Piezoelectric Wafer Research Articles

Detecting fatigue in aluminum alloys based on internal friction measurement using an electromechanical impedance method

Detecting mechanical fatigue of metallic components is always a challenge in industries. In this work, we proposed to monitor the low-cycle fatigue of a 6061 aluminum alloy based on internal friction (IF) measurement, which is realized by a quantitative electromechanical impedance (Q-EMI) method using a small piezoelectric wafer bonded on the specimen. Large stress amplitude (230 MPa) was employed in the testing; thus, the fatigue life can always be below 105 cycles. It was found that except for the initial testing stage, the IF always increases steadily with the increasing fatigue cycles. Before the fatigue failure, the IF can reach 2.5–3.4 times the initial value, which is thought to be caused by the micro-cracks forming and growing. In comparison, the resonance frequency of the specimen just drops by about 2% compared with the initial value. Finally, a fatigue criterion based on IF measurement is suggested for aluminum alloys and it can also be extended to other metals.

Immunity of the second harmonic shear horizontal waves to adhesive nonlinearity for breathing crack detection

High-order harmonic guided waves are sensitive to micro-scale damage in thin-walled structures, thus, conducive to its early detection. In typical autonomous structural health monitoring (SHM) systems activated by surface-bonded piezoelectric wafer transducers, adhesive nonlinearity (AN) is a non-negligible adverse nonlinear source that can overwhelm the damage-induced nonlinear signals and jeopardize the diagnosis if not adequately mitigated. This paper first establishes that the second harmonic shear horizontal (second SH) waves are immune to AN while exhibiting strong sensitivity to cracks in a plate. Capitalizing on this feature, the feasibility of using second SH waves for crack detection is investigated. Finite element (FE) simulations are conducted to shed light on the physical mechanism governing the second SH wave generation and their interaction with the contact acoustic nonlinearity (CAN). Theoretical and numerical results are validated by experiments in which the level of the AN is tactically adjusted. Results show that the commonly used second harmonic S0 (second S0) mode Lamb waves are prone to AN variation. By contrast, the second SH0 waves show high robustness to the same degree of AN changes while preserving a reasonable sensitivity to breathing cracks, demonstrating their superiority for SHM applications.

Inverse analysis for damage detection in a rod using EMI method

The electro-mechanical impedance (EMI) method has been demonstrated to be a powerful tool to detect the small local damages in various engineering structures, due to its high-frequency vibration characteristics. However, this technique is difficult to accurately determine the degree and location of structural damages. In this paper, an inverse analysis combining the measured EMI signatures and the Transfer Matrix Method (TMM) is proposed to identify the damages in the steel rods. A milled groove is introduced into each steel specimen to simulate the local damage. By measuring the EMI signatures of the piezoelectric wafers bonded symmetrically on the upper and lower surfaces of the rectangular specimens respectively, the damage can be detected clearly, as well as natural frequencies being extracted in the relatively lower frequency range. The damage sizes and locations are further determined by connecting the frequency equations and any two measured natural frequencies. Tests on three samples show both damage sizes and locations are accurately detected, which indicates that the present method is quite feasible and effective for damage identification in the bar-type structures.

A machine learning framework for guided wave-based damage detection of rail head using surface-bonded piezo-electric wafer transducers

Due to repeated heavy loads, environmental conditions and non-frequent monitoring, the rail is subjected to heavy damage resulting in sudden failure. Hence, a frequent, faster, and efficient monitoring strategy is required. This paper attempts to investigate the application of guided wave (GW) generated through surface-bonded piezo-electric wafer transducer (PWT) to detect damages in rail at high frequencies. Firstly, a combined experimental and simulation study is presented in an effort to understand the dispersion characteristics of guided wave and its interaction with head damages in a relatively small rail specimen. The numerical simulation results are validated with those obtained from the experiments showing a good agreement between them. Secondly, a framework based on the machine learning algorithm is proposed to efficiently detect damage in rail head. Numerous inseparable guided wave modes are observed at higher frequencies implying the inability to detect damage through specific mode. Therefore, a machine learning framework is trained using time, frequency, and time–frequency domain features of the signal. Total 672 numerical simulations of different types of damage with different severity and location in the rail head are carried out to train and validate the model. It is found that GW generated through surface bonded PWTs is able to detect minimum defect size of 5% of head area with 1 mm thickness. Finally, the proposed framework is tested using simulation and experiment results of arbitrary damage in the rail head. The error in estimating severity was found to be in the range from 2.00% to 16.67%.

