Abstract
The effect of the change of structural integrity to the change of the reactive power flow of a vibrating structure at resonance is explored both analytically and numerically. When an undamped structure undergoes free vibration at one of its natural frequencies, the reactive component is of modal pattern and it can be used as a new modal signature. The reactive 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. The inverse problem of detecting structural damage due to the identification of variation of modal power flow pattern is investigated. Modal power flow of an orthotropic composite plate with a region of reduced stiffness in the plate is analyzed. Numerical tests show that the proposed method is effective for detection of the damage and the modal power flow is more sensitive to the change of plate stiffness than the strain mode shape in the test cases.
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