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

Table 1

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

Delamination length (L2/L)	1st natural frequency
	Present 10 elements	Wang et al. [4]	FEM [19]	DSM [18]	Della and Shu [17]	Layerwise FEM [6]
0.00	22.39	22.39	22.39	—	22.37	22.36
0.10	22.37	22.37	22.37	22.37	22.37	22.36
0.20	22.36	22.35	22.36	22.36	22.36	22.35
0.30	22.24	22.23	22.24	22.24	22.24	22.23
0.40	21.84	21.83	21.84	21.83	21.83	21.82
0.50	20.89	20.88	20.89	20.89	20.89	20.88
0.60	19.29	19.29	19.29	19.30	19.30	19.28