An Electromechanical <i>In Situ</i> Viscosity Measurement Technique for Shear Thickening Fluids

This paper presents the feasibility of developing an electromechanical in-situ viscosity measurement technique by analyzing the detectability of small variations in the viscosity of different shear thickening fluids and their different compositions. Shear thickening fluid (STF) is a kind of non-Newtonian fluid showing an increasing viscosity profile under loading. STF is utilized in several applications to take advantage of its tunable rheology. However, process control in different STF applications requires rheological measurements, which cause a costly investment and long-lasting labor. Therefore, one of the most commonly used in-situ structural health monitoring techniques, electromechanical impedance (EMI), was used in this study. In order to actuate the medium electromechanically, a piezoelectric wafer active sensor (PWAS) was used. The variations in the spectral response of PWAS resonator that can be submerged into shear thickening fluid are analyzed by the root mean square deviation, mean absolute percentage deviation and correlation coefficient deviation. According to the results, EMI metrics provide good correlations with the rheological parameters of STF and thereby enabling quick and low-cost rheological control for STF applications such as vibration dampers or stiffness control systems.

FRF-based lamb wave phased array

In the former work, a SHM system was proposed by Kudela et al based on the concept of Lamb wave focusing by the piezoelectric array. According to the pre- and post-compensations, the Lamb wave is focused on the interested point. This allows the system to scan the structure point by point, and then get the damage localization results with high-resolution compared with the beamforming method. However, the efficiency of the method is limited by the ways of signal processing and scanning: 1) the amount of measurement should be equal to the number of inspection points; 2) and the compensation calculations must be done for every measurement. The situation is further compounded by the average step for inspection points. 3) the central frequency of excitation is fixed in the whole processing, to optimize the input waveform means redoing the scan. To address these problems, a novel mode of signal processing for the piezoelectric phased array is proposed based on the Frequency Response Function (FRF). In the present method, the point-by-point scan is replaced by a single measurement for FRF with the “Single Input, Multiple Output” (SIMO) mode, which ensures the scan work can be established in N times excitations (N is the number of piezoelectric wafer, much smaller than the amount of inspection points). Furthermore, the present method is based on FRF, which means the excitation waveform can be virtually selected and changed after recording. It provides a more flexible path for the piezoelectric array concept in SHM. Experiments shows that the developed method is effective for one-dimensional and two-dimensional arrays. The work enriches the intension and implementation of piezoelectric phased array.

Nonreciprocal Elastic Wave Beaming in Dynamic Phased Arrays

Beam forming using phased arrays forms the basis of several sonar communication and biomedical imaging techniques. However, to date, such arrays remain constrained by wave reciprocity in addition to being confined to their operational frequency; two limitations that have severely hindered imaginative advancements in this domain. In the context of sound propagation, nonreciprocity typically refers to unidirectional elastic and surface acoustic wave devices. However, a breakage of reciprocity in phased arrays manifests itself in reception and transmission patterns, which can be independently tuned, which has thus far been elusive. This work reports on a class of nonreciprocal phased arrays, which operate independently and simultaneously within different directions and frequency channels, thus breaking transmission-reception symmetry and offering enhanced capabilities in guided wave engineering. The system comprises an array of transceiving piezoelectric wafer discs bonded to an elastic medium and incorporates a prescribed dynamic modulation on top of a static phase gradient, which enables concurrent phononic transitions in energy and momentum spaces that mitigate the constraints imposed by Lorentz reciprocity. Following the theory and predictive analysis, the entire array and its associated capabilities are demonstrated experimentally.

