Thin Piezoelectric Plate Research Articles

Propagation of bending waves along the edge of a point-loaded piezoelectric plate on elastic foundation

An investigation on the propagation of bending waves along the edge of a piezoelectric thin plate resting on an elastic foundation (cf. Pasternak foundation) and under the action of a point-load is carried out in this paper. The displacement field of the plate is based on the classical plate theory. The Kelvin-Voigt type viscoelastic model is used to examine the viscous effect on the characteristics of the bending wave. The Moore-Gibson-Thompson (MGT) thermoelastic equation is solved for an external time variant harmonic heat source at the upper surface of the plate. The piezoelectric potential is obtained for an electrode-covered upper surface and an electrically shorted lower surface. The displacements of the propagating bending wave along the edge are examined under a time-harmonic point-load acting near the vicinity of the free edge of the plate. The well-known Green function technique and Fourier transform method are implemented to generate an analytical solution for the non-homogeneous boundary value problem. The examination of the derived explicit form of the dispersion relationship and the displacements of the bending edge wave under external loading are discussed and presented both analytically and graphically, and the results are summarized.

Physical Sensors Based on Lamb Wave Resonators

A Lamb wave is a guided wave that propagates within plate-like structures, with its vibration mode resulting from the coupling of a longitudinal wave and a shear vertical wave, which can be applied in sensors, filters, and frequency control devices. The working principle of Lamb wave sensors relies on the excitation and propagation of this guided wave within piezoelectric material. Lamb wave sensors exhibit significant advantages in various sensing applications due to their unique wave characteristics and design flexibility. Compared to traditional surface acoustic wave (SAW) and bulk acoustic wave (BAW) sensors, Lamb wave sensors can not only achieve higher frequencies and quality factors in smaller dimensions but also exhibit superior integration and multifunctionality. In this paper, we briefly introduce Lamb wave sensors, summarizing methods for enhancing their sensitivity through optimizing electrode configurations and adjusting piezoelectric thin plate structures. Furthermore, this paper systematically explores the development of Lamb wave sensors in various sensing applications and provides new insights into their future development.

Enhancement in performance of SAW resonator on LN/SiC substrate by take slowness asymmetry into account

Abstract Layered structures comprising high-coupling lithium niobate (LiNbO3, LN) piezoelectric thin plates bonded to high-velocity SiC substrates have attracted much attention of high-performance surface acoustic wave (SAW) devices. However, such these layered structures exhibit severe Rayleigh mode spurious responses that degrade the performances of SAW devices. This paper explores the generation mechanism of spurious modes on LN/SiC layered structure, and proposes an optimized layered structure with suppressed Rayleigh spurious modes. The investigation involves deriving the Euler angle range of LN by analysing the slowness surface of both LN and SiC. In addition, it is worth noting that slowness surface overlaps at some Euler angle ranges, which will cause coupling between different modes, thus generating spurious mode. Simulation result shows the frequency characteristics of SAW resonator at resonant and anti-resonant frequencies of 4.3 GHz and 4.88 GHz of SH mode, achieving a K 2 of up to 26.5% and a quality factor Q of 828. It is proved that the optimization structure offering larger K 2, higher velocity and improved Q values and Rayleigh spurious mode suppression, which is favourable for wideband and high frequency SAW devices applications.

Nonlinear Analysis of Electric Potential in a Piezoelectric Thin Plate as Pressure Sensor

Piezoelectric materials are widely applied in electronic components due to their ability to couple electric and mechanical fields. For the piezoelectric thin plate as a pressure sensor, we extend the modified first-order piezoelectric plate theory to explore the nonlinear solution of electric potential and discuss the relevant regulation mechanisms. Based on the piezoelectric effect, the electric potential generated by deformation is not linear with thickness. A quadratic function of electric potential across thickness is introduced. However, the electric potential on upper and lower electrodes is an unknown constant, which can be determined by the nonlinear complementary equation based on the Gauss theorem. It is shown that the nonlinear results of electric potential are consistent with outcomes by the three-dimensional finite element method. Furthermore, relevant regulation mechanisms are discussed on electric potential, including supported conditions, plate thickness, and load area. In addition, the influence of load locations on the electric potential response is analyzed. It is expected that these findings will be instructive to the structural design of piezoelectric pressure sensors.

