Modelling a Cracked Beam Structure Using the Finite Element Displacement Method

Table 1

Comparisons of the first two natural frequencies from the proposed model, FEFM, and the experimental investigation for a cracked cantilever beam with open crack.

Crack (mm)		Method	Natural frequencies (Hz)		Difference (%)
X	a		The first mode	The second mode	The first mode	The second mode
80	2	Exp. [29]	184.0	1160.0	—	—
		FEFM [18]	184.0	1159.8	0	0.02
		This study	184.2	1159.3	0.11	0.06
80	6	Exp. [29]	174.7	1155.3	—	—
		FEFM [18]	177.1	1154.7	1.37	0.05
		This study	175.3	1153.9	0.34	0.12
140	2	Exp. [29]	184.7	1153.1	—	—
		FEFM [18]	184.7	1153.2	0	0
		This study	184.7	1153.1	0	0
140	6	Exp. [29]	181.2	1092.9	—	—
		FEFM [18]	181.8	1102.9	0.33	0.91
		This study	181.4	1091.1	0.11	0.16
200	2	Exp. [29]	185.0	1155.0	—	—
		FEFM [18]	185.0	1155.0	0.05	0.8
		This study	185.0	1154.9	0	0.01
200	6	Exp. [29]	184.3	1106.3	—	—
		FEFM [18]	184.4	1114.8	0.05	0.77
		This study	184.3	1106.2	0	0.01
No crack		Exp. [29]	185.2	1160.6	—	—
		FEFM [18]	185.1	1160.4	0.05	0.02
		This study	185.1	1159.9	0.05	0.06

FEFM: finite element model with force method.