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

Table 2

First 10 natural frequencies (Hz) for the cantilever C-shaped beam with localized inertia at the tip cross-section (Figure 9).

Mode	Classical and refined models based on TE					LE models		MSC Nastran^©
	EBBM	TMB	𝑁=4	𝑁=6	𝑁=8	6 L9	10 L9	FEM-2D	FEM-3D
1	1.15^b	1.15^b	1.15^b	1.13^c	1.12^c	1.11^c	1.11^c	1.10^c	1.11^c
2	1.97^b	1.96^b	1.89^b	1.73^c	1.65^c	1.58^c	1.58^c	1.53^c	1.57^c
3	8.67^b	8.63^b	7.62^t	5.70^t	5.16^t	4.90^t	4.88^t	4.88^t	4.56^t
4	14.69^b	14.48^b	11.37^t	9.28^t	8.37^t	7.77^t	7.73^t	7.39^t	7.67^t
5	25.76^b	25.44^b	12.60^c	10.09^c	9.82^c	9.73^c	9.72^c	9.52^c	9.86^c
6	41.50^b	40.48^b	25.28^c	20.64^c	18.23^c	16.92^c	16.81^c	16.08^c	16.63^c
7	49.00^b	48.07^b	30.46^c	23.37^c	22.83^c	22.71^c	22.64^c	22.59^c	22.23^c
8	54.78^b	53.78^b	35.77^c	29.79^c	28.69^c	27.42^c	27.16^c	26.09^c	26.71^c
9	85.83^b	81.86^b	42.93^c	33.48^c	30.51^c	29.70^c	29.64^c	29.27^c	29.51^c
10	89.33^b	85.37^b	51.67^c	40.65^c	38.24^c	39.12^c	38.16^c	37.90^c	34.35^c
DOFs	93	155	1395	2604	4185	3627	5859	38250	177000

bBending; ccoupled; ttorsional.