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

Table 6

First 10 natural frequencies (Hz) for the hollow-rectangular box beam.

Mode	Classical and refined models based on TE					LE models		MSC Nastran^©
	EBBM	TMB	𝑁=4	𝑁=6	𝑁=8	10 L9	16 L9	FEM-2D	FEM-3D
1	25.48^b	25.36^b	25.15^b	24.73^b	24.52^b	24.53^b	24.07^b	24.42^b	23.89^b
2	75.70^b	72.79^b	72.58^b	72.42^b	72.35^b	62.08^d	57.02^d	55.34^d	54.55^d
3	158.03^b	153.20^b	137.79^b	127.58^b	90.87^d	72.62^b	72.67^b	70.43^s	69.59^s
4	411.74^a	357.95^b	146.19^t	134.29^d	111.68^s	100.61^s	74.19^s	73.98^s	72.51^b
5	435.12^b	406.88^b	330.86^b	265.87^s	127.00^s	103.42^s	77.60^s	74.31^b	73.12^s
6	435.23^b	411.74^a	346.16^b	274.47^d	131.29^s	109.38^s	80.88^s	75.35^s	75.03^s
7	833.29^b	745.94^b	413.68^a	344.10^b	139.88^s	118.52^d	84.76^s	81.38^s	80.48^s
8	1089.50^b	808.29^b	428.76^t	361.71^s	141.44^d	119.24^s	96.36^s	89.73^s	89.56^s
9	1235.23^a	1146.76^b	549.40^b	388.13^d	152.86^s	122.01^b	97.79^s	93.33^s	92.30^s
10	1338.69^b	1284.52^b	690.19^t	413.49^a	166.72^s	133.77^s	109.87^s	101.87^s	101.58^s
DOFs	93	155	1395	2604	4185	5580	8928	15000	38400

aAxial; bbending; ccoupled; ddifferential bending; ttorsional; sshell-like.