Determination of Buckling Loads by Frequency Measurements

Author: Chu, Tao Hung

Year: 1949

Degree: Engineer's thesis

Advisor: Hudson, Donald E.

Committee Member: Unknown, Unknown

Option: Mechanical Engineering

DOI: 10.7907/chf2-y477

Abstract

Analytic solutions for the relation between compressive load and natural frequency are obtained for a simple column and a circular ring under uniform radial load. The relation is of the form [Formula. See abstract in scanned thesis for details]. An implicit analytic solution for a rectangular frame under symmetrical axial load and for symmetrical buckling is also obtained. The complexity of the final transcendental equation indicates that the relation between P and λn will not be linear.

The relation is checked experimentally for a simple column. The extrapolated critical load is within 2% of the computed value.

The experiment on a rectangular frame shows that the relation between P and λn can be very closely approximated by a linear one. The extrapolated critical load is 17,500 lbs. which is about 49% higher than that for the lowest symmetrical mode and about 3% higher for the lowest unsymmetrical mode. Evidently, the measured frequency is in the latter mode. The misleading result is due to the fact that these modes have frequencies very close to each other, and the unsymmetrical mode becomes more stable because of restraints at the supports and dynamic coupling between the modes.

Some interesting points in this work are stressed in the conclusion and some suggestions for the additional experiments are made.

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