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Piezoelectric micromachined ultrasonic transducers (PMUTs) have advantages to those of traditional ultrasonic transducers in small form factor, low cost, low power consumption, large bandwidth, and good acoustic impedance matching. A bimorph pinned dual-electrode PMUT is developed for improved vibrational displacement, output sound pressure, and electro-mechanical coupling for several demonstration examples, including 3D space imaging, directional loudspeaker, and non-contact temperature sensing. Analytically, an equivalent circuit model has been built for bimorph, pinned dual-electrode PMUTs and finite element simulation result has shown a 380% boost for the sound pressure per volt per area and increased center displacement at the resonant frequency as compared to those of conventional unimorph PMUTs. Experimentally, prototype devices have been designed, fabricated, and tested with a 58% measured increase in the electromechanical coupling factor and pulse-echo tests have shown a 4-meter traveling distance in air under a 133 kHz driving frequency. As a proof-of-concept, a long-distance (>1.5 meters) ultrasound imaging is demonstrated using a 4×4 array prototype system based on the transmit beamforming scheme in air. A small form factor (6×6 mm2) design and a more than 135o field of view have display the capability of real time 3D object detection with up to 125 fps (frames per second) based on the scheme of ultrasound receive beamforming toward applications such as drone navigation, machine vision and so on. A highly directional air-coupled parametric loudspeaker using a single PMUT chip has been validated based on a parametric array design to generate highly directional audible sound with a half power beam width of less than 5 degrees. The multiple audible frequency sound has been generated by using a single chip with 246 PMUT elements in a footprint of 13 × 13 mm toward low-power and portable directional loudspeakers for private communications. In another example, non-contact surface temperature measurements via a single PMUTs array have been established based on the time-of-flight (ToF) changes. The key advantages of this scheme include the independence of surface material properties, e.g. emissivity; the possible integration with an ultrasonic analog front-end circuitry for both transmitting and receiving. A recorded sensitivity of 143 ns/oC has been achieved in non-contact temperature sensing in various media such as air, liquid, and tissue for broad applications.

This study investigates complex acoustical intensity using a polyvinylidene fluoride (PVDF) bimorph. Analytical models of the open-circuit voltage outputs of an infinite-strip-shaped PVDF bimorph cantilever in an underwater sound field are developed. Results show that the sound pressure generates the sum of the outputs, while the particle velocity normal to the PVDF surface generates the difference. The sensitivities of the pressure- and velocity-generated voltage responses with respect to an incident plane sound field demonstrate uniform directivity in a low-frequency range, which is suitable for acoustical intensity determination. The higher velocity sensitivity confirms the advantage of using a PVDF bimorph as a velocity sensor, owing to its light weight and flexibility. An algorithm for determining the complex acoustical intensity normal to the surface is proposed by utilizing those voltage responses and the probe gain calibrated with a given angle of incident sound. This algorithm allows accurate determination of sound intensity of a plane wave field, where the reactive part of intensity is absent. However, a small error may exist when the reactive intensity is large and active intensity is small. This small discrepancy arises from the inherent variation in the phase directivity of the gains, which decrease with frequency.

Piezoelectric energy harvesting (PEH) remains a key area of interest for academic research due to its fast advancement and growing demand for low-powered electronics. In this study we have investigated various energy harvesting scenarios including PZT bimorph cantilever, circular bimorph with a fixed constraint at the center and at the perimeter, roller constraint at the center and at the perimeter, and circular unimorph disc with a fixed constraint at the center and at the perimeter, as well as a unimorph with two different dimensions. Modeling and simulation are performed in COMSOL for all scenarios starting from an aluminum shim (for stress/strain analysis) then bimorph/unimorph (for analysis of voltage/power). Samples are prepared in accordance with model analysis and tested on a custom-made experimental setup. Simulated and experimental results are compared and found to be in agreement. Surprisingly, a circular unimorph disc with a fixed constraint at the center shows the best result producing 7.1 V at 500 Hz with a broadband curve (450 Hz to 650 Hz). The PZT circular unimorph disc with the highest power density of 1.6234 mW/cm2 is found to be the most efficient variant.

