Study and design of a composite acoustic sensor to characterize an heterogeneous media presenting a complex matrix

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1 19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, -7 SEPTEMBER 007 Study and design of a composite acoustic sensor to characterize an heterogeneous media presenting a complex matrix PACS: e Georges, Nassar; Alain, Skaf; Fabrice, Lefebvre; Bertrand, Nongaillard I.E.M.N. - U.M.R. C.N.R.S D.O.A.E. - Université de Valenciennes - B.P Valenciennes Cedex 09, France. gnassar@univ-valenciennes.fr ABSTRACT In this work, we designed an acoustic device to study the evolution of physical parameters related to the evolution of complex heterogeneous media. This composite device is composed of a piezoelectric disk embedded in a metallic ring. The disk and the ring have the same thickness. The equations governing the radial and torsional vibrations of the device are derived and solved by analytical and numerical ways. The solution is used to prepare the design charts showing how the vibration parameters depend on the choice of the material properties of the ring and its dimensions. After calibration, we used a system to characterize a complex medium such as dough in the fermentation phase. The measurements show its aptitude to follow the evolution of the physical properties of the dough. The experimental set up presented here is able to monitor on line the evolution kinetic of dough with varying additive elements and technological parameters. INTRODUCTION In this paper we describe an initial series of calculations for the resonant frequencies and mode shapes of thin discs in radial or torsional vibration, such as those used for ultrasonic applications. Sound radiation from a thin circular disk has been examined by several investigators [1 5], focusing on either flexural vibration modes or rigid body piston motions. In such studies, sound radiation from the in-plane modes of a disk has been assumed to be negligible compared to that from the out-of-plane modes. But, if the thickness of a disk is beyond the range of the thin plate theory, radial vibration could generate sufficient sound, giving specific structural excitation. In this context, the composite disk studied plays the role of a low frequency sensor with which the medium can be adapted with broad frequency values according to the choice of the resonance mode. The radial modes give access to the shear components while the piston or membrane modes give access to the pressure components. CRITERIA OF THE CHOICE Taking into account the heterogeneity of the complex media and multi-scale interactions resulting from this, there are numerous ways of characterizing these materials. It is difficult to give an exhaustive list of the experimental techniques available to characterize them. But, it is clear that for such media their characterization becomes quasi-impossible using ultrasonic because of attenuation and scattering phenomena. Consequently, the choice of characterization by non-destructive acoustics is crucial. In this work, a theoretical and experimental study of radial and bending modes in a circular acoustic composite sensor based on a piezoelectric disk

2 embedded in a metallic ring with a controlled radius is presented. The elements composing the sensor have the same thickness. Low frequency acoustic device The basic element constituting the measurement system is an acoustic sensor composed of a piezoelectric disk embedded in a controlled diameter ring (fig. 1). The choice of the dimension of these elements is at the same time a function of the medium investigated, its degree of heterogeneity and the adapted request frequency. Piezoelectric disk Metallic ring Figure 1 - Schematic illustration of the composite sensor The efficiency of such sensors has led here to a detailed analytical and numerical study: Due to the fact that the materials that constitute the sensor have very close acoustic impedances, it can be admitted, with a good approximation, that analytical expressions giving the resonant frequencies of a disk are applicable. The different calculation results will be in function of the choice of the limit conditions. The vibrational modes studied are: Flexural or out-of-plane modes Radial or in-plane modes Out-of-plane disk modes The classic equation for transversal movement of a plate [6]: + ɺɺ = = 4 D z ρ h z 0 ; D 3 Ε h ν 1(1 ) (Eq.1) With D being the flexural rigidity of the plate, h the thickness, ρ the density, E and ν the Young s modulus and the Poisson s ratio respectively. When free vibrations are assumed, the motion is expressed as: Z( r, θ ) cosωt z = (Eq.) Substituting equation () into (1) yields: 4 4 ρω ( k ) Z = 0 ; k = (Eq.3) D From this equation, whilst applying the boundary conditions of a free circular plate, we obtained specific frequencies f for the different resonance modes of a disk with a radius a. f 1 D = λs n ; λ, π a ρ h s n =, (Eq.4) ka Radial or in-plane modes The radial mode resonant frequencies for a disk with a radius a are obtained using equation based on the Bessel functions [7]: J 1 αa) = αa J 1 ν ( α ) 1( 0 a ω π f α = = V V (Eq.5) 19 th INTERNATIONAL CONGRESS ON ACOUSTICS ICA007MADRID

