Analytical and Coupled Field FEA Modeling for E/M Impedance of Shear Horizontal Piezoelectric Wafer Active Sensors to Measure Liquid Properties

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1 Analytical and Couled Field FA Modeling for /M Imedance of Shear Horizontal Piezoelectric Wafer Active Sensors to Measure Liquid Proerties T. Kamas, V. Giurgiutiu Deartment of Mechanical ngineering, skisehir Osmangazi University, skisehir, Turkey, Deartment of Mechanical ngineering, University of South Carolina, Columbia, SC, USA, Abstract This aer resents analytical and couled field finite element model develoment for the electromechanical imedance sectroscoy (MIS) of iezoelectric wafer active sensors olarized and excited by electric field such that it can vibrate in shear horizontal mode (). First, interacting with liquid medium is modeled by -D analytical model using resonator theory solving the wave differential equation and the iezoelectric constitutive equations for shear horizontal (d5) mode. Then, the analytical MIS model for SH- PWAS in contact with liquid is simulated and the results are obtained for different liquid material roerties such as density and viscosity. Commercial ANSYS multi-hysics software is used to generate -D couled field finite element (CF-FA) models for MIS of in different liquid media. The CF-FA simulation results are used to validate corresonding -D analytical models by comarison. The aer ends with summary and conclusions. Keywords: Shear horizontal, iezoelectric, MIS, Couled field, Multi-hysics FA Introduction Piezoelectric wafer active sensor (PWAS) is light-weighted, inexensive, unobtrusive, minimally intrusive sensor requiring low-ower (Giurgiutiu, 8). PWAS is made of iezoelectric ceramic with electric field olarization across the electrodes deosited on both surfaces. It has recently been extensively emloyed in many alications for in-situ insection. MIS techniques where PWAS is emloyed as a resonator are used to generate standing waves in local field of a substrate structure. MIS method has been utilized to determine the local dynamic characteristics of PWAS interacting with a medium for in-situ ultrasonics. (Liang, Sun, & Rogers, 994; Sun, Liang, & Rogers, 994; Zagrai & Giurgiutiu, ), and (Park, Sohn, Farrar, & Inman, ) utilized the MIS method for high frequency local modal sensing. Conventional PWAS is thin rectangular or circular wafer that is oled in thickness direction, with electrodes on to and bottom surfaces; those tyes of PWAS are either used in in-lane or thickness mode (Kamas, Lin, & Giurgiutiu, ). In in-lane mode, alying an electric field in thickness direction causes the sensor lateral dimensions to increase or decrease, a longitudinal strain will occur ε = d where d is the iezoelectric couling coefficient measured in [m/v]. Thickness mode is a mode that occurs simultaneously with extension mode, but dominates at higher frequencies in MHz, in which strain in the

2 ACM5 thickness direction will occur ε = d, where d is the iezoelectric couling coefficient in thickness direction (Kamas, Giurgiutiu, & Lin, 4). A different mode of oscillation can be achieved when the alied electric field is alied erendicular to the oling direction; and it is referred as shear mode. For most iezoelectric materials, the couling coefficients associated with shear mode have the largest value of all coefficients (Kamal, Giurgiutiu, & Lin, ). The higher values of shear couling coefficients make suerior in actuation and sensing. SH waves are also referable because the first symmetric mode is nondisersive, i.e. wave seed is constant at different frequencies. On the other hand, one of the imortant disadvantages of is that thicker transducers are needed to sustain and generate the shear actuation and due to high density of iezoceramic materials ( 76 kg/m for APC85 iezoceramic Navy II tye); using of shear mode iezoelectric elements increases the mass of the system considerably. Kanazawa & Gordon (985) roosed an analytical definition of the resonance frequency shift by urely mechanical analysis which couled the standing shear wave in the quartz to a damed roagating shear wave in / Newtonian fluid i.e. f = fo ηlρl / πµ qρq and verified by the exerimental results in terms of the changes in resonance frequency of the quartz resonator whose one surface is in contact with water that owned varying concentration of glucose and ethanol. In the aer, the boundary layer was identified as the characteristic length of exonentially decaying viscous effects of the liquid on the resonance frequency because the dislacement exonentially dies out in the liquid. The aroach has been alied for quartz crystal resonators with overlying viscous liquids, thin elastic films and viscoelastic layers (Josse & Shana, 988; Martin et al., ; Nwankwo & Durning, 998; Suh & Kim, ). However the theoretical method derived by Kanazawa & Gordon is only valid for overlying viscous fluid of infinite extent therefore the method analyzes bulk acoustic waves (BAW) which remains the sensor sensitivity low. The sensors utilizing surface acoustic waves (SAW) are suerior to the conventional BAW devices in liquid sensor alications since SAW devices can oerate at much higher frequencies and more mass sensitive since SAW ossesses large attenuation and energy loss due to a mode conversion in the liquid and dissiates due to the viscous effects (Josse & Shana, 988). Guo & Sun (8) found that shear tye SAW is a good candidate for liquid sensing alications. Other alternative to the SAW resented was the shear horizontal (SH) surface wave. Kamal et al., () develoed a one dimensional analytical model for MIS of under stress-free boundary condition using the resonator theory with constant electric field assumtion as seen in q. () that defines the /M admittance of free. They verified the analytical model by finite element simulation and exerimental MIS measurement. Iˆ Y = = iωc K5 Vˆ φcotφ () d5 where κ 5 is the shear horizontal electromechanical couling coefficient and can be defined as κ = 5 T εs, 55 φ is the roduct of the half of the wave number and the characteristic length of PWAS i.e. φ = γl / and C is the caacitance of PWAS. In this aer, we resent one-dimensional analytical model for MIS of in contact with different liquids in different density and viscosity. The MIS of with different fuels are also simulated by using -D couled field finite element models in ANSYS. The trends of the /M imedance and admittance simulation results are discussed by comaring the liquids with different viscosity. Analytical Modeling of in contact with Liquid Medium In this section, the resonse of a iezo-resonator couled with liquid layer (Fig. ) is resented in terms of /M imedance and admittance sectra. The shear horizontal waves and the corresonding iezoelectric constitutive equations were taken into account to derive the MIS resonse of a resonator in contact with liquid layer (Kamas, 4). The -D analytical MIS model including the liquid layer effects was derived as shown in q. ().