This paper reports a bimorph pinned piezoelectric micromachined ultrasonic transducer (PMUT) for enhanced sound pressure output and electromechanical coupling factor for space imaging applications. An equivalent circuit model has been built to analyze the dynamic behavior of PMUTs and prototype devices have been designed, fabricated. Experimental results show a 58% measured increase in the electromechanical coupling factor and pulse-echo measurements show a 4-meter traveling distance in air under a 133 kHz driving frequency. As a demonstration example, a relatively long-distance (>1.5 meters) ultrasound imaging test in air is conducted using a $4\times 4$ bimorph, pinned dual-electrode PMUTs array based on the transmission beamforming scheme. As such, this work enhances and extends the PMUT performances and capabilities for potential broad applications. [2021-0102]

3-D-printed structures integrated with laser-cut spiral PZT bimorphs are used to obtain low mechanical resonance frequencies for energy harvesting and a vibration-activated mechanical switch. This structure is used to realize a batteryless vibration event detector and RF transmitter, using the energy in the vibration and a mechanical switch as a comparator. The low-resonance frequency of the 3-D-printed mechanical resonators is used to supply significant mechanical resonance gain and trigger the impulse response of the PZT bimorphs, resulting in an upconversion of resonance frequencies. RF pulses are generated by an LC resonator and transmitted by a loop antenna for reporting event detection. The 3-D-printed structure has resonances as low as 17.5 to 40 Hz corresponding to the vibration energy spectrum readily available in the environment. Theory and experiments to verify RF output are presented. At 40 Hz and 0.75 g excitation, the resulting RF pulse is at a carrier frequency of 10.9 MHz with energy extracted from the bimorph of 0.95 nJ per pulse. As a demonstration of the device, the wireless sensor node is used to identify operational modes of a portable gasoline electric generator.

A nonlinear developed model for various PZT wind energy harvesters with arbitrary dimensions and location of electroceramics has been prepared. This model can describe unimorph and bimorph harvesters with different cantilever cross-sections attached to a tip body with different shapes. The system model has been validated with results reported in the literature. A set of parametric studies has been conducted to examine the influences of the cantilever shape in addition to the shape of the tip body. Furthermore, the impacts of load resistance and wind speed on the output power have been analyzed. The effects of number, position, and dimensions of piezoceramics on the harvester performance have also been investigated. It is found that by increasing the total area of electroceramics (including the length, width, or the number of PZT patches), the peak of the wind critical speed and the middle resistance range where the instability speed is very sensitive to the electrical load shifts toward the lower resistances. Moreover, several instrumental points to design efficient and affordable vibrating wind harvesters at low and high flows have been obtained.

In this paper, the stress behaviour and power generation of cymbal bimorph transducer of different piezoelectric ceramics are studied. Comparison of stress, deformation and power is done between di...

Piezoelectric energy harvesting (PEH) provides an essential mode for the transformation of mechanical vibration to electrical form for providing continuous power to wireless sensor nodes in today’s...

In this article, proposed is a hysteresis effects model of a bimorph circular flexural-mode piezoelectric actuator for a deformable mirror of adaptive optics system. The analytical solutions are derived from the three-dimensional equations of piezoelectricity, and the dependence of the nonlinear hysteresis performance of the actuator on the physical parameters is evaluated. Numerical results illustrate that the hysteresis loops of the strokes of the actuator are affected by the start values of the electric field and the thickness of the metallic layer. Besides, the results also suggest that an appropriate thickness of metallic layer could compensate some hysteresis effects. Moreover, the results of the analytical method have been demonstrated by those of the finite element method.

A nonlinear micro-piezoelectric–electrostatic energy harvester is designed and studied using mathematical and computational methods. The system consists of a cantilever beam substrate, a bimorph piezoelectric transducer, a pair of tuning parallel-plate capacitors, and a tip–mass. The governing nonlinear mathematical model of the electro-mechanical system including nonlinear material and quadratic air-damping is derived for the series connection of the piezoelectric layers. The static and modal frequency curves are computed to optimize the operating point, and a parametric study is performed using numerical methods. A bias DC voltage is used to adapt the system to resonate with respect to the frequency of external vibration. Furthermore, to improve the bandwidth and performance of the harvester (and achieve a high level of harvested power without sacrificing the bandwidth), a nonlinear feedback loop is integrated into the design.

