Impedance method for measuring shear elasticity of liquids

Experimental results of studying low-frequency (74 kHz) shear elasticity of polymer liquids by the impedance method (analogous to the Mason method) are presented. A free-volume thick liquid layer is placed on the horizontal surface of a piezoelectric quartz crystal with dimensions 34.7 × 12 × 5.5 cm. The latter performs tangential vibrations at resonance frequency. The liquid layer experiences shear strain, and shear waves should propagate in it. From the theory of the method, it follows that, with an increase in the layer thickness, both real and imaginary resonance frequency shifts should exhibit damped oscillations and tend to limiting values. For the liquids under study, the imaginary frequency shift far exceeds the real one, which testifies to the presence of bulk shear elasticity.     

QCM based sensor for detecting volumetric properties of liquids

We introduce a microacoustic sensor, which combines the quartz crystal microbalance, a liquid-filled cavity and an intermediate artificial layer with effective acoustic properties. Each of the three components fulfils a specific task. The quartz vibrates in its thickness shear mode and acts as source and detector of shear waves, which penetrate the intermediate artificial layer and excite a resonance in the liquid-filled cavity. Both the piezoelectric transducer and the liquid-filled cavity are high-Q resonators with well-adjusted resonance frequencies very close to each other. The intermediate artificial layer couples the two resonators in a distinct manner via control of the propagation of acoustic waves between the quartz crystal and the liquid-filled cavity layer. The origin of the sensor signal is a change of the resonance frequency of the liquid-filled cavity caused by variations of acoustic properties of the liquid analyte inside the cavity, first of all speed of sound. This resonance appears as second resonance peak in the admittance spectrum of the quartz crystal.     

Shear elasticity of fluids at low-frequent shear influence

The visco-elastic properties of liquids have been investigated using acoustical resonance method. Piezoquatrz performed tangential oscillations on the main resonance frequency of 74 kHz contacts by the one end of horizontal surface with the studied liquid layer covered by quartz cover-plate. So the stagnant shear waves are installed in layer. The solution of interaction of piezoquartz-liquid layer-cover-plate gives three methods of determination of the real shear modulus (G) and the tangent of mechanical loss angle (tan theta) of liquid. The first method is realized at smaller thickness of liquid layer then the length of shear wave. Liquids of different classes have been studied using this method: polymer liquids, oils, glycols and alcohols. The second method is connected with the propagation of shear wave in liquid layer, parameters of which are determined the G and tan theta. And the third method is based on the determination of limit shift of resonance frequencies at completes damping of shear wave in thick layer of liquid. All these three methods give satisfactory agreement of results.     

Ultrasonic interferometry for the measurement of shear velocity and attenuation in viscoelastic solids

A method for the measurement of the shear properties of solid viscoelastic materials is presented. The viscoelastic material is cut into a cylindrical sample which is clamped between two rods. The transmission and reflection coefficient spectra of the fundamental torsional mode through the sample are measured by means of two pairs of piezoelectric transducers placed at the free ends of the rod-sample-rod system. Such spectra exhibit maxima and minima which occur approximately at the resonance frequencies of the free viscoelastic cylinder. Therefore, the shear velocity can be obtained by measuring the frequency interval between two consecutive maxima or minima. The shear attenuation is derived by best fitting the analytical expression of the reflection and transmission coefficients to the experimental spectra. The test is very quick to set up as the sample is simply clamped between the two rods.     

Shear horizontal acoustic waves at the boundary of two piezoelectric crystals separated by a liquid layer

Transverse acoustic waves that occur at the boundary of two piezoelectric halfspaces separated by a viscoelastic liquid layer are studied theoretically. Three variants of layered structures with different numbers of metallized interfaces are considered. It is demonstrated that two types of waves exist in each of these structures. The waves are localized near the boundaries and differ in both their structure and the dependences of the complex wave numbers on the frequency or the gap width. The properties of this family of shear horizontal waves are described.     