Theoretical study on multi-physics coupling problems of functionally-graded lead-free piezoelectric rectangular thin plates

This paper carried out a theoretical research on multi-physics coupling problems of functionally-graded lead-free piezoelectric rectangular thin plates. Firstly, the perturbation theory was used to study the bending problem of functionally-graded lead-free piezoelectric rectangular thin plates, and the nonlinear governing equations for this bending problem were established. Then, the three piezoelectric coefficients reflecting the piezoelectric property were taken as the perturbation parameters, and the nonlinear governing equations were transformed into multiple sets of linear equations by the multi-parameter perturbation method. Finally, the solutions of these linear equations were solved by the semi-inverse solving method. Based on the finite element simulations, the effectiveness of the perturbation solutions obtained here was verified. The research results showed that it was reasonable to choose three piezoelectric coefficients as perturbation parameters, which was accord with the basic idea of perturbation theory. The analysis results indicated that there was a cross transfer relationship between external loads and perturbation solutions of every order, which could be used to simplify the perturbation expansion. Moreover, the deformation of the functionally-graded lead-free piezoelectric thin plate was less than that of the functionally-graded thin plate, that is, piezoelectric properties in lead-free piezoelectric materials had a piezoelectric enhancement effect.

Nonlinear combination resonance analysis of parametric-forced excitation for an axially moving piezoelectric rectangular thin plate in thermal- electromechanical coupling field

In this paper, the combination resonance of parametric-forced excitation characteristics for an axially moving rectangular piezoelectric plate under a thermal-electromechanical field is studied. Based on Kirchhoff-Love plate theory and Von Karman theory, the transverse vibration governing equations are derived from Hamilton's principle. The equations are discretized to ordinary differential equations by the Galerkin method. Then, the multiple scales method is applied to solve the system combination resonance equation, two different resonance states and corresponding amplitude-frequency response equations are obtained by eliminating the secular term, respectively. Additionally, the stability of the steady-state responses is analyzed by Lyapunov stability. Based on the numerical analysis, the influence of axial velocity, external voltage, central temperature difference, structural damping, and other parameters on nonlinear combination resonance response are investigated. The effect of parameter variation on period-doubling bifurcation and the chaotic motion of the system are also discussed by the system global bifurcation diagram.

Research on tunable bandgap characteristics of the phononic crystal duct with piezoelectric thin plates for the broad noise reduction

To achieve adjustable mid-low frequency noise reduction characteristics in pipeline systems, one hybrid phononic crystal duct with piezoelectric thin plates is proposed. Firstly, phononic crystal duct model with Helmholtz mufflers and built-in piezoelectric thin plates is established to reduce low-to-mid frequency noise in the duct. The theoretical transmission loss is verified using simulation methods, revealing the sound attenuation law and bandgap mechanism. Under the shunting effect of the RLC circuit, three locally resonant bandgaps are generated: the mechanical locally resonant band gap introduced by the thin plate, acoustic locally resonant band gaps caused by the Helmholtz muffler cavity structure, and the electromechanical locally resonant band gaps dominated by the shunting circuit. By adjusting the shunting circuit, the acoustic impedance of the piezoelectric thin plate can be controlled, and then the acoustic characteristics of low and medium frequencies will change. For the shunting circuit composed of inductance, capacitance and resistance in series, the inductance and capacitance can adjust the position of the three band gaps; the negative capacitance can effectively enhance the tunability of the electromechanical locally resonant band gap, which is helpful to obtain the low-frequency band gap; while resistance primarily affects the magnitude of acoustic attenuation within the bandgap. Subsequently, based on the analysis of the noise characteristics of the air-assisted system of one fuel cell vehicle, one hybrid phononic crystal duct with compact structures is designed to achieve a broadband duct noise reduction of 330 Hz–4000 Hz.