The challenge of continuously powering the wireless sensor network located at remote areas has been resolved by the emergence of piezoelectric energy harvester. This paper evolved a new idea of using different piezoelectric materials together within segmented doubly clamped bimorph piezoelectric energy harvester (DCBPEH). The finite element modeling of the device has been presented here using COMSOL multiphysics software. This paper starts with concept of strain nodes and further better performance of segmented electrodes-based beam over the continuous electrode-based beam has been achieved. Next, a performance analysis study with continuous electrode-based beam has been carried out for different variants of two piezoelectric materials, namely, PMN-xPT and PZT. From this study, PMN-35%PT and PZT-5H piezoelectric materials are found to be best variants. Finally, the performance of segmented DCBPEH has been observed for different positioning formats of PMN-35%PT (M1) and PZT-5H (M2) piezoelectric materials on different segments of the beam. From this analysis, M1–M1–M2 and M2–M1–M1 are noted to be two favorable positioning formats which provide similar and maximum performance (7.78 mW) as compared to other formats.

We present an analytical modeling framework and its analysis for thin piezoelectric metamaterial plates to enable and predict low-frequency bandgap formation in finite structural configurations with specified boundary conditions. Using Hamilton’s extended principle and the assumptions of classical (Kirchhoff) plate theory, the governing equations and boundary conditions for the fully coupled two-dimensional electromechanical system are obtained. The two surfaces of the piezoelectric bimorph are segmented into non-overlapping opposing pairs of electrodes of arbitrary shape, and each pair of electrodes is shunted to an external circuit. This formulation can be used to study the effect of electrode shape on plate response for topology optimization and other vibration control applications. Using modal analysis, we show that for a sufficient number of electrodes distributed across the surface of the plate, the effective dynamic stiffness of the plate is determined by the shunt circuit admittance applied to each pair of electrodes and the system-level electromechanical coupling. This enables the creation of locally resonant bandgaps and broadband attenuation, among other effects, in analogy with our previous work for one-dimensional piezoelectric structures with synthetic impedance shunt circuits. It is also demonstrated that piezoelectric bimorph plates display significantly improved performance (i.e. electromechanical coupling) over bimorph beams, but require additional electrode segmentation to achieve metamaterial-type performance. The governing equations are also used for dispersion analysis using the plane wave expansion method, enabling the analytical dispersion analysis of unit cells with arbitrary electrode shapes. The modeling framework and approximate closed-form bandgap expressions are numerically validated using finite element analysis.

Autonomous sensors that receive their energy from an energy harvester or directly from the environment have the potential to save energy for applications in numerous sectors. For humidity sensing, the swelling behaviour of a water vapour-sensitive hydrogel is used. To trigger an electrical contact the mechanical energy is taken from the hydrogel swelling by the bimorph effect. As long as a defined threshold is not reached, the electrical microcontact remains open. By passing the threshold value, a switching will be triggered causing the closure of the contact. This sensor principle does not need any electrical power supply because the switching power is provided directly by the surrounding humidity as quantity to be measured. For the description of the deflection versus the hydrogel pattern of such a sensor, a model was developed by means of the beam theory. Goal of the model was to derive design guidelines for the dimensioning of the sensors bending plate and the patterned hydrogel layer. Experiments then should show the applicability of the model approaches. The deflection of the bending plate depends on the ratio between the lengths of the uncoated and the coated part of the bending plate where the maximum occurs at a ratio of ca. 0.5. The swelling behaviour of the hydrogel shows a high sensitivity with regard to slight changes in relative humidity. This can be used for humidity threshold sensors that open and close microcontacts with respect to very small changes in relative humidity. To avoid voltage peaks and arcs during the switching process that could arise and destroy the microcontact, a bistable characteristic with hysteresis is needed. Experiments demonstrate the feasibility of this concept and are in good agreement with the modelling results.