Vibration analysis of a new polymer quartz piezoelectric crystal sensor for detecting characteristic materials of volatility liquid

We present a new polymer quartz piezoelectric crystal sensor that takes a quartz piezoelectric crystal as the basal material and a nanometer nonmetallic polymer thin film as the surface coating based on the principle of quartz crystal microbalance (QCM). The new sensor can be used to detect the characteristic materials of a volatile liquid. A mechanical model of the new sensor was built, whose structure was a thin circle plate composing of polytef/quartz piezoelectric/polytef. The mechanical model had a diameter of 8 mm and a thickness of 170 μ. The vibration state of the model was simulated by software ANSYS after the physical parameters and the boundary condition of the new sensor were set. According to the results of experiments, we set up a frequency range from 9.995850 MHz to 9.997225 MHz, 17 kinds of frequencies and modes of vibration were obtained within this range. We found a special frequency f_sp of 9.996358 MHz. When the resonant frequency of the new sensor’s mechanical model reached the special frequency, a special phenomenon occurred. In this case, the amplitude of the center point O on the mechanical model reached the maximum value. At the same time, the minimum absolute difference between the simulated frequency based on the ANSYS software and the experimental measured stable frequency was reached. The research showed that the design of the new polymer quartz piezoelectric crystal sensor perfectly conforms to the principle of QCM. A special frequency value f_sp was found and subsequently became one of the most important parameters in the new sensor design.     

FINITE ELEMENT FORMULATION AND ACTIVE VIBRATION CONTROL STUDY ON BEAMS USING SMART CONSTRAINED LAYER DAMPING (SCLD) TREATMENT

This work deals with the active vibration control of beams with smart constrained layer damping (SCLD) treatment. SCLD design consists of viscoelastic shear layer sandwiched between two layers of piezoelectric sensors and actuator. This composite SCLD when bonded to a vibrating structure acts as a smart treatment. The sensor piezoelectric layer measures the vibration response of the structure and a feedback controller is provided which regulates the axial deformation of the piezoelectric actuator (constraining layer), thereby providing adjustable and significant damping in the structure. The damping offered by SCLD treatment has two components, active action and passive action. The active action is transmitted from the piezoelectric actuator to the host structure through the viscoelastic layer. The passive action is through the shear deformation in the viscoelastic layer. The active action apart from providing direct active control also adjusts the passive action by regulating the shear deformation in the structure. The passive damping component of this design eliminates spillover, reduces power consumption, improves robustness and reliability of the system, and reduces vibration response at high-frequency ranges where active damping is difficult to implement. A beam finite element model has been developed based on Timoshenko's beam theory with partially covered SCLD. The Golla-Hughes-McTavish (GHM) method has been used to model the viscoelastic layer. The dissipation co-ordinates, defined using GHM approach, describe the frequency-dependent viscoelastic material properties. Models of PCLD and purely active systems could be obtained as a special case of SCLD. Using linear quadratic regulator (LQR) optimal control, the effects of the SCLD on vibration suppression performance and control effort requirements are investigated. The effects of the viscoelastic layer thickness and material properties on the vibration control performance are investigated.     

Nonlinear vibration of viscoelastic embedded-DWCNTs integrated with piezoelectric layers-conveying viscous fluid considering surface effects

This article studies the nonlinear vibration of viscoelastic embedded nano-sandwich structures containing of a double walled carbon nanotube (DWCNT) integrated with two piezoelectric Zinc oxide (ZnO) layers. DWCNT and ZnO layers are subjected to magnetic and electric fields, respectively. This system is conveying viscous fluid and the related force is calculated by modified Navier–Stokes relation considering slip boundary condition and Knudsen number. Visco–Pasternak model with three parameters of the Winkler modulus, shear modulus, and damp coefficient is used for simulation of viscoelastic medium. The nano-structure is simulated as an orthotropic Timoshenko beam (TB) and the effects of small scale, structural damping and surface stress are considered based on Eringen's, Kelvin-voigt and Gurtin–Murdoch theories. Energy method and Hamilton's principle are employed to derive motion equations which are then solved using differential quadrature method (DQM). The detailed parametric study is conducted, focusing on the combined effects of small scale effect, fluid velocity, thickness of piezoelectric layer, boundary condition, surface effects, van der Waals (vdW) force on the frequency and critical velocity of nano-structure. Results indicate that the frequency and critical velocity increases with assume of surface effects.     