Analysis on Thermo-Electrical Principal Parametric Resonance of an Axially Moving Piezoelectric Thin Plate

In this paper, principal parametric resonance of an axially moving piezoelectric rectangular thin plate under thermal and electric field is investigated. Based on Kirchhoff–Love plate theory and Von Karman theory, the transverse vibration differential equation of a piezoelectric rectangular thin plate under thermal and electric field is derived by using Hamilton’s principle. The dimensionless vibration equation of piezoelectric rectangular thin plate with parametric excitations is discretized by Galerkin’s method. Then, the multiple scales method is applied to derive amplitude-frequency response equation and the stability conditions of the steady-state solution are obtained by Lyapunov stability theory. Numerical method is used to find the influences of specific parameters on the vibration performance and stability of the system. Based on the global bifurcation diagram and corresponding response diagram, the influences of bifurcation control parameters on the nonlinear dynamic characteristics of the system are discussed. Numerical results illustrate that the system amplitude frequency characteristic curve presents soft spring characteristics. There are periodic and chaotic motions with the increase of velocity and the central temperature difference, and the decrease of plate thickness and velocity will result in the decrease of chaotic threshold. The results also show that increase the velocity perturbation amplitude can prolong the chaotic motion.

Dual-functional synergetic energy harvesting and flow-induced vibration control of an electromagnetic-based square cylinder integrated with a flexible bimorph piezoelectric wake splitter plate

A dual-purpose FIV-based hydroelastic energy harvesting and cylinder response suppression strategy that functions based on the synergy of piezoelectric and electromagnetic transduction (EMT) mechanisms is proposed and numerically implemented. The hybrid harvester consists of a linearly sprung (1DOF) square cylinder fitted on the wake side with a thin flexural-mode cantilever bimorph piezoelectric (PVDF) splitter plate in real-time collaboration with a transversely hooked induction-based magnet-coil type transducer. The Reynolds averaged Navier–Stokes (RANS) equations with the shear stress transport (SST) k-ω turbulence closure model are selected for qualitative/quantitative prediction of hydrodynamic flow behavior in a relatively wide Reynolds numbers range. Numerical simulations show that increasing Reynolds number for the single-alone EMT-equipped cylinder in the low to intermediate range (2×103≤Re≤3×104) can noticeably improve the system hydrokinetic energy harvesting performance where a distinct coupled VIV/galloping effect is observed. Also, the hybrid piezoelectromagnetic harvester is capable of effectively suppressing the key response parameters and considerably increase the total system electrical output in an extended working bandwidth (3×104<Re≤4×105). In particular, in contrast to the conventional fixed-base cylinder configurations, maximum power extraction can be achieved over most span of the flexible piezoelectric splitter plate at Re=4×105 where the flapping oscillations of splitter plate synchronizes with the downstream alternating wake vortices.

Analysis of longitudinal leaky surface acoustic waves on piezoelectric thin plates bonded to diamond substrate

Using the finite element method, we analyzed the resonance properties of a longitudinal leaky surface acoustic wave (LLSAW) on the structure of a piezoelectric LiTaO3 (LT) or LiNbO3 (LN) thin plate bonded to a diamond support substrate. When the plate thickness was 0.3 wavelength or larger, the particle displacements of the LLSAW were substantially concentrated near the surface, and the resonance properties were significantly improved compared to those of the single LT or LN. However, spurious responses due to other SAW modes also emerged. Regarding the LN thin plate, we obtained a phase velocity and fractional bandwidth of approximately 7300 m s−1 and 9.4%, respectively. Furthermore, a structure was proposed to suppress spurious responses in which the piezoelectric thin plate is divided into two layers with different Euler angles. The spurious responses were significantly suppressed after dividing the thin plate, while the main response of the LLSAW was maintained.

