Curvature Effects on the Vibration Characteristics of Doubly Curved Shallow Shells with General Elastic Edge Restraints

Table 3

Frequency parameters of shallow shells with different boundary conditions (, , , and ).

	Mode number	Boundary conditions
		F-F-F-F	C-F-F-F	C-C-F-F	C-F-C-F	C-C-C-F	C-C-C-C
1	1	13.41	3.739	7.860	25.28	26.79	40.27
		(13.46^a)	(3.754)	(7.894)	(25.30)	(26.62)	(40.26)
		[13.43^b]	[3.756]	[7.891]	[25.32]	[26.84]	[40.25]
	2	19.50	8.456	23.80	25.28	42.58	74.43
		(19.56^a)	(8.492)	(23.90)	(25.30)	(42.71)	(74.17)
		[19.54^b]	[8.467]	[23.84]	[25.32]	[42.57]	[74.39]
	3	25.92	21.44	27.83	45.44	63.39	74.43
		(25.99^a)	(21.53)	(27.92)	(45.53)	(63.56)	(74.17)
		[25.82^b]	[21.46]	[27.78]	[45.45]	[63.41]	[74.39]
	4	34.72	28.17	49.08	61.32	77.62	108.7
		(34.85^a)	(28.26)	(49.27)	(61.34)	(77.64)	(108.7)
		[34.73^b]	[28.12]	[49.09]	[61.33]	[77.60]	[108.7]
∞	1	13.44	3.802	7.201	22.72	24.44	37.75
		(13.46^a)	(3.806)	(7.218)	(22.36)	(24.34)	(37.56)
		[13.45^b]	[3.807]	[7.216]	[22.73]	[24.46]	[37.75]
	2	20.08	8.507	24.23	26.46	40.47	73.31
		(20.12^a)	(8.526)	(24.30)	(26.43)	(40.53)	(72.59)
		[20.07^b]	[8.509]	[24.23]	[26.47]	[40.46]	[73.30]
	3	24.74	21.96	27.03	43.63	63.65	74.28
		(24.77^a)	(21.98)	(27.08)	(43.59)	(62.56)	(72.66)
		[24.73^b]	[21.96]	[27.02]	[43.63]	[63.69]	[74.30]
	4	34.70	27.21	48.09	61.67	76.58	108.3
		(34.79^a)	(27.29)	(48.21)	(61.59)	(76.47)	(108.4)
		[34.67^b]	[27.19]	[48.08]	[61.70]	[76.57]	[108.3]
−1	1	13.41	3.794	7.041	25.06	26.68	38.59
		(13.46^a)	(3.814)	(7.071)	(25.07)	(26.78)	(38.51)
	2	21.84	8.444	25.47	28.57	41.54	74.02
		(21.90^a)	(8.480)	(25.58)	(28.62)	(41.60)	(74.09)
	3	24.16	22.28	26.92	44.82	63.48	74.02
		(24.24^a)	(22.38)	(27.03)	(44.92)	(63.92)	(73.97)
	4	34.81	27.80	48.02	61.44	77.31	108.1
		(34.94^a)	(27.89)	(48.22)	(61.47)	(77.26)	(108.0)

Results from [16].
^bResults are obtained from FEM models.