
Rotary Inertia ◽  
Beam Vibration ◽  
Lumped Constant ◽  
Electric Analog

Abstract The authors have developed a true dynamic analogy which has been used with the Cal Tech electric-analog computer for the rapid and accurate solution of both steady-state and transient beam problems. This analogy has been found well suited to the study of beams having several coupled degrees of freedom, including torsion, simple bending, and bending in a plane. Damping and effects such as rotary inertia may be handled readily. The analogy may also be used in the study of systems involving combined beams and “lumped-constant” elements.

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.

scholarly journals Excitation of Spectra of Multiply Ionized Atoms by Capacitor Discharges

1974 ◽  
Vol 28 (3) ◽  
pp. 223-234 ◽  
Author(s):  
Cornelius H. H. Van Deurzen ◽  
John G. Conway
Keyword(s):  
Differential Equation ◽  
Electrical Circuit ◽  
Spectral Lines ◽  
Circuit Parameter ◽  
Excitation Energies ◽  
Time Resolved ◽  
Transfer Rates ◽  
Line Intensities ◽  
Relative Line ◽  
Varied Intensity

Spectra of vanadium have been produced in a vacuum sliding spark, and their relative line intensities have been measured as parameters of the electrical circuit were varied. Intensity maxima of the spectral lines are interpreted as representing excitation energies and have been found to depend in a definitive manner on the power delivered to the source and on the duration of the discharge. The differential equation of the circuit is solved for the charge and energy transfer rates from the capacitor to the source, and two functions of the continuous circuit parameter [Formula: see text] are defined which greatly assist in interpreting the effect of the circuit parameters on the excitation in the source. A relationship was found between the excitation in the source and the electrical circuit parameters. By means of this relationship one may obtain a good estimate of the excitation gained in the spark source. It is shown that by exercising careful control over the circuit parameters it is possible to separate spectra of neighboring ionization stages through either total pulse or time-resolved observations.

Pinned-Pinned Slender Solid Struts with Parabolic Taper

1942 ◽  
Vol 46 (378) ◽  
pp. 146-151 ◽  
Author(s):  
F. J. Turton
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Linear Equation ◽  
Elastic Stability ◽  
Formal Integration ◽  
Linear Differential ◽  
Homogeneous Linear ◽  
Homogeneous Linear Differential Equation

In 1917–19, Barling and Webb, Berry, Cowley and Levy, and Webb and Lang discussed the elastic stability of struts of various tapers, but it appears to have escaped notice that one of the few cases in which formal integration is possible is that in which the tapered profile of axial longitudinal sections is part of a parabola; this gives a “ homogeneous linear “ differential equation, i.e., a linear equation of the form f (xd/dx) y = F (x).

Existence of conjugate points for self-adjoint linear differential equations

1989 ◽  
Vol 113 (1-2) ◽  
pp. 73-85 ◽  
Author(s):  
Ondřej Došlý
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equations ◽  
Conjugate Points ◽  
General Differential Equation ◽  
Linear Differential

SynopsisThe conjecture of Muller-Pfeiffer [4] concerning the oscillation behaviour of the differential equation (–l)n(p(x)y(n))(n) + q(x)y = 0 is proved, and a similar conjecture concerning the more general differential equation ∑nk=0(−l)k(Pk(x)y(k)(k + q(x)y= 0 is formulated.

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