Influence of different ultrasonic transducers on the precision of fastening force measurement

In the assembly process of aero-engines, the accurate measurement of bolt fastening force is particularly important, which is related to the normal operation of the entire system. Ultrasonic non-destructive testing has been applied to bolt fastening force measurement and has a broad application background. The core device of the ultrasonic transducer is a piezoelectric ceramic wafer, and the normal operation of the wafer is affected by the power frequency and external stress. For the same type of bolt with the same nominal diameter, the ultrasonic transducer wafers of different diameters will cause the transducer wafers to be subjected to different external stresses. According to the acoustoelastic effect, the relationship between the variation of time of flight (TOF) and bolt fastening force of different types of ultrasonic transducers is established. Then the measurement errors of various models are calculated and analyzed. The experimental results show that when the nominal diameter of the bolt is close to the diameter of the wafer of the ultrasonic transducer, the fastening force measurement accuracy of the bolt is the highest. When small or large size transducer is used, the measurement accuracy will be reduced due to energy and external stress. When a transducer with a higher center frequency is used to measure the fastening force of the bolt rod, the accuracy of the model established due to the faster attenuation of the sound wave is reduced, and the accuracy of the measurement result is reduced. Therefore, in order to ensure the accuracy of the fastening force measurement in the aerospace field, when selecting an ultrasonic transducer, the impact of the transducer size and center frequency should be fully considered.

Use of the Ferroelectric Ceramic Bismuth Titanate as an Ultrasonic Transducer for High Temperatures and Nuclear Radiation.

Ultrasonic transducers are often used in the nuclear industry as sensors to monitor the health and process status of systems or the components. Some of the after-effects of the Fukushima Daiichi earthquake could have been eased if sensors had been in place inside the four reactors and sensed the overheating causing meltdown and steam explosions. The key element of ultrasonic sensors is the piezoelectric wafer, which is usually derived from lead-zirconate-titanate (Pb(Zr, Ti)O3, PZT). This material loses its piezoelectrical properties at a temperature of about 200 °C. It also undergoes nuclear transmutation. Bismuth titanate (Bi4Ti3O12, BiTi) has been considered as a potential candidate for replacing PZT at the middle of this temperature range, with many possible applications, since it has a Curie–Weiss temperature of about 650 °C. The aim of this article is to describe experimental details for operation in gamma and nuclear radiation concomitant with elevated temperatures and details of the performance of a BiTi sensor during and after irradiation testing. In these experiments, bismuth titanate has been demonstrated to operate up to a fast neutron fluence of 5 × 1020 n/cm2 and gamma radiation of 7.23 × 1021 (gamma/cm2). The results offer a perspective on the state-of the-art for a possible sensor for harsh environments of high temperature, Gamma radiation, and nuclear fluence.

Explainable 1-D convolutional neural network for damage detection using Lamb wave

Recently researchers are exploring the data-driven machine learning techniques to identify damage from Lamb wave response. This is primarily because the physics based model are often difficult to implement for complicated aerospace structures. In this study, one-dimensional convolutional neural network (1D CNN) is used for automated damage detection using Lamb wave response of a thin aluminium plate. An attempt is made to interpret the 1D CNN model in terms of damage feature contributions using Local Interpretable Model-Agnostic Explanations (LIME) and find that the interpretation corresponds to insightful damage signature. The database consists of finite element (FE) simulated data (180 cases) along with experimental data (48 cases) which is divided into Training, Testing, and Validation datasets. Each of the training and validation datasets contains FE simulated data with the major part used for training, whereas, experimental data are used for testing. Here, FE simulation responses are only used as a surrogate of experimental results. FE model is not used in the damage detection process rendering the technique to be purely data-driven. Finite element simulations of Lamb wave response are obtained using commercial package (ABAQUS) for different frequencies (100 KHz, 125 KHz, 150 KHz). The experimental data was generated for a 1.6 mm thick aluminium plate using piezoelectric wafer transducers. The 1D CNN architecture gave around 100% accuracy. Using the significant features affecting classification which is obtained from LIME, damage localization was achieved with around 7% deviation from actual damage localization.

