Crack Detection in Plate-Like Structures Using Modal Strain Energy Method considering Various Boundary Conditions

Table 1

Change in natural frequencies (Hz) of undamaged plates due to mesh sizes.

Mode	Mesh size
	2 × 2	4 × 4	8 × 8	12 × 12	24 × 24	48 × 48
Case 1: free conditions
1	119.49	115.75	113.43	112.75	112.36	112.29
2	194.37	175.42	167.54	165.97	164.92	164.66
3	230.03	232.92	214.65	211.24	209.27	208.72
4	268.33	300.71	297.02	294.35	292.43	291.82
Case 2: hinged conditions
1	167.24	172.57	169.64	168.89	168.16	167.92
2	14225	547.18	447.1	431.86	422.97	420.79
3	22517	901.84	720.1	691.63	675.48	671.69
4	24622	1797.7	986.67	900.83	854.87	843.92
Case 3: fixed conditions
1	5633.4	367.42	320.07	312.75	308.53	307.49
2	14225	1126.2	699.68	656.37	633.06	627.51
3	414212	1643.2	1033.2	968.05	932.69	924.23
4	—	11317	1435.9	1241.6	1148	1126.7