Modal power flow with application to damage detection

Features of power flow of an undamped beam at resonance are studied in the present paper. It is found that when an undamped beam undergoes free vibration at one of its natural frequencies, the active component of the power flow becomes zero while the reactive component is of modal pattern, whose characteristic frequency is twice of the natural frequency. The power flow in this case can thus be termed as modal power flow. The instantaneous energy density associated with the vibration mode consists of a static component and a dynamic component, related to the mean total and Lagrangian energy densities, respectively. The modal power flow is relevant to the latter but independent of the former. Potential application of modal power flow to structural damage detection is investigated. Two typical damages, transverse cracks and delaminations, are considered. A damage index based on the modal power flow is proposed, and compared with the damage indices based on the slope, the bending strain, and the strain energy through numerical examples. The imperfection of boundary conditions is also considered. It is shown that the proposed damage index is sensitive to both types of damage, thus can be used as an universal damage indicator.