Boundary Conditions in 2D Numerical and 3D Exact Models for Cylindrical Bending Analysis of Functionally Graded Structures

Table 4

Sandwich cylindrical shell panel embedding FGM core with . Analytical 3D versus 2D numerical models. Frequency in Hz.

	Mode	3D exact	2D FE	2D FE (CB)	2D GDQ	2D GDQ (CB)
	I	1.948	—	1.951	—	1.941
	I	8.856	—	8.872	—	8.823
	I	11.04	11.10	—	11.04	—
	I	18.50	18.73	—	18.50	—
	I	20.38	—	20.42	—	20.30
	I	21.16	21.28	—	21.16	—
	I	22.21	22.42	—	22.21	—
	I	24.84	24.96	—	24.84	—
	I	32.35	32.54	—	32.35	—
	I	36.49	—	36.60	—	36.34
	I	36.92	37.39	—	36.92	—
	I	37.14	37.45	—	37.14	—
	I	39.40	39.65	—	39.41	—
	I	42.26	42.61	—	42.26	—
	I	43.78	44.03	—	43.78	—
	I	45.68	46.64	—	45.68	—
	I	50.35	50.64	—	50.35	—
	I	50.40	51.28	—	50.40	—
	I	19.05	—	19.63	—	18.84
	I	30.54	31.45	—	30.55	—
	I	62.09	64.09	—	62.09	—
	I	83.26	—	88.57	—	82.54
	I	87.10	—	NA	—	NA
	II ()	88.20	89.56	—	88.20	—
	I	88.80	95.31	—	88.82	—
	I	91.76	—	NA	—	NA
	I	95.76	99.83	—	95.67	—
	I	103.6	—	NA	—	NA
	I	106.6	114.7	—	106.7	—
	I	129.1	—	NA	—	NA
	I	133.5	141.3	—	133.5	—
	I	136.4	147.5	—	136.4	—
	II ()	166.5	173.8	—	166.5	—
	I	168.3	—	NA	—	NA
	I	175.5	191.8	—	175.5	—
	II ()	176.4	179.1	—	176.4	—