Scattering of flexural waves in a semi-infinite piezoelectric thin plate with a circular hole

The scattering of flexural waves in piezoelectric thin plates with defects effects the electro-mechanical coupling property. Theoretical analysis for flexural waves is lack of a suitable decoupling function. Here, we have developed a method based on applied electric field to make a solution of the dynamic moment concentration factor (DMCF) for flexural waves scattering problems. The DMCFs of the piezoelectric materials have been found that it is significantly larger than those of the ordinary elastic materials because of electro-mechanical coupling. In the region of low frequency, DMCFs have a dependence on applied electric field and independent on the incident angle. Those opposite phenomena are observed as the frequency increasing. Those results provide theoretical guidance for dynamic analysis and strength design of piezoelectric material structures.

Vibration energy harvesting via piezoelectric bimorph plates: An analytical model

Vibration energy harvesting using piezoelectric cantilevers has been widely studied during the past decade. As an alternative to piezoelectric cantilevers, plate-like energy harvesters can be much more effective in marine, aerospace, and automotive applications. This work presents an exact two-dimensional model that can be used for analyzing thin, moderately thick, and thick piezoelectric bimorph plate vibration harvesters. The model allows to consider for the substrate layer both homogenous materials, and those with varying properties along the thickness direction. For the latter case, porous materials with various porosity distributions are herein considered, and the piezoelectric layers are assumed to be wired in both parallel and series configurations. Rayleigh damping assumptions are also used to model the structural damping of the harvesting system. Using Hamilton’s principle and Gauss’s law, the energy harvesting model is established based on the first-order and the third-order shear deformation theories. Applying an analytical procedure to the electromechanical governing equations, closed-form steady-state response expressions, which relate the voltage output and the vibration response of the harvester to harmonic input force, are derived. Finally, the proposed model is validated, and the power generation performance of the plate harvester is discussed through conducting extensive parametric studies, covering the effect of design parameters, such as the applied electric load, porosity characteristics, electrical configuration, and geometrical parameters.

Symplectic Method for the Thin Piezoelectric Plates

The symplectic method for a thin piezoelectric plate problem is developed. The Hamiltonian canonical equation of thin piezoelectric plate is given by using the variational principle. By applying the separation of variables method, we can obtain symplectic orthogonal eigensolutions. As an application, the problem of a thin piezoelectric plate with full edges simply supported under a uniformly distributed load is discussed, and analytical solutions of the deflection and potential of a piezoelectric thin plate are obtained. A numerical example shows that the solutions converge very rapidly. The advantage of this method is that it does not need to assume the predetermined function in advance, so it has better universality. It may also be applied to the problem of thin piezoelectric plate buckling and vibrating.

Electromechanical characterization and kinetic energy harvesting of piezoelectric nanocomposites reinforced with glass fibers

Piezoelectric composites are a significant research field because of their excellent mechanical flexibility and sufficient stress-induced voltage. Furthermore, due to the widespread use of the Internet of Things (IoT) in recent years, small-sized piezoelectric composites have attracted a lot of attention. Also, there is an urgent need to develop evaluation methods for these composites. This paper evaluates the piezoelectric and mechanical properties of potassium sodium niobate (KNN)-epoxy and KNN-glass fiber-reinforced polymer (GFRP) composites using a modified small punch (MSP) and nanoindentation tests in addition to d33 measurements. An analytical solution for the piezoelectric composite thin plate under bending was obtained for the determination of the bending properties. Due to the glass fiber inclusion, the bending strength increased by about four times, and Young's modulus in the length direction increased by approximately two times (more than that of the KNN-epoxy); however, in the thickness direction, Young's modulus decreased by less than half. An impact energy harvesting test was then performed on the KNN-epoxy and KNN-GFRP composites. As a result, the output voltage of KNN-GFRP was larger than that of KNN-epoxy. Also, the output voltage was about 2.4 V with a compressive stress of 0.2 MPa, although the presence of the glass fibers decreased the piezoelectric constants. Finally, damped flexural vibration energy harvesting test was carried out on the KNN-epoxy and KNN-GFRP composites. The KNN-epoxy was broken during the test, however KNN-GFRP composite with a load resistance of 10 MΩ generated 35 nJ of energy. Overall, through this work, we succeeded in developing piezoelectric energy harvesting composite materials that can withstand impact and bending vibration using glass fibers and also established a method for evaluating the electromechanical properties with small test specimen.