Optimizing the placement of piezoelectric wafers on closed sections using a genetic algorithm – Towards application in structural health monitoring

Sensor network design is essential to efficiently integrate Structural Health Monitoring (SHM) systems in aerospace, automotive, and civil structures. This study describes an optimization model for piezoelectric (PZT) wafer placement on curved structures and closed sections.The proposed approach relied on the transformation of any complex/closed surface regardless of the shape of its cross-section into a flat plate and imposed a set of boundary conditions to account for the wave propagation characteristics. Because the structure was continuous and the wave could propagate in every direction, for simplicity and without sacrificing accuracy, our model assumed that a pair of PZT elements communicated information in the two shortest directions. Thus, the concept of having two paths for each PZT couple was introduced to tackle this multidirectional behavior. The plate was then discretized into a set of control points that represented the structure geometry. The PZT couples covered the control points along the line of sight and in the neighborhood of their direct and indirect paths. The objective function was to maximize the number of covered points while minimizing the number of PZT wafers.The proposed model was solved using a genetic algorithm and was validated on circular and square sections. Sensors were spread on the circumference of the structure rather than mounting them in the form of rings or axial lines. The optimized PZT networks had high coverage that reached 99% in simulations. Notably, the optimized model improved the preliminary solution coverage by 14%. Experimental validation was performed on the circular section (pipe). The results demonstrated the proficiency of the developed model in distributing the PZT wafers on closed sections. The coverage was further evaluated by assessing if damaged areas on the pipe surface could be identified. Artificial damage was accurately located within 18 mm from the actual location. These results demonstrate that our model efficiently distributes PZT wafers on closed structures.

Role of transducer inertia in generation, sensing, and time-reversal process of Lamb waves in thin plates with surface-bonded piezoelectric transducers

An analytical model is presented for the generation, sensing, and time-reversible process of Lamb waves in thin isotropic plates with surface-bonded piezoelectric wafer transducers, incorporating the shear-lag effect of the bonding layer and inertia effects of the system in transducer modeling. A one-dimensional dynamic shear-lag model for the actuator-plate interaction is used to obtain the shear stress distribution at the actuator-plate interface. The Lamb wave solution for the plate under this shear traction excitation is obtained using the two-dimensional (2D) elasticity equations. A consistent sensor-plate interaction model incorporating the shear-lag and inertia effects is developed to determine the induced sensor voltage from the Lamb strain at the plate surface. The model is validated by comparing it with the 2D coupled piezoelasticity-based finite element simulation and experimental data. Detailed parametric studies are conducted to illustrate the effect of inclusion of inertia of actuator, sensor, adhesive, and plate in the transducer modeling on the Lamb wave generation, sensing, time reversibility, and the system’s best reconstruction frequency, and to ascertain how various geometrical and material parameters of the system influence the same. The developed closed-form solution will be immensely useful for the design of Lamb wave based structural health monitoring systems.

Investigation on modulation of multi-frequency ultrasonic waves in structures with quadratic nonlinearity

