Nondestructive Detection of a Crack in a Triangular Cantilever Beam Based on Frequency Measurement
Triangular cantilevers are usually used as small force sensors in the transverse direction. Analyzing the effect of a crack on transverse vibration of a triangular cantilever will be of value to users and designers of cantilever deflection force sensors. We present a method for prediction of location and size of a crack in a triangular cantilever beam based on measurement of the natural frequencies in this paper. The crack is modeled as a rotational spring. The beam is treated as two triangular beams connected by a rotational spring at the crack location. Formulae for representing the relation between natural frequencies and the crack details are presented. To detect crack details from experiment results, the plots of the crack stiffness versus its location for any three natural modes can be obtained through the relation equation, and the point of intersection of the three curves gives the crack location. The crack size is then calculated using the relation between its stiffness and size. An example to demonstrate the validity and accuracy of the method is presented.
Yu Zhou, Shan-Tung Tu and Xishan Xie
F. Wang and X. Z. Zhao, "Nondestructive Detection of a Crack in a Triangular Cantilever Beam Based on Frequency Measurement", Key Engineering Materials, Vols. 353-358, pp. 2285-2288, 2007