Nonlinear ESO-based vibration control for an all-clamped piezoelectric plate with disturbances and time delay: Design and hardware implementation

Considering the problems of model uncertainties, higher harmonics, uncertain boundary conditions, external excitations, and system time delay in practical vibration control system, a novel active vibration control method is proposed to suppress the vibration of a thin plate structure with acceleration sensor and piezoelectric bimorph actuator in this paper. First, a nonlinear extended state observer (NESO)-based controller is designed to ensure the anti-disturbance performance of the structural vibration control system. Then, an enhanced differentiator-based time delay compensation method is introduced to improve the vibration suppression performance of the NESO-based controller. A real time hardware-in-the-loop benchmark for an all-clamped piezoelectric thin plate is designed to verify and compare the performance of the developed controller against conventional ESO-based methods (linear ESO with/without time delay compensation, NESO without time compensation). The best vibration suppression and disturbance rejection performance of the proposed NESO-based controller with an enhanced time delay compensator is verified in the comparative experimental results. This work is able to provide practitioners with vital guidance in designing active vibration control system in the presence of disturbances and time delay.

Thickness-Stretch Vibration of an Infinite Piezoelectric Plate with Flexoelectricity

In this paper, the thickness-stretch vibration of an infinite piezoelectric plate is studied, with consideration of the flexoelectric effect. The theoretical model developed herein is based on a one-dimensional formulation, with the assumption that the displacement and electric potential vary through the thickness. The Gibbs energy density function and variational principle are adopted to derive the constitutive equation with flexoelectricity, governing equations, and boundary conditions. For the effect of flexoelectricity, the coupling between the strain gradient through the thickness and the electric field is considered. Two electric boundary conditions are used in this work and the corresponding frequency shift due to the flexoelectricity is calculated. The present results demonstrate that the flexoelectric effect decreases the fundamental frequency of the thickness-stretch vibration and has a significant effect on the vibrational frequencies of the thickness-stretch mode of a thin piezoelectric plate. The results also show that the flexoelectric effect has a significant size dependency, and should be taken into consideration for the design and development of next-generation high-precision and high-frequency piezoelectric transducers and resonators in the future.

Flexoelectric effect on thickness-shear vibration of a rectangular piezoelectric crystal plate

Thickness-shear (TSh) vibration of a rectangular piezoelectric crystal plate is studied with the consideration of flexoelectric effect in this paper. The developed theoretical model is based on the assumed displacement function which includes the anti-symmetric mode through thickness and symmetric mode in length. The constitutive equation with flexoelectricity, governing equations and boundary conditions are derived from the Gibbs energy density function and variational principle. For the effect of flexoelectricity, we only consider the shear strain gradient in the thickness direction so as to simply the mathematical model. Thus, two flexoelectric coefficients are used in the present model. The electric potential functions are also obtained for different electric boundary conditions. The present results clearly show that the flexoelectric effect has significant effect on vibration frequencies of thickness-shear modes of thin piezoelectric crystal plate. It is also found that the flexoelectric coefficients and length to thickness ratio have influence on the thickness-shear modes. The results tell that flexoelectricity cannot be neglected for design of small size piezoelectric resonators.

