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

Table 3

One-layered FGM cylinder with . Analytical 3D versus 2D numerical models. Frequency in Hz.

	Mode	3D exact	2D FE	2D FE (CB)	2D GDQ	2D GDQ (CB)
	I	0.896	—	0.897	—	0.883
	I	2.532	—	2.538	—	2.511
	I	4.854	—	4.867	—	4.819
	I	7.848	—	7.871	—	7.801
	I	11.51	—	11.55	—	11.46
	I	13.56	13.60	—	13.57	—
	I	14.41	14.49	—	14.45	—
	I	15.84	—	15.89	—	15.77
	I	16.38	16.40	—	16.36	—
	I	17.56	17.67	—	17.63	—
	I	20.83	—	20.90	—	20.70
	I	22.07	22.22	—	22.16	—
	I	24.41	24.42	—	24.38	—
	I	26.49	—	26.58	—	26.40
	I	27.42	27.52	—	27.46	—
	I	27.51	27.72	—	27.63	—
	I	28.75	28.90	—	28.83	—
	I	29.21	29.26	—	29.22	—
	I	8.774	—	9.085	—	8.679
	I	24.56	—	25.71	—	24.30
	I	39.78	40.89	—	39.79	—
	I	43.88	43.57	—	43.88	—
	I	46.54	—	49.20	—	46.02
	I	55.75	59.05	—	55.76	—
	I	72.02	71.01	—	72.02	—
	I ()	73.22	73.90	—	73.19	—
	I	74.19	—	79.33	—	73.47
	I	81.10	82.61	—	81.11	—
	I	81.89	88.11	—	81.91	—
	I	87.83	91.73	—	87.85	—
	I	90.16	90.84	—	90.17	—
	I	107.1	—	115.9	—	106.1
	I	108.1	115.5	—	108.1	—
	I	108.9	110.5	—	108.9	—
	I	114.2	124.5	—	114.3	—
	I	126.3	128.6	—	126.3	—