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

Table 7

First 10 natural frequencies (Hz) for the hollow-rectangular box beam with localized inertia at the tip cross-section (Figure 20(a), Case A).

Mode	LE models		MSC Nastran^©
	10 L9	16 L9	FEM-2D	FEM-3D
1	6.20^d	6.04^d	6.11^d	5.98^d
2	18.54^d	18.23^d	18.94^d	17.97^d
3	43.77^d	39.75^d	38.66^d	38.02^d
4	44.07^d	43.20^d	69.36^d	52.90^d
5	95.47^d	74.18^s	70.43^s	69.60^s
6	100.62^s	77.59^s	73.98^s	73.12^s
7	103.41^s	79.15^s	78.77^s	74.72^s
8	109.34^s	84.75^s	81.38^s	80.47^s
9	118.77^s	93.54^s	89.90^s	89.07^s
10	119.60^s	96.37^s	93.33^s	90.49^s
DOFs	5580	8928	15000	38400

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