3 T. Kamaş, V. Giurgiutiu y y y y Liquid layer ρ L, µ L F F + dx ρ, 55 PWAS zt c x dx x F Fig. Schema of iezo-wafer resonator deformed in shear horizontal d mode by induced 5 T5 = T shear stress Proerty Table Proerties of APC 85 iezoelectric ceramic ( ρ T ε / ε κ (kg/m ) d (m/v) d (m/v) g (Vm/N) g (Vm/N) s (m /N) s (m /N) κ κ ν APC x - 75x - 6x -.4x - 7. x - 5. x ( ) ( ) ( ) ( ) ( ) ( ) ( ) φsh φsh φsh φsh φsh φsh κ s55hγω L L he φsh e e + s55hγω L L he φsh e e 5 φ SH Y = iωc κ 5 e + () φ φsh φsh φsh φsh SH φsh e + + s55hγω L L h e + φsh e + + s55hγω L L h e + The frequency and amlitude shifts occur due to the existence of the liquid layer. The magnitudes of the shifts deend on the liquid density and viscosity roerties. In the analytical simulation, first MIS of under stress-free boundary condition was simulated. Then two liquids with different density and viscosity are used as a layer on to of as seen in the model (Fig. ). ReZ, Ohm ImZ, Ohm.5 x Imedance of PWAS-Liquid Visc=x - Pa.s Liquid Dens=x kg/m Liquid Dens=x kg/m x 4 - Liquid Dens=x kg/m Liquid Dens=x kg/m ReY, /Ohm ImY, /Ohm 5 4 Admittance of PWAS-Liquid Visc=x - Pa.s Liquid Dens=x kg/m Liquid Dens=x kg/m Liquid Dens=x kg/m Liquid Dens=x kg/m Fig. Analytical simulation results for real and imaginary arts of /M imedance and admittance of interacting with liquid in different density The analytical model for the /M imedance (Z) and admittance (/Z) of and of in contact with liquid have been simulated and comared for liquids in different density (Fig. ) and in different viscosity (Fig. ) values. In Fig., the continuous curves reresent the MIS results for under traction-free boundary conditions. The dashed curves with dots reresent the MIS results for in contact with liquid in the density of kg/m and the dashed curves without dots reresent in the density of kg/m. The resence of the liquid layer shifts the amlitudes of both admittance and imedance down and also slightly shifts the anti-resonance (Fig. ) frequency u whereas the resonance frequency remains the same. The density increase also results in further downshift in the imedance amlitude and further ushift in the