This paper presents a new way to design a broadband harvester for harvesting high energy over a low-frequency range of 10–15 Hz. The design comprises a cantilever beam with two parallel grooves to form three dissimilar length parallel branches, each with an unequal concentrated tip mass. The piezoelectric material covers the whole length on both sides of the beam to form a bimorph. Appropriate geometry and mass magnitudes are obtained by a parametric study using the Finite Element Method. The design was simulated in COMSOL Multiphysics to study its response. The first three bending modes were utilized in energy harvesting, resulting in three power peaks at their respective fundamental frequencies. The adequate load resistance determined was 5.62 kΩ, at which maximum power can be harvested. The proposed harvester was compared to two other harvesters presented in the literature for validation: First, an optimized conventional harvester while the proposed harvester is operating at adequate load resistance. Second, a multimodal harvester, while the proposed harvester is operating at a 10 kΩ load. The suggested harvester proved to be more efficient by harvesting sufficiently higher broadband energy and is applicable in a wide range of vibration environments because of its adaptability in design.

This paper presents a study on the design and multiobjective optimization of a bimorph-segmented linearly tapered piezoelectric harvester for low-frequency and multimode vibration energy harvesting. The procedure starts with a significant number of FEM simulations of the structure with different geometric dimensions—length, width, and tapering ratio. The datasets train the artificial neural network (ANN) that provides the fitting function to be modified and used in algorithms for optimization, aiming to achieve minimal resonant frequency and maximal generated power. Levenberg–Marquardt (LM) and scaled conjugate gradient (SCG) methods were used to train the ANN, then the goal attainment method (GAM) and genetic algorithm (GA) were used for optimization. The dominant solution resulted from optimization by the genetic algorithm integrated with the ANN fitting function obtained by the SCG training method. The optimal piezoelectric harvester is 121.3 mm long and 71.56 mm wide and has a taper ratio of 0.7682. It ensures over five times greater output power at frequencies below 200 Hz, which benefits the low frequency of the vibration spectrum. The optimized design can harness the power of higher-resonance modes for multimode applications.

This paper presents a cost-effective and simple structured lead zirconate titanate (PZT) film-based wearable device for smartly monitoring gait and pace count. The device possesses the interconnected structures of serpentine-shaped strips and square nodes, which causes the large stress and strain gradients when the external force is applied to the terminal nodes of the device. The bimorph configuration of metal/PZT/metal thin-film makes the wearable device thinner than a regular paper. This device responses to the strain with simultaneously piezoelectric and capacitive signal outputs. By attaching this device to the skin around human knee joint with athletic tape laminate units, the information of step counting and rapid change in gait of the walking person could be precisely obtained by the capacitive and piezoelectric detections, respectively. The design, fabrication and characterization of the developed device are described in the text. A subject wears the device to walk on a treadmill with different speed settings of 3 km/h and 9 kmh are performed. The resulting signals successfully demonstrate the device functionality of monitoring gait and counting steps.

Cantilever piezoelectric energy harvesting from ambient vibrations is a viable solution for powering wireless sensors and low-power electronics. However, the greatest issue preventing these systems from being widely used is their poor reliability. With the aim to maximise their power output, the devices are often operated close the fracture strength, which results in cracks in the brittle piezoceramic layer. Tapered cantilevers are suggested to improve the mechanical reliability. A relative comparison is made between tapered piezoelectric cantilevers and conventional rectangular cantilevers in terms of reliability and power output. Tensional strains causing fractures show a serious reduction of power output and eigenfrequency. Experiments show that tapered cantilevers have a higher power output per unit area.

In order to harvest ambient renewable or recovery energy, a novel piezoelectric energy harvester which mainly includes vibrators, a rotor and a cylindrical outer casing is presented in this paper. The vibrator is made of a U-shaped bimorph piezoelectric beam with a magnet slab mounted on its free end, and the rotor is a disc with magnet slabs embedded in the grooves along its periphery. The theoretical analysis model of the harvester is established and the mechanical and electrical responses are obtained. The results indicate that the harvester can achieve a maximum response by adjusting the rotor speed to make it work near resonance. As the beam section width or the substrate thickness decreases, or the piezoelectric patch thickness increases, the effective power of the harvester generally increases. On the whole, the substrate thickness has the greatest influence on the responses of the harvester, the piezoelectric patch thickness follows, and the influence of the beam section width is the smallest. In particular, the electric power generated from the harvester can reach 8.19 KW by adjusting the values of the related design parameters, which is comparable to a traditional small windmill generator, and therefore the proposed harvester has an appealing application prospect.

