A Finite Element Formulation for Bending-Torsion Coupled Vibration Analysis of Delaminated Beams under Combined Axial Load and End Moment

Table 2

The second nondimensional natural frequency () of an isotropic beam with a midplane delamination, clamped-clamped boundary conditions.

Delamination length (L2/L)	2nd natural frequency
	Present 10 elements	Wang et al. [4]	FEM [19]	DSM [18]	Della and Shu [17]	Layerwise FEM [6]
0.00	61.61	61.67	61.67	—	61.67	61.61
0.10	60.76	60.76	60.80	60.76	60.76	60.74
0.20	55.99	55.97	55.99	55.99	55.97	55.95
0.30	49.03	49.00	49.00	49.03	49.00	48.97
0.40	43.90	43.87	43.89	43.90	43.87	43.86
0.50	41.55	41.45	41.52	41.55	41.45	41.50
0.60	41.03	40.93	41.03	41.04	40.93	41.01