Influence of Non-Structural Localized Inertia on Free Vibration Response of Thin-Walled Structures by Variable Kinematic Beam Formulations

Table 4

First 10 natural frequencies (Hz) for the I-shaped beam.

Mode	Classical and refined models based on TE				LE models		MSC Nastran^©
	EBBM	TMB	𝑁=6	𝑁=8	7 L9	12 L9	FEM-1D	FEM-2D	FEM-3D
1	15.67^b	15.65^b	15.73^b	15.73^b	15.75^b	15.72^b	15.63^b	15.11^b	15.68^b
2	35.28^b	35.01^b	34.93^b	34.90^b	34.87^b	34.86^b	34.73^b	34.73^b	34.80^b
3	97.91^b	96.08^b	96.16^t	88.74^t	77.68^t	76.58^t	96.26^b	68.45^t	75.61^t
4	217.27^b	206.05^b	97.06^b	96.99^b	97.13^b	96.88^b	196.99^b	93.04^b	96.63^b
5	272.62^b	265.09^b	198.27^b	197.28^b	196.28^b	196.10^b	262.81^b	191.98^b	195.71^b
6	439.19^a	439.01^a	265.24^b	264.79^b	246.78^t	243.49^t	439.09^a	220.31^t	240.63^t
7	529.90^b	507.02^b	298.13^t	277.27^t	265.12^t	264.20^b	486.79^b	253.52^b	263.49^b
8	592.06^b	533.06^b	440.66^a	440.64^a	440.64^a	440.62^a	497.53^b	413.86^c	440.23^a
9	866.98^b	811.08^b	491.81^b	487.36^b	453.27^t	448.06^t	788.63^b	439.82^a	443.55^t
10	1117.81^b	950.08^b	502.74^t	495.78^t	482.74^b	481.97^b	828.65^b	464.45^b	480.95^b
DOFs	93	155	2604	4185	4185	6975	126	12200	127800

aAxial; bbending; ccoupled; ttorsional.