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

Table 3

First 10 natural frequencies (Hz) for the clamped-clamped C-shaped beam with localized inertia at 𝑦=(3/4)𝐿 (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	10.09^b	9.99^b	9.50^b	7.13^c	6.34^c	5.90^c	5.86^c	5.55^c	5.57^c
2	17.18^b	16.70^b	11.62^b	10.32^c	10.21^c	10.14^c	10.13^c	9.86^c	9.91^c
3	24.52^b	24.01^b	19.39^t	14.82^t	13.33^t	12.49^t	12.41^t	11.99^t	12.45^t
4	41.73^b	39.38^b	26.06^t	23.00^t	22.54^t	22.34^t	22.30^t	22.02^t	21.76^t
5	51.56^b	49.97^b	31.58^c	28.12^c	27.59^c	26.33^c	26.13^c	25.15^c	26.26^c
6	85.41^b	79.17^b	45.77^c	31.47^c	28.50^c	27.99^c	27.96^c	27.63^c	27.81^c
7	91.67^b	87.63^b	49.97^c	47.70^c	44.95^c	42.40^c	41.92^c	39.70^c	41.22^c
8	108.39^b	105.88^b	64.95^c	50.60^c	48.43^c	48.14^c	47.96^c	46.89^c	46.82^c
9	142.65^b	135.53^b	76.50^c	61.84^c	56.29^c	52.94^c	52.18^c	48.26^c	48.43^c
10	154.97^b	139.71^b	83.10^c	63.53^c	62.81^c	62.63^c	62.41^c	61.33^c	56.38^c
DOFs	93	155	1395	2604	4185	3627	5859	37995	176115

bBending; ccoupled; ttorsional.