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

Table 8

First 10 natural frequencies (Hz) for the hollow-rectangular box beam with two localized masses at the tip cross-section (Figure 20(b), Case B).

Mode	LE models		MSC Nastran^©
	10 L9	16 L9	FEM-2D	FEM-3D
1	6.86^b	6.86^b	7.02^b	6.84^b
2	13.68^d	12.08^d	11.79^d	11.66^d
3	19.96^b	19.89^b	20.54^b	19.75^b
4	55.69^s	54.27^d	66.47^s	54.22^d
5	62.60^d	60.69^s	66.78^d	64.12^s
6	65.02^s	62.80^s	70.43^s	69.21^s
7	94.04^b	73.64^s	73.98^s	71.08^s
8	97.95^s	74.55^s	81.38^s	73.56^s
9	101.2^s	77.86^s	83.15^s	80.21^s
10	100.4^s	84.96^s	85.66^s	80.67^s
DOFs	5580	8928	15000	38400

bBending; ccoupled; ddifferential bending; ttorsional; sshell-like.