3 E( 1 ν ) ( 1+ ν )( 1 ν ) V = (Eq.6) ρ Results obtained Figure and table1 show the resonance modes and the associated frequencies calculated on the basis of the analytical equations and numerically by finite elements. n s X X Figure - Resonance modes and the associated frequencies s : circular nodes number n : axial nodes number Global sensor (F Hz) Analytical FEM x x x x Table. 1 Experimental results The composite sensor is made up of a mm thick piezoelectric disk with a diameter of cm embedded in an aluminium ring of the same thickness as the piezo element and with a diameter of 10 cm. Figure 3 shows the resonant frequencies of an experimental sensor measured by a network analyser. The variation in electrical impedance Z around the frequencies of 35 khz and 95 khz shows the good concordance between the analytical, numerical and experimental models. Figure 3. Experimental conception and results showing the radial modes given by the electrical impedance measurement 19 th INTERNATIONAL CONGRESS ON ACOUSTICS ICA007MADRID 3

4 APPLICATION The purpose of this study was to use an acoustic transmission technique according to two models: 1. Radio frequency (Burst) with radial modes of very low and low frequency. The case if the investigated medium is either homogeneous or has a relatively low heterogeneity. The exploited acoustic magnitudes are the velocity and the attenuation of a propagated wave.. Broad spectrum through a very short duration mechanical shock playing the role of an acoustic emitter, the case if the medium shows a relatively high absorbing phenomenon. The measured magnitudes are the frequency drift and the rate of received energy. Figure 4 gives a schematic diagram of the measuring system. Figure 4. Schematic diagram of the measuring system Radio frequency excitation Synthetic polymer disks have been used as calibrators. These disks, having the same diameter as the sensor were differentiated by their hardness and their viscoelastic properties. The graph in Figure 5 shows the evolution of the amplitude and the acoustic velocity for a radial mode excitation at a frequency of 36 khz. This for the different calibrators placed successively between the transmitter and the receiver. The results show the capacity of the measurement system to detect variations in viscoelastic properties of the different media. The results on the variation of velocity are in agreement with the rheological measurements obtained with the compression test (Fig.6). Amplitude (mv) Hardness (Shore D) V(m/s) Hardness (Shore D) Figure 5. Evolution of the amplitude and the acoustic velocity versus hardness of the polymer disk calibrators 19 th INTERNATIONAL CONGRESS ON ACOUSTICS ICA007MADRID 4

5 The results show the capacity of the measurement system to detect variations in viscoelastic properties of the different media. The results on the variation of speed are in agreement with the rheological measurements obtained with the compression test (Fig. 6). 6 Elasticity component (MPa) Hardness ( Shore D ) Figure 6. Evolution of the elasticity component versus hardness of the polymer disks measured by a rheological compression test Excitation by mechanical shock The radio frequency measurements showed their limits in strongly diffusing complex matrices such as in fermenting dough. To remedy this constraint the preceding excitation is replaced by a mechanical shock of controlled duration in order to orientate the sensors resonance towards a very low frequency in flexural mode. By transmission measurement at a frequency of around khz, Figure 7 shows the evolution in the delay of the acoustic wave received through the medium and this for three different dough making processes. Measurements were quasi-impossible within a frequency band of around 40 khz for a dough thickness of cm between the sensors. Figure 7. Evolution in the delay of the received acoustic signal for three different dough making processes. CONCLUSION This work has examined an acoustic method to study a complex matrix such as dough. The 19 th INTERNATIONAL CONGRESS ON ACOUSTICS ICA007MADRID 5

6 measurements can be used to determine the critical time in the process of dough development. After the development of the sensor technologies, it has been shown that the received signals in this technique evolve differently according to the properties of the product used. The results from this technique in the fermentation phase appear to be sensitive to the different technological parameters in dough making. Nevertheless, from these results it appears that the acoustic measurement through acoustic magnitude deviation can potentially be used as an effective on-line quality control technique in viscoelastic complex media processes. AKNOWLEDGEMENTS This work has been supported by the FEDER & the Region Nord Pas de Calais. References: [1] W. Thompson Jr.: The computation of self- and mutual-radiation impedances for annular and elliptical pistons using Bouwkamp integral, Journal of Sound and Vibration 17 () (1971) [] M.R. Lee, R. Singh: Analytical formulations for annular disk sound radiation using structural modes, Journal of the Acoustical Society of America 95 (6) (1994) [3] H. Levine, F.G. Leppington: A note on the acoustic power output of a circular plate, Journal of Sound and Vibration 11 (5) (1988) [4] W.P. Rdzanek Jr., Z. Engel: Asymptotic formula for the acoustic power output of a clamped annular plate, Applied Acoustics 60 (5) (000) [5] H.W. Wodtke, J.S. Lamancusa: Sound power minimization of circular plates through damping layer placement, Journal of Sound and Vibration 15 (5) (1998) [6] A.W. Leissa: Vibration of Plates, SP-160, NASA, US Government Printing Office, Washington, DC, [7] Michel Brissaud: Characterization of piezoceramics, IEEE transactions on ultrasonics Ferroelectrics And frequency control 38 (6) November th INTERNATIONAL CONGRESS ON ACOUSTICS ICA007MADRID 6