On the Finite Element Free Vibration Analysis of Delaminated Layered Beams: A New Assembly Technique

Table 1

First frequency () of the delaminated beam, with a split occurring symmetrically about the midsection along the midplane; proposed FEM, DSM, CM, and standard FEM models.

Delamination length; /	Six 2-node FEM^†; elements	Ten 2-node FEM^†; elements	DSM [27]	Wang et al. [6], reported by [31]	Della and Shu [31]	Layerwise; FEM [17]
	Mode 1	Mode 1	Mode 1	Mode 1	Mode 1	Mode 1
Intact	—	—	22.39	22.39	22.37	22.36
0.1	22.37	22.37	22.37	22.37	22.37	22.36
0.2	22.36	22.36	22.36	22.35	22.36	22.35
0.3	22.24	22.24	22.24	22.23	22.24	22.23
0.4	21.84	21.84	21.83	21.83	21.83	21.82
0.5	20.89	20.89	20.89	20.88	20.89	20.88
0.6	19.29	19.29	19.30	19.29	19.30	19.28

^†Conventional FEM displays numerical instabilities with delamination lengths approaching 0.