A small disc type piezoelectric motor was developed that can be used for micro flying vehicles. The operating principle of the motor is based on radial-bending type hybrid vibrations. The stator of the motor is a bimorph disc with the special quadrilateral shaped waveguides in the inner circumference of the disc. Waveguides are aligned with the tangential direction of the contacting ring. Such configuration of the actuator allows transforming radial vibrations of the disc into rotational vibrations of the contacting ring. Elliptical motion of the contact points is obtained by superposition of radial and bending vibration modes. The motor has two truncated cone-shaped rotors. Although the actuator is asymmetrical, two coaxial shafts of the motor can be rotated in both directions depending on the phase of excitation signals. Moreover, the proposed piezoelectric motor allows controlling the rotation speed of the rotors in different directions depending on the amplitude of the applied voltage. Numerical and experimental investigation of the piezoelectric motor was performed to validate the operating principle and to analyze vibrations of the contact points. Electrical and mechanical output characteristics of the piezoelectric motor were measured. The motor achieved a maximum no load rotational speed of 7108 rpm at 15 V while maximum torque is 0.0647 mN m.

A low-frequency structure-control-type inertial actuator using miniaturized bimorph piezoelectric vibrators is proposed in this paper to achieve high resolution and high stability with a large linear stroke. These vibrators are fabricated by bonding, thinning, and patterning fabrication processes, which are beneficial to realize miniaturization and increase output performance for the system. A theoretical model based on work-energy analysis is established to predict the output displacement characteristics. An experimental system is built to evaluate the performance of the proposed actuator. Experimental results indicate that the stable minimum step displacement is 0.03 μm under a square wave signal of 5 V, 50 Hz, and a clamping difference of 3.5 mm. Under the condition of 7 V and 50 Hz, the sample standard deviation is 0.0337 μm in repeatability test. The proposed actuator achieves a stable and accurate linear bidirectional motion with high resolution, high stability, low power consumption, and a large working stroke.

Cantilever-based piezoelectric energy harvesters have been utilized as structures to extract mechanical energy from the ambient mechanical vibrations and transfer it into the electrical output. In this article, the performance of bimorph piezoelectric beam energy harvesters is investigated. The cantilever beam is modeled by using both Timoshenko and Euler–Bernoulli beam theories. The equations are discretized using the conventional finite element method and superconvergent element. Besides the high rate of convergence, easy switching between the above beam theories is enabled by such type of element. The current model is presented for a Timoshenko beam model, but it could as well be used for a Euler–Bernoulli beam model. In addition, voltage, current, and power frequency response functions for different ranges of load resistance varying from the short-circuit to open-circuit conditions are determined to reach the maximum values. Effects of the slenderness ratio and the required beam model based on the geometric properties of the piezoelectric energy harvesters are discussed in the final part of this study. The results show that only for smaller values of the slenderness ratio (below 5), it is necessary to model the beam using the Timoshenko assumptions; otherwise both beam theories provide approximately the same responses.

