Nonlinear instability of angle section beams subjected to static and dynamic sudden step loads

To realize starting operation and reduce position estimation error of switched reluctance motor (SRM) without position sensor, a novel control method based on pulse injection, divided angle section and variable threshold is presented. The starting operation of SRM can be accomplished by injecting high frequency pulse and judging position sectors. Variable threshold is used to reduce position estimation error. The value of threshold is obtained by looking up table prestored in controller. The method avoids complicated mathematical model and is suitable for starting operation with two phases. Besides, rotor position estimation error of this method is analyzed and the method which can decreased the error is proposed. At last, the experiment has been done to verify the performance of the control method.

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Sinusoidal Torsional Buckling of Bars of Angle Section Under Bending Loads, as a Problem in Plate Theory

Journal of Applied Mechanics ◽

10.1115/1.4010336 ◽

1951 ◽

Vol 18 (3) ◽

pp. 285-292

Author(s):

H. J. Plass

Keyword(s):

Infinite Series ◽

Plate Theory ◽

Ritz Method ◽

Compressive Load ◽

Series Solutions ◽

Torsional Buckling ◽

Bending Load ◽

Angle Section ◽

Bending Loads

Abstract Timoshenko has applied plate theory to each leg of an angle-section bar to determine the critical compressive load needed to cause sinusoidal torsional buckling. In this paper his idea is used to calculate the critical bending load needed to cause sinusoidal torsional buckling of an angle bar. The bending is assumed to be applied so that the extreme fibers of the angle are in compression, the vertex in tension. Approximate results are first obtained by means of the Rayleigh-Ritz method. The approximate deflection functions from which the energy terms are computed are based upon certain infinite-series solutions. After having obtained approximate results, exact values are obtained, using the approximate values as a guide to limit the amount of calculation. The results of this calculation are shown in Fig. 5, where they are compared with those predicted by bar theory. Differences between the two theories become more noticeable as the bar becomes short compared to its flange width. It is found that the critical bending load becomes larger very rapidly as the ratio of length to width of the flanges decreases. Bar theory predicts no such increase. The reason for this difference is explained.

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