Abstract:
Structural intensity has been used to describe the power transferred by elastic waves through mechanical structures. In this work, the structural intensity is first expressed using the Timoshenko beam theory as an approximation to model Lamb wave propagation of the A0 and A1 modes. Simulations are conducted to illustrate localized structural intensity for a burst propagating in a semi-infinite beam with a notch represented by a thickness variation. The results show that a burst with a center frequency below the cut-off frequency of the beam propagates as a shear-dominated wave (A0 wave) while a moment-dominated burst also propagates above the cut-off frequency (A1 wave). An experimental setup 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 anechoic termination at the other end, excited by piezoceramic transducers. Finite differences, the wavenumber Fourier transform, wave decomposition and filter synthesis are implemented to estimate the structural intensity from discrete measurements of the transverse velocity over a few centimeters using a laser vibrometer. The experimental results show that both shear and moment components of intensity can be measured for frequencies below and above the cut-off frequency and that the notch can be detected, but also indicate that care should be taken in the spacing of the measurement points due to the presence of waves of different wavelengths.