In this study, the modulation of multiple frequency content of a single ultrasonic wave in nonlinear structures is investigated analytically, numerically and experimentally. An experimental technique is proposed based on nonlinear lamb wave propagation in aluminum bars using piezoelectric wafer active sensors (PWAS) to study intrinsic nonlinearity of structures. First, a one-dimensional analytical procedure is developed to study the modulation of one dimensional wave with multiple-frequency content in isotropic medium with quadratic nonlinearity. This procedure is implemented to study modulation of frequency contents of a well-known tone burst signal in nonlinear medium. Then, predictions obtained by the proposed analytical procedure are compared with the results of finite element model, which show strong correlations. The experimental and analytical results reveal that in excitation with a train of tone burst, due to frequency modulation, some new harmonics including a strong sub harmonic generation with frequency of f0/Np appear in the response. The amplitude of this harmonic is even higher than common second harmonic generation (2f0). This can be seen in the experimental results when the excitation frequencies are correctly selected. Finally, it is explained that, why the new sub harmonic generation is less affected by the nonlinearity induced by the excitation system.

Crack-Length Estimation for Structural Health Monitoring Using the High-Frequency Resonances Excited by the Energy Release during Fatigue-Crack Growth.

Acoustic waves are widely used in structural health monitoring (SHM) for detecting fatigue cracking. The strain energy released when a fatigue crack advances has the effect of exciting acoustic waves, which travel through the structures and are picked up by the sensors. Piezoelectric wafer active sensors (PWAS) can effectively sense acoustic waves due to fatigue-crack growth. Conventional acoustic-wave passive SHM, which relies on counting the number of acoustic events, cannot precisely estimate the crack length. In the present research, a novel method for estimating the crack length was proposed based on the high-frequency resonances excited in the crack by the energy released when a crack advances. In this method, a PWAS sensor was used to sense the acoustic wave signal and predict the length of the crack that generated the acoustic event. First, FEM analysis was undertaken of acoustic waves generated due to a fatigue-crack growth event on an aluminum-2024 plate. The FEM analysis was used to predict the wave propagation pattern and the acoustic signal received by the PWAS mounted at a distance of 25 mm from the crack. The analysis was carried out for crack lengths of 4 and 8 mm. The presence of the crack produced scattering of the waves generated at the crack tip; this phenomenon was observable in the wave propagation pattern and in the acoustic signals recorded at the PWAS. A study of the signal frequency spectrum revealed peaks and valleys in the spectrum that changed in frequency and amplitude as the crack length was changed from 4 to 8 mm. The number of peaks and valleys was observed to increase as the crack length increased. We suggest this peak–valley pattern in the signal frequency spectrum can be used to determine the crack length from the acoustic signal alone. An experimental investigation was performed to record the acoustic signals in crack lengths of 4 and 8 mm, and the results were found to match well with the FEM predictions.

Ultrasound tomography for health monitoring of carbon fibre–reinforced polymers using implanted nanocomposite sensor networks and enhanced reconstruction algorithm for the probabilistic inspection of damage imaging

Irrespective of the popularity and demonstrated effectiveness of ultrasound tomography (UT) for damage evaluation, reconstruction of a precise tomographic image can only be guaranteed when a dense transducer network is used. However, a network using transducers such as piezoelectric wafers integrated with the structure under inspection unavoidably lowers local material strength and consequently degrades structural integrity. With this motivation, an implantable, nanocomposite-inspired, piezoresistive sensor network is developed for implementing in situ UT-based structural health monitoring of carbon fibre–reinforced polymer (CFRP) laminates. Individual sensors in the network are formulated with graphene nanosheets and polyvinylpyrrolidone, fabricated using a spray deposition process and circuited via highly conductive carbon nanotube fibres as wires, to form a dense sensor network. Sensors faithfully respond to ultrasound signals of megahertz. With ignorable intrusion to the host composites, the implanted sensor network, in conjunction with a UT approach that is enhanced by a revamped reconstruction algorithm for the probabilistic inspection of damage–based imaging algorithm, has proven capability of accurately imaging anomaly in CFRP laminates and continuously monitoring structural health status, while not at the cost of sacrificing the composites’ original integrity.

