Modified and Simplified Sectional Flexibility of a Cracked Beam

Table 2

Natural frequency ratio with the crack depth at location 0.5.

Crack location	Crack depth	Natural frequency ratio
𝐿1/𝐿	𝑎/ℎ	𝜔1/𝜔01	𝜔2/𝜔02	𝜔3/𝜔03	𝜔4/𝜔04	𝜔5/𝜔05
0.5	0.0	1.0000	1.0000	0.9999	1.0000	0.9999
0.5	0.1	0.9902	1.0000	0.9904	1.0000	0.9905
0.5	0.2	0.9770	1.0000	0.9778	1.0000	0.9786
0.5	0.3	0.9586	1.0000	0.9613	1.0000	0.9636
0.5	0.4	0.9321	1.0000	0.9391	1.0000	0.9448
0.5	0.5	0.8927	1.0000	0.9094	1.0000	0.9218
0.5	0.6	0.8314	1.0000	0.8699	1.0000	0.8948
0.5	0.7	0.7328	1.0000	0.8199	1.0000	0.8654
0.5	0.8	0.5723	1.0000	0.7634	1.0000	0.8377
0.5	0.9	0.3245	1.0000	0.7144	1.0000	0.8175