Effects of mode coupling on the admittance of an AT-cut quartz thickness-shear resonator

We study the effects of couplings to flexure and face-shear modes on the admittance of an AT-cut quartz plate thickness-shear mode resonator. Mindlin’s two-dimensional equations for piezoelectric plates are employed. Electrically forced vibration solutions are obtained for three cases: pure thickness-shear mode alone; two coupled modes of thickness shear and flexure; and three coupled modes of thickness shear, flexure, and face shear. Admittance is calculated and its dependence on the driving frequency and the length/thickness ratio of the resonator is examined. Results show that near the thickness-shear resonance, admittance assumes maxima, and that for certain values of the length/thickness ratio, the coupling to flexure causes severe admittance drops, while the coupling to the face-shear mode causes additional admittance changes that were previously unknown and hence are not considered in current resonator design practice.     

A simple-shear rheometer for linear viscoelastic characterization of vocal fold tissues at phonatory frequencies

Previous studies reporting the linear viscoelastic shear properties of the human vocal fold cover or mucosa have been based on torsional rheometry, with measurements limited to low audio frequencies, up to around 80 Hz. This paper describes the design and validation of a custom-built, controlled-strain, linear, simple-shear rheometer system capable of direct empirical measurements of viscoelastic shear properties at phonatory frequencies. A tissue specimen was subjected to simple shear between two parallel, rigid acrylic plates, with a linear motor creating a translational sinusoidal displacement of the specimen via the upper plate, and the lower plate transmitting the harmonic shear force resulting from the viscoelastic response of the specimen. The displacement of the specimen was measured by a linear variable differential transformer whereas the shear force was detected by a piezoelectric transducer. The frequency response characteristics of these system components were assessed by vibration experiments with accelerometers. Measurements of the viscoelastic shear moduli (G' and G") of a standard ANSI S2.21 polyurethane material and those of human vocal fold cover specimens were made, along with estimation of the system signal and noise levels. Preliminary results showed that the rheometer can provide valid and reliable rheometric data of vocal fold lamina propria specimens at frequencies of up to around 250 Hz, well into the phonatory range.     

An improvement of tilted AlN for shear and longitudinal acoustic wave

This study investigates c-axis tilted aluminum nitride (AlN) piezoelectric films for the improvement of both shear and longitudinal acoustic wave resonances. Solidly-mounted resonator (SMR) structure is adopted for the applications of high frequency wireless communications and high sensitivity sensors. As to the piezoelectric layer, c-axis tilted AlN has the capability to excite the dual-mode resonances, namely, the longitudinal and shear mode resonances. In this study, SMR devices made with a seven-layer molybdenum/silicon dioxide (Mo/SiO₂) Bragg reflector and the c-axis tilted AlN are carried out. A conventional off-axis sputtering technique is applied to grow the tilted AlN. The outcome frequency responses show dual resonant characteristics. However, the longitudinal resonance fades away with the AlN c-axis tilted angle, and the quality factor of the longitudinal resonance decreases. Consequently, we make an improvement by tilting the off-center substrates toward the sputtering source and successfully enhance the longitudinal resonance while preserving the shear resonance at the same time. Not only the shear resonance for the liquid-based sensing application, but also an outstanding longitudinal resonance could be obtained. The practicability of the dual-mode resonator is extended.     

Determination of the complex Young and shear dynamic moduli of viscoelastic materials

The Young and shear dynamic moduli of viscoelastic materials are determined from laser vibrometric measurements of the surface motion of a three-dimensional sample excited by a piezoelectric actuator inside a chamber with controllable temperature and static pressure. The moduli are estimated from an inversion code that minimizes the difference between the data and the predictions from a finite element model in which the elastic moduli are the adjustable parameters. The technique is first used to measure the dynamic properties of homogeneous samples and the results are compared with those obtained by the standard rod resonance technique. Results are then obtained with microvoided samples in the 0.5-3 kHz frequency range, at temperatures ranging from 7 to 40 degrees C, and static pressures ranging from ambient to 34 atm (3.45 MPa or 500 psi). The limitations of the technique are discussed.     