Optimization of placement of piezoelectric wafers based on a hybrid model using pitch-catch and pulse-echo configurations

The development of Structural Health Monitoring (SHM) systems and integration in our structures is a necessity. It has proven to provide a robust and low-cost solution for monitoring structural integrity and can predict the remaining life of our structures. One of the most important aspects of SHM systems is the design and implementation of sensor networks. This study proposes a new hybrid model for optimizing sensor placement on convex and non-convex structures. We propose a novel framework in which two detection mechanisms are considered: pitch-catch and pulse-echo to provide coverage for a given surface. These two mechanisms will complement each other to minimize the number of sensors used while maintaining a high coverage. This combination also allows for better coverage of the corners and regions in the proximity of geometrical discontinuity (such as holes and openings). The monitored area is discretized into a set of control points. For a control point to be covered, it should satisfy the user-defined coverage level which is the number of sensing paths crossing that point. These sensing paths are provided by two modes of communications (pitch-catch and pulse-echo) between the actuator-sensor pairs. The model, which is solved using a genetic algorithm (GA), provides flexibility by allowing the user to input different parameters such as the attenuation distance of the propagating waves and the sensing path limits of both coverage configurations that can be determined through experimentation. The efficiency of the proposed model is then demonstrated by simulating different geometrical shapes. Significant improvement in the coverage of the monitored area, reaching 34.6%, was achieved when compared to the coverage provided by some preliminary solutions such as uniformly placing the sensors on the plate under study. Also, the advantage of combining both configurations (pitch-catch and pulse-echo) in the same model was investigated. It was shown that the latter highly impacted the coverage in the blind zones (corners and edges) where a single configuration is not effective. Afterward, experimental validation was carried out to evaluate the model’s accuracy in damage localization within the optimized sensor networks. The results demonstrated the proficiency of the model developed in distributing the sensors on the tested specimens.

Guided wave monitoring of Nano-Fe3O4 reinforced thermoplastic adhesive in manufacturing of reversible composite lap-joints using targeted electromagnetic heating

Targeted heating of nano-Fe3O4 reinforced thermoplastics using electromagnetic (EM) radiations allows for rapid dis-assembly and re-assembly of bonded structural joints. Alternate EM field causes local heating of the dispersed ferromagnetic nanoparticles (FMNP), thereby melting the surrounding thermoplastic. However, it is essential to accurately measure the temperature of the adhesive since overheating may cause degradation and underheating may introduce inefficient bonding. This paper presents an ultrasonic guided wave (GW) technique for monitoring the adhesive state and provides feedback to control the electromagnetic process. Experiments were performed on single lap-shear joints FMNP reinforced thermoplastics and non-conductive glass fiber reinforced polymer (GFRP) adherends. GW were made to propagate across the bond-line of the joint by actuating and sensing them using miniature piezoelectric wafers. Dispersion relations and dynamic wave propagation were obtained using finite element (FE) modeling. Fundamental longitudinal mode L0 at 35 kHz was found optimal for bond process monitoring. Mapping between the FE-simulated transmission coefficient of L0 and actual temperature of the thermoplastic adhesive was established using the dynamic mechanical analysis (DMA) test data. Real-time GW measurements were used as a feedback in the discrete control of the induction heater to provide optimal bonding. The developed ultrasonic technique was successfully validated by a high resolution, optical frequency domain reflectometer (OFDR) based fiber-optic temperature sensor which was embedded inside the adhesive bond-line. Experiments demonstrated good agreement between GW measurements and OFDR system. Overall, the results indicate the potential of GW technique for in-situ monitoring and controlled bonding of reversible lap-joints using electromagnetic heating.

