Abstract
This paper aims to present an original method for the estimation of the area of thin plates of arbitrary geometrical shapes. This method relies on the acquisition and ensemble processing of reverberated elastic signals on few sensors. The acoustical Green's function in a reverberant solid medium is modeled by a nonstationary random process based on the image-sources method. In that way, mathematical expectations of the signal envelopes can be analytically related to reverberation properties and structural parameters such as plate area, group velocity, or source-receiver distance. Then, a simple curve fitting applied to an ensemble average over N realizations of the late envelopes allows to estimate a global term involving the values of structural parameters. From simple statistical modal arguments, it is shown that the obtained relation depends on the plate area and not on the plate shape. Finally, by considering an additional relation obtained from the early characteristics (treated in a deterministic way) of the reverberation signals, it is possible to deduce the area value. This estimation is performed without geometrical measurements and requires an access to only a small portion of the plate. Furthermore, this method does not require any time measurement nor trigger synchronization between the input channels of instrumentation (between measured signals), thus implying low hardware constraints. Experimental results obtained on metallic plates with free boundary conditions and embedded window glasses will be presented. Areas of up to several meter-squares are correctly estimated with a relative error of a few percents.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have