Kinetic study of silica gels by a new rheological ultrasonic investigation

The last decades have seen the development of sol-gel (SG) process currently used to develop new materials in a wide range of scientific applications. The SG process leads to an oxide macromolecular network through a sol (liquid phase) to gel transition. To optimize this process, the control of the kinetic of the chemical reaction is required. This kinetic can be deduced from the temporal evolution of the viscoelastic parameters. Upto date no complete investigation during the SG formation can be achieved by a unique non-destructive technique. In this paper, we present an ultrasonic technique to measure the viscoelastic parameters (storage G' and loss G' shear moduli) of the gel material during its formation. By using a suitable model which takes into account the mass loading on the surface, the viscoelastic parameters of these materials are accurately deduced. In order to study the efficiency of this technique, silica gels transition is monitored at various formation temperatures and for different initial hydrolysis molar ratio (h). In addition, the monitoring is performed at different oscillatory shear measurements in the 6-54 MHz frequency range to determine a new characteristic time t(vs) corresponding to the moment when the material is no more a newtonian liquid. This characteristic time is then compared to the gelation time t(g) determined by rheological or acoustic audible range methods. Thus the new characteristic time is also a good criterion to characterize earlier the SG matrix transition. Our AT-cut quartz technique using our model can also be used as a high frequency rheometer for the sol-gel materials.     

Flexural vibration analyses of piezoelectric ceramic tubes with mass loads in ultrasonic actuators

Based on Timoshenko beam model, a theoretical model of radially polarized piezoelectric ceramic tubes is investigated. In the model, the piezoelectric effects are considered, and the shear correction factor is introduced which reveals effects of the size of the cross-section and Poisson’s ratio. Based on the model, the particular attentions are devoted to effects of the boundary conditions at two ends on flexural resonance frequencies of the piezoelectric ceramic tubes. Changing the sizes of the tubes and the mass loads at both free ends, the variations of the flexural resonance frequencies of free–free piezoelectric ceramic tubes are calculated theoretically. Besides, the flexural resonance frequencies of the piezoelectric ceramic tube cantilevers with mass loads at one free end are also investigated theoretically. To verify accuracy of the theoretical mode, the flexural resonance frequencies for different lengths of the piezoelectric ceramic tubes and different loaded masses are measured experimentally. The theoretical results agree well with the experimental measurement, which demonstrates that the model is accurate for analyzing the flexural resonance frequencies of the piezoelectric ceramic tubes with mass loads.     

Magnetoelectric effect in layered disk-shaped magnetostrictive–piezoelectric structures: Theory and experiment

Theoretical and experimental studies of the magnetoelectric effect in a disk-shaped magnetostrictive–piezoelectric structure in the electromechanical resonance region are presented. An expression for the magnetoelectric voltage coefficient is derived based on the simultaneous solution of elastodynamic and electrostatic equations separately for magnetostrictive and piezoelectric layers. The conditions at the interface were taken into account based on the premise that the interaction between layers is implemented by shear. It is shown that the inhomogeneity of the voltage and strain distribution over the sample thickness, caused by the interface, leads to a significant contribution to the effect in the case of thick layers. The theoretical and experimental dependences of the frequency characteristic of the effect are presented for the permendur–lead zirconate-titanate–permendur structure. The theoretical calculations are in good agreement with experimental data.     