In the literature of vibration energy harvesting, mechanically nonlinear frameworks have mostly employed linear electrical circuitry to formulate AC input–AC output problems, while the existing efforts on nonlinear power conditioning circuits have assumed linear mechanical behavior. However, even for the simplest case of a stiff (geometrically linear) piezoelectric cantilever, material softening and dissipative nonlinearities in the mechanical domain have to be accomodated to accurately predict the response for moderate to high excitation levels, and likewise a stable DC signal must be obtained to charge a storage component in realistic energy harvesting applications. Furthermore, often times the voltage output is not large enough to assume ideal diode behavior to reduce diodes to switches in AC–DC conversion modeling. Therefore, a relatively complete representation of piezoelectric energy harvesting requires accounting for the mechanical (e.g., material and dissipative) nonlinearities as well as the nonlinear process of AC–DC conversion with non-ideal circuit elements, such as real diodes. To this end, we present and experimentally validate a multiphysics framework and harmonic balance analysis that combines these mechanical and electrical nonlinear non-ideal effects to predict the DC electrical output (DC voltage across the load) in terms of the AC mechanical input (base vibration) for arbitrary vibration and voltage levels. The focus is placed on a bimorph cantilever with piezoelectric laminates under base excitation. The terminals of the piezoelectric layers are combined in series and connected to a bridge rectifier with non-ideal diodes and a filter capacitor. The multi-term harmonic balance framework can capture the ripple in the DC signal as well as amplitude-dependent nonlinear dynamics accounting for realistic diode behavior. In addition to quantitative comparisons and validations by comparing the experimental data and model simulations, important qualitative trends are unveiled for mechanically and electrically nonlinear non-ideal dynamics of piezoelectric energy harvesting.

Frequency up-conversion is an effective approach to increase the output power of a piezoelectric energy harvester (PEH). In this work, we studied a piezoelectric energy harvesting system, which converts low-frequency vibration from ambient sources to the resonant vibration of the PEH to improve the energy harvesting efficiency. The PEH includes two beams, a pair of rack and pinions, and a slider crank mechanism to retrieve energy from ambient low-frequency vibrations through impacts. The soft driving beam is subjected to a sinusoidal base excitation along the transverse direction. The piezoelectric bimorph undergoes both slow longitudinal motion as well as transverse vibrations. The transverse vibration of the bimorph is induced by impacts which is the vibration source to generate output power. The longitudinal motion of the bimorph is used to control the impact with the soft driving beam, which guarantees the harvester to pump in more kinetic energy from the driving beam. Using the discontinuous dynamic theory, the energy harvesting performance of the impact-controlled system was studied in period one and period two motions. The stability of periodic solutions was investigated and bifurcation diagrams of impact velocities, times and displacements were obtained. The harvested power of the piezoelectric beam versus the based excitation frequency was also obtained, and the results were compared to the power generation of a piezoelectric beam directly subjected to the base excitation along the transverse direction.

A micro-electro-mechanical system (MEMS) trenched piezoelectric energy harvester based on a cantilever structure has been proposed. The trenched piezoelectric layer has increased the output voltage and the generated power. It also provides three additional design parameters such as the trench position, depth and length. A particle swarm approach has been used for optimisation of the piezoelectric energy harvester geometry with the aim of finding the optimum design which transfers the maximum harvested power to a definite load. The optimisations and comparisons have been made for unimorph, bimorph, trenched and non-trenched cantilever beams. The results are quite revealing that the generated power for a trenched bimorph energy harvester is much larger than other structures. The optimum design found by particle swarm optimisation algorithm has asymmetric trenches in the top and bottom piezoelectric layers and can generate much more power than the unoptimised structure.

A novel oscillator structure consisting of a bimorph piezoelectric cantilever beam with two steps of different thicknesses is proposed to improve the energy harvesting performance of a vibration energy harvester (VEH) for use in low-frequency vibration environments. Firstly, the piezoelectric cantilever is segmented to obtain the energy functions based on the Euler–Bernoulli beam assumptions, then the Galerkin approach is utilized to discretize the energy functions. Applying boundary conditions and continuity conditions enforced at separation locations, the coupled electromechanical equations governing the piezoelectric energy harvester are introduced by means of the Lagrange equations. Furthermore, expressions for the steady-state response are obtained for harmonic base excitations at arbitrary frequencies. Numerical results are computed, and the effects of the ratio of lengths, ratio of thicknesses, end thickness, and load resistance on the output voltage, harvested power, and power density are discussed. Moreover, to verify the analytical results, finite element method simulations are also conducted to analyze the performance of the proposed VEH, showing good agreement. All the results show that the present oscillator structure is more efficient than the conventional, uniform beam structure, specifically for vibration energy harvesting in low-frequency environments.

