Structural power flow analysis of Timoshenko beam with an open crack

In this paper, the structural power flow characteristics of cracked Timoshenko beams are presented. The case of an infinite Timoshenko beam with an open crack is considered. The crack in the Timoshenko beam structure is modeled as a rotational spring with a constant flexibility which is deduced from the relationship between the strain energy and stress intensity factor in fracture mechanics. The flexural wave motions of perfect Timoshenko beam and cracked Timoshenko beam are investigated, then the input power flow and transmitted power flow of perfect and cracked beams are calculated. The results show that the vibrational power flow of cracked beam is highly related to the location and depth of the crack. Contours of input power flow with different frequencies are constructed to identify the location and depth of the crack. This method is very promising for the detection and location of structural damage in the future work.