Modelling a Cracked Beam Structure Using the Finite Element Displacement Method

Table 3

Comparison of the fundamental natural frequency from the proposed model with those from the FEA and experimental investigation for a cantilever beam with open crack and breathing crack.

Crack (mm)		Method	fc (Hz)	fo (Hz)	fb (Hz)	Frequency ratio fo/fc	Frequency ratio fb/fc	Difference of fo/fc with exp.	Difference of fb/fc between FEA and proposed model (%)
X	a
80	2	FEA [31]	183.3	182.7	182.9	0.997	0.998	0.003	—
		This study	185.1	184.2	184.7	0.995	0.998	0.001	0.21
		Exp. [29]	185.2	184.0	—	0.994	—	—	—
80	6	FEA [31]	183.3	177.0	178.5	0.966	0.974	0.023	—
		This study	185.1	175.3	180.1	0.947	0.973	0.004	0.08
		Exp. [29]	185.2	174.7	—	0.943	—	—	—
140	2	FEA [31]	183.3	183.1	183.2	0.999	0.999	0.002	—
		This study	185.1	184.7	184.9	0.998	0.999	0.001	0.05
		Exp. [29]	185.2	184.7	—	0.997	—	—	—
140	6	FEA [31]	183.3	180.0	182.0	0.982	0.993	0.004	—
		This study	185.1	181.4	183.2	0.980	0.990	0.002	0.32
		Exp. [29]	185.2	181.2	—	0.978	—	—	—

FEA: finite element analysis.