Curve/Probabilistic Fitting of Damage Metrics for Al-7075 Materials Behavior by Using Electromechanical Impedance Method

The purpose of structural health monitoring is to provide information by making a simultaneous diagnosis of the status of the structure. Despite aging, environmental conditions and unforeseen circumstances, the construction should remain as specified in the design. Changing the environmental conditions causes the sensor and the host structure to change material properties. It is essential to take into account environmental conditions to prevent misdiagnosis. Therefore, the real cause of the change can be determined.In this study, the behavior of constrained piezoelectric wafer active sensor (PWAS)/Al 7075 was investigated by using electromechanical impedance method (EMI) under changing environmental conditions. Numerical studies on this material in the literature are limited and all the experimental/ numerical results are compensated for the temperature effect and analyzed using curve/probabilistic fitting approach for the first time. The sample used in the experimental work was modeled in ANSYS finite element program. In the experimental and numerical results, it has been observed that as the temperature decreases, the frequency shifts to the right and the amplitude increases. The experimental and simulation results were nearly the same. The temperature effect was compensated using the compensation algorithm for experimental and numerical studies. The results were compared using damage metrics. The experimental results analyzed using a curve/probabilistic fitting approach

A time-frequency analysis of the correlation between the electromechanical impedance (EMI) of surface bonded piezoelectric wafer active transducers (PWaTs) and the pitch-catch signal

Ultrasound based Structural Health Monitoring (SHM) commonly uses surface-bonded piezoelectric wafer active transducers (PWaTs) for ultrasound wave generation and sensing. Both the electromechanical impedance (EMI) of the surface bonded PWaT and the ultrasound pitch-catch signal have been studied extensively for damage detection. However, these two signals were studied separately. The correlation between the EMI and the pitch-catch signal has not been studied in detail. In this paper, a broadband spectral analysis method is presented to analyze the influence of the EMI resonances on the fundamental symmetric (S0) pitch-catch signal. First, the broadband responses of the PWaT actuator and sensor are measured and analyzed in the time-frequency domain. The results clearly demonstrate that the S0 pitch-catch signal can deviate significantly from the excitation signal when the excitation frequency is above a threshold. Next, a simulation model was implemented to explain the observed distortions. The simulation model was first validated by adjusting the adhesive parameters to reproduce the experiment measurements. The resonant characteristics of the PWaT actuator and sensor were then analyzed separately. The study reveals that the S0 deviations are due to the resonances and anti-resonances of the PWaT EMI. Furthermore, this study demonstrates that the resonance characteristics of surface-bonded PWaTs are more complicated than previously known. The research framework presented in this paper lays the theoretical foundation for future more in-depth analysis of the PWaT resonances.

On the in-plane vibrations and electromechanical resonance characteristics of non-uniformly polarized rectangular piezoelectric wafers: Selective mode-type excitation and specific mode enhancement

We investigate the in-plane vibrations and electromechanical resonance characteristics of non-uniformly polarized rectangular piezoelectric wafers. Non-uniform polarization is represented as a non-uniform electromechanical coupling coefficient using a polarization function. Governing equations are derived for the forced in-plane vibrations of a thin wafer under the assumption of generalized plane stress. The effect of non-uniform polarization is explicitly obtained in the forcing terms of the governing equations. These equations are then recast into a variational weak form that is then solved using the finite element method to obtain the displacement fields for different modes. The electromechanical response of a non-uniformly polarized piezoelectric wafer is derived in terms of the out-of-plane displacement profile on the surface of the wafer. Using the derived analytical expression, a necessary and sufficient condition for the presence/absence of a vibrational mode in the electromechanical impedance spectrum is obtained. Based on this condition, criteria for selective mode-type excitation and specific mode enhancement of vibrational modes in the electromechanical impedance spectrum are postulated. Selective mode-type excitation of in-plane extensional and shear modes is demonstrated for a square wafer and that of in-plane bending modes is demonstrated for a rectangular wafer. Specific mode enhancement is demonstrated for both square and rectangular wafers. In addition, it is also demonstrated how the criteria can be used to suppress specific vibrational modes in the electromechanical impedance spectrum. The proposed methodology of using non-uniformly polarized piezoelectric wafers finds application in the design of single element transducers with multi-frequency operation, frequency-tuned receivers/sensors, acoustic holograms, designing acoustic beams of prescribed shape/lobes, and other non-traditional applications such as information storage.