The modeling and analysis of piezoelectric cantilevers are critically important in the design of micro intelligent systems, where piezoelectric beams serve as major components in micro sensors, actuators or energy harvesters. In this paper, we propose an analogy modeling method for the unimorph and bimorph piezoelectric beams, which helps to improve the accuracy of the neutral plane location of piezoelectric beams with different thickness ratios and total thicknesses. In particular, the strains of each layer are obtained by employing the analogy modeling method with the consideration of the transverse strain effect, where the force balance and moment balance equations of the final state of piezoelectric beams are derived under electric fields to reveal the relationship between the external deflection and the internal stress distribution of piezoelectric beams. To verify the effectiveness of the proposed approach, the bending characteristics of unimorph and bimorph piezoelectric beams (PZT-5A) are comprehensively tested under various electric fields, where theoretical values agree well with experiments and simulations. Compared with existing results, the proposed method provides a more general and accurate approach to characterize the properties of deflection and internal stress distribution for piezoelectric beams, which can be better used to study the stress of the adhesive layers, the geometric dimension optimization and the dynamics of piezoelectric beams in micro sensor or actuator applications.

Piezoelectric vibration energy harvesting (PVEH) has been emerged as an alternative solution for sustainable powering to electronics. It has been well known that a PZT stack operating in 33-mode has higher mechanical to electrical energy conversion efficiency and higher mechanical reliability, compared to a cantilevered PZT bimorph operating in 31-mode. However, there are two challenges to improve the output performance of a PZT stack at a low frequency environment. First, the lower tensile strength of a PZT stack compared to the compressive strength makes it difficult to fully utilize maximum strain at harsh vibration conditions. Second, the relatively high stiffness of a PZT stack prevents being resonant with a base structure vibrating at a low frequency. To solve these challenges, this study thus proposes a double acting compression mechanism (DACM)-based PVEH stack operating in 33-mode. The DACM-based PVEH stack can convert mechanical vibration into elevated two-way compressive loading. The analytic model is used to investigate the electroelastic behaviors of the DACM-based PVEH device at given vibration conditions. The comparative study is performed to verify the effectiveness of the DACM-based PVEH stack over other mechanisms. It can be concluded that the DACM-based PVEH stack enables to generate higher power with the same volume of PZT using elevated two-way compressive loading.

Wave propagation control in piezoelectric meta-structures has been developed in recent years, which focuses on coupling proper electric media via piezoelectric materials for elastic wave filtering properties within a low frequency range. In order to develop broadband band gaps and diversified wave propagation characteristics of mechanical meta-structures for different complex practical applications, the research proposes an innovative piezoelectric beam meta-structure using electronic negative capacitance dual-adjacent/staggered electrical connections. In the proposed meta-structures, a unit periodic cell composed of four adjacent primitive periodic cells (including four piezoelectric patches with different polarization directions) are connected to negative capacitance circuit shunts using electrical dual-adjacent/staggered patterns. Based on the Timoshenko beam theory and wave propagation theory, a theoretical modeling of the proposed meta-structure is established for evaluating wave propagation properties. Furthermore, wave attenuation performance of the proposed structure is investigated and compared with the traditional meta-structure with negative capacitance independent electronic networks in which negative capacitance shunts are independently applied to single piezoelectric patch or bimorph piezoelectric patches within a unit primitive periodic cell. Results show that the proposed innovative meta-structure utilizes less negative capacitance shunts for achieving better wave attenuation performance, and has more stable negative capacitance control system in practical applications.

This study proposed a painted flexible piezoelectric device (FPED) for harvesting wave energy. The painted FPED had a laminated structure consisting of an elastic material and a piezoelectric paint. The device could be easily deformed by an external force such as wind, wave, current, or mechanical vibration, and it could generate electrical power from an ambient, non-utilised energy source. The results revealed the mechanical deformation and electrical performance of the painted FPED excited by wave conditions. They also clarified the influence of some key parameters, such as the submerged depth, wave steepness, aspect ratio, actuator pattern (unimorph and bimorph), and thickness of the painted piezo-material and elastomer on the output