The use of time domain localized structural intensity for damage characterization

Abstract

Structural intensity has been used to describe the power transferred by elastic wavesthrough mechanical structures. In this work, the structural intensity is first expressed usingthe Timoshenko beam theory as an approximation to model Lamb wave propagation of theA0 and A1 modes. Simulations are conducted to illustrate localized structural intensity fora burst propagating in a semi-infinite beam with a notch represented by a thicknessvariation. The results show that a burst with a center frequency below the cut-off frequencyof the beam propagates as a shear-dominated wave (A0 wave) while a moment-dominatedburst also propagates above the cut-off frequency (A1 wave). An experimentalsetup for demonstrating the technique with real measurements is then presented.This consists of a 5 m long notched beam, free at one end and with an anechoictermination at the other end, excited by piezoceramic transducers. Finite differences,the wavenumber Fourier transform, wave decomposition and filter synthesis areimplemented to estimate the structural intensity from discrete measurementsof the transverse velocity over a few centimeters using a laser vibrometer. Theexperimental results show that both shear and moment components of intensity can bemeasured for frequencies below and above the cut-off frequency and that the notchcan be detected, but also indicate that care should be taken in the spacing ofthe measurement points due to the presence of waves of different wavelengths.