Modelling elastic wave propagation in thin plates
D. Rovetta, A. Sarti, S. Tubaro, G. Colombo
In this work we propose an in-depth study of elastic wave propagation in thin plates, based on the theory of Viktorov. We show that at the frequency range of interest and for modest plate thicknesses, the only waves that can be excited and propagate in the structure are guided waves (also called Lamb waves). As the elastic properties of the panel and the finger touch signature are usually unknown, therefore we propose two different methods for estimating them through simple experimental procedures (calibration). The first is an active method based on the use of a transducer, while the second one is a passive original method which infers the elastic properties of the board from the information given by a single tactile interaction. The obtained estimates are then used to simulate the propagation in the boards. Our approach is to implement the general solution of the elastic wave equation for infinite plates, and introduce the boundary conditions afterwards using a real-time beam tracer. We finally prove the effectiveness of the approach by comparing the predicted response of a finger touch with the measured one on a MDF (Medium Density Fiberboard) plate, showing how the active and the passive calibration procedures give comparable results.
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The board was hanged at the ceiling using two wires from the top corners of the plate. Free boundary condition was assumed in the calculations: the board is free to vibrate without any external constraint. Anyway we tested the system with good result even putting the plate on a common table, without removing the free boundary condition assumption.
Diego Rovetta.
Hi, thanks for you answer. I have two further questions. :-)
From the amplitudes of these boundary reflections, I think that the attenuation has been considered for the computation. Right?
One more question is if there is any consideration of energy that is lost during the reflection or refraction?
Thanks very much.
Ze
The board response is computed as the result of the sum of the signals due to the direct arrival and to the most energetic reflected rays. It can be proved that the reflected signals are attenuated and delayed copies of the incident one. The attenuation (energy lost during the reflection) and the delay time of the reflected rays (reflection coefficients) are evaluated from the observations.
Q. What is the sampling rate of the data acquisition device used in the experiment?
Thank you.
Quite interesting content in the paper.
I have one question regarding the part 5: prediction of the board response. It is interesting to see the high accuracy of the predicted waveform. My question is how the board was hanged? And what boundary condition was assumed for the calculation of the reflections?
Thanks