Resonance method of measuring shear viscoelastic properties of liquid media based on excitation of torsional oscillations in tubes

Possibilities of using torsional oscillations for measuring viscoelastic properties of liquids are discussed. The theory of torsional oscillations of an elastic tube filled with the media to be investigated possessing viscosity and shear elasticity is developed. It is shown that to determine a complex shear modulus it is sufficient to determine the resonance frequency and Q-factor of torsional oscillations. An experimental installation and the results of measurements of viscoelastic modulus of glycerin and oil of one oilfield within the temperature range from −10° to 60°C are given. The experimental installation allows measuring a viscoelastic modulus within the range of acoustic logging frequencies (10–20 kHz). The obtained results are compared with the results of rheometric measurements.     

Wide-range viscoelastic measurement using resonating sensors

We have developed a specially designed sensor with its associated instrumentation using a so called acoustical near-field technique based on small resonating horns. Contrary to the conventional measuring devices used in the rheology industry, this sensor enables wide-range and continuous viscosity measurements, including liquid to solid material transition. The sensor is composed of a small piezoelectric element which enables the horn to resonate. Shear waves are generated by means of the thinner part of the sensor (dipped into the material) confining the acoustic field to the tip to ensure local measurements. The frequency is scanned across the resonating frequencies in order to perform these measurements with the maximum of speed and efficiency. The shear moduli G' and G' of the material is deduced from the electrical impedance measurement at the resonance frequencies. In case of rapidly changing materials, such as quick setting cements or polyesters, we have developed a specific fast instrumentation based on the impulse response of the sensor, which realizes very fast measurements, typically 30 measurements per second. Modelization and experiments are reported.     

Ultrasonic scattering cross sections of shell-encapsulated gas bubbles immersed in a viscoelastic liquid: first and second harmonics

The oscillations of gas bubbles, without shell, immersed in viscoelastic liquids and driven by an acoustic wave have been the subject of several investigations. They demonstrate that the viscosity coefficient and the spring constant of the liquid have significant influence on the scattering cross section of the gas bubble. For shell-encapsulated gas bubbles, the investigations have been concentrated to bubbles immersed in a pure viscous liquid. This present work computes the ultrasonic scattering cross section, first and second harmonics, of shell-encapsulated gas bubbles immersed in a viscoelastic liquid. The theoretical model of the bubble oscillation is based on the generalized Rayleigh-Plesset equation of motion of a spherical cavity immersed in a viscoelastic liquid represented by a three-parameter linear Oldroyd model. The scattering cross section is computed for Albunex type of bubble (shell thickness=15 nm, shell shear viscosity=1.77 Pas, shell modulus of rigidity=88.8 MPa) irradiated by a 3.5 MHz ultrasonic pressure wave with an amplitude of 30 kPa. The results demonstrate that encapsulated bubbles respond independently of the surrounding liquid being pure viscous or viscoelastic as long as the surrounding liquid shear viscosity is as low as 10(-3) Pas. Nevertheless, for higher shear viscosities, the bubble responds differently if the surrounding liquid is pure viscous or viscoelastic. In general, the scattering cross sections of first and second harmonics are larger for the viscoelastic liquid.     

КВАРЦЕВЫЕ РЕЗОНАТОР Ы С ПРЯМОУГОЛЬНЫМИ ПЬЕЗОЭЛЕМЕНТАМИ СРЕ ЗА ДТ

The authors studied the properties of piezoelectric quartz resonators of DT cut in the form of rectangular plates with a width-to-length ratio of 0.4. They determined how the resonance frequency, its temperature dependence, the parameters of the electric equivalent circuit and the oscillation spectrum depend on the geometric dimensions and orientation of the crystal unit.     

The influence of deposited electrodes on longitudinally vibrating resonators

The resonance frequency of the longitudinal vibrations of rods, and of the extensional and shear vibrations of plates is influenced by electrodes. It was found experimentally that the relative change in resonance frequency caused by depositing electrodes is proportional to the ratio of the masses of the electrodes and resonator. The paper gives the theoretical derivation of an expression for the proportionality constantK for longitudinal types of vibrations of plates and rods. The proportionality constantK is dependent on the density, elastic properties and dimensions of the piezoelectric resonator and electrodes. The theoretical behaviour of the constantK for a piezoelectric resonator of orientation GT is compared with the experimentally obtained values.