Precise and target-oriented control of the low-frequency Lamb wave bandgaps

Precise and target-oriented control of acoustic/elastic wave bandgaps in phononic crystals or acoustic metamaterials according to particular requirements is of both theoretical and practical importance. A very challenging and also interesting task is to tune the widths and the overall positions of the bandgaps of interest independently and arbitrarily. This work presents a simple and smart acoustic metamaterial structure, which can achieve the above mentioned goal by considering the symmetric Lamb waves. The proposed acoustic metamaterial structure consists of a homogenous piezoelectric plate which is connected to the LC circuits through an array of periodic surface electrodes. The control of the resonance bandgaps (RBGs), which are generated by the coupled resonance of the piezoelectric plate with the external LC circuits, is the focus of this study. To solve the problem at hand, we develop a two-dimensional (2D) spectral element method (SEM) considering the full electro-mechanical coupling, and the high tunability of the RBGs is demonstrated numerically in the low-frequency range. Especially, we find that the upper/lower boundary of a RGB can be intentionally fixed at any specified frequency while changing its’ bandwidth. To explore the corresponding physical phenomena and reveal the regulation mechanism, a simplified theory is developed based on the assumption of thin piezoelectric plates. Several simple analytical formulas are established, which are essential to the precise control of the RBGs for both the thin and thick piezoelectric plates. A numerical example is given to demonstrate the detailed procedure of precisely tuning a RBG in a targeted frequency range, which is also verified by the transmission spectrum for the corresponding finite piezoelectric acoustic metamaterial plate.

Energy harvesting array materials with thin piezoelectric plates for traffic data monitoring

This study developed energy harvesting arrays (EHA) composed of multiple piezoelectric elements for traffic monitoring and energy harvesting. The developed EHA was investigated through compression tests to simulate the effects of different vehicle axle loads and speeds. The effect of the number and configuration of piezoelectric elements on piezoelectric response was explored. To quantify the sensitivity of EHA under different loads, the concept of loading utilization efficiency was proposed. The influence of temperature and surface layer type on the output signal of EHA covered with asphalt surface layer was investigated using wheel rolling test. The compression test showed that the response of EHA was affected by both axle load and vehicle speed. The output voltage and loading utilization efficiency increased gradually with the increase of load and load frequency. The response law of EHA provided ideas for monitoring vehicle axle load and speed information. The open-circuit voltage signal decreased as the number of piezoelectric elements in parallel increased. The recommended number of piezoelectric elements was identified. To reduce the impact of temperature and surface covering material on the perceived traffic information, EHA was recommended to be encapsulated with thermal insulation materials for embedment. The open circuit voltage of EHA in the wheel rolling test was found higher than that in the compression test. This difference was further explained by finite element modeling results showing that the polyurethane plate increased the deformation of thin piezoelectric plates. Considering the strength of the piezoelectric response signal, the recommended thickness of polyurethane underlayment was determined.

Two-frequency parametric excitation and combination resonance of a nanocomposite laminated piezoelectric trapezoidal plate in subsonic airflow

In this study, an analytical approach is presented to analyze the bifurcations and nonlinear dynamics of a cantilevered piezoelectric nanocomposite trapezoidal actuator subjected to two-frequency parametric excitations in the presence of subsonic airflow. The assumption of uniformly distributed single-walled carbon nanotubes along the thickness is taken into the consideration. The governing equations are built by the von-Karman nonlinear strain-displacement relations to consider the geometrical nonlinearity and the linear potential flow theory. The present study focuses on a specific resonance case deals with the occurrence of simultaneous resonances in the principal parametric resonance of the first mode and combination of the parametric resonance of the difference type involving two modes. The multiple scales method is employed to obtain the four nonlinear averaged equations which are solved by using the Runge-Kutta method. Moreover, the frequency-response curves, bifurcation diagrams, time history responses, and phase portrait are obtained to find the nonlinear dynamic responses of the plate. The effects of the amplitude of piezoelectric excitation, piezoelectric detuning parameter, and aerodynamic pressure are also studied. The results indicate that, the chaotic, quasi-periodic and periodic motions of the plate exist under certain conditions and the variation of controlling parameters can change the form of motions of the nanocomposite piezoelectric trapezoidal thin plate.