An Experimental Study of Natural Vibrations of Cantilevered Triangular Plates

Abstract

Experimental results are obtained for the lowest six natural frequencies and the associated nodal lines of triangular plates of uniform thickness clamped on one edge. Two series of plates are examined. In one series, a delta-wing plan form of fixed span is maintained, and five plates are examined having aspect ratios ranging from 2 to 20. In the other series, a fixed span and a fixed root chord are maintained, and five plates are examined having mean chord-line sweepback angles ranging from 0 to 45°. Test results are presented by graphs and photographs. These results show that in the delta-wing plan form of fixed span, the frequency of each of the six modes increases as the aspect ratio increases—that is, as the root chord is made smaller. No such general property is exhibited by the plates in the sweepback series, except for the ' 'bending'' modes, where the frequencies decrease with increasing angle of sweepback. A simple method is described for finding the natural frequencies of a plate of any size, thickness, and material as long as its plan form is similar to one of the plates used in the experiments, or any other plate whose frequencies are known.