4 ACM5 ReZ, Ohm ImZ, Ohm.5 x Imedance of PWAS-Liquid Dens=x kg/m x 4 - m=.4x - Pa.s m=4x - Pa.s m=.4x - Pa.s m=4x - Pa.s ReY, /Ohm ImY, /Ohm 5 4 Admittance of PWAS-Liquid Dens=x kg/m m=.4x - Pa.s m=4x - Pa.s m=.4x - Pa.s m=4x - Pa.s Fig. Analytical simulation results for real and imaginary arts of /M imedance and admittance of interacting with liquid in different viscosity anti-resonance frequency. The increase in viscosity of the liquid layer shows the similar results in the /M imedance (Fig. ) and admittance results (Fig. ). Couled Field Finite lement Modeling of in Contact with Incomressible and Viscous Liquid Medium We first modeled three dimensional (-D) 5mmx5mmxmm under traction-free boundary conditions in ANSYS without introducing the liquid layer by using APC 85 ceramic iezoelectric material roerties that were introduced in Table. ANSYS multi-hysics software with the imlicit solver was used to obtain MIS comutation in frequency domain. To erform the couled stress and electric field analysis of PWAS transducers, couled field iezoelectric elements were used. These couled field finite elements consist of both mechanical and electrical fields. The elements that reresent iezoelectric effects in our analysis are the -D couled field solid elements i.e. SOLID5. The electrical charge Q is the electrical reaction corresonding to the voltage DOF. The charge Q is then used to calculate the admittance and imedance data. The admittance Y is calculated as I / V, where I is the current in amere and V is the alied otential voltage in volts. The current comes from the charge accumulated on the PWAS surface electrodes and is calculated as I = iω Qi with ω being the oerating frequency, i is the comlex number, and Qi is the summed nodal charge C = GPa ε 65 = F/m e.84 = C/m where C is the stiffness matrix, ε is the dielectric matrix, and e is the iezoelectric matrix. The density of the PWAS material is assumed to be ρ = 77 kg/m. () (4) (5) 4

5 T. Kamaş, V. Giurgiutiu Liquid layer Fig. 4 -D CF-FA model for interacting with viscous liquid layer: meshed liquid layer and the stress field (T xz ) mode shae of couled with a liquid layer (viscosity 4x - Pa.s) vibrating in shear horizontal mode at 96 khz We introduced the liquid layer in the same geometric shae and sizes by using the FLUID8 element tye for - D liquid layer modeling merged with the elements (Fig. 4). Real Imedance Imaginary Imedance 4 x 4 CF-FA for Imedance of SHPWAS-Liquid Dens=x kg/m.5 In-lane modes m=.4x - Pa.s.5 m=4x - Pa.s Shear Horizontal x 4 - m=.4x - Pa.s m=4x - Pa.s Real Admittance Imaginary Admittance x - CF-FA for Admittance of SHPWAS-Liquid Dens=x kg/m.5 m=.4x - Pa.s m=4x - Pa.s x - m=.4x - Pa.s m=4x - Pa.s Fig. 5 Couled field finite element analysis (CF-FA) simulation results for real and imaginary arts of /M imedance and admittance of interacting with liquid in different viscosity The simulations have been conducted with the same viscosity values through couled field finite element analysis using the multi-hysics ANSYS models as defined above. The simulations with different density were not carried out due to the FLUID8 element being incomressible. Further investigation is required to erform such CF-FA simulation and obtain insightful information for density effect on the /M imedance and admittance results. So far, we obtained good results in Fig. 5 to indicate the effect of resence of a liquid layer and the effect of viscosity increase in the MIS of. The first shear horizontal mode as well as the inlane MIS modes was shown in Fig. 5. SH MIS mode is better indicator in comarison with the in-lane MIS modes in terms of anti-resonance frequency shift due to the viscosity increase so that SH MIS mode can be used to develo an in-situ continuous quantitative method to measure the viscosity of a liquid in contact with a surface of a. 4 Summary and Conclusions In this work, the -D analytical model and -D couled field finite element model (CF-FM) were develoed for the electromechanical imedance sectroscoy (MIS) of shear horizontal (d5) iezoelectric wafer active sensor (). The analytical simulations indicated that the resence of the liquid layer shifts the amlitudes of both admittance and imedance down and also slightly shifts the anti-resonance frequency u whereas the resonance frequency remains the same. The density increase also results in further downshift in the imedance amlitude and further ushift in the anti-resonance frequency. The increase in viscosity of the liquid layer shows the similar results in the /M imedance and admittance results. The CF-FA simulations demonstrated the first shear horizontal (SH) mode and the in-lane MIS modes. SH MIS mode is better indicator of viscosity effects in comarison with the in-lane MIS modes in terms of anti-resonance frequency shift due to the viscosity increase so that SH MIS mode can be used to develo an in-situ continuous quantitative method to measure the viscosity of a liquid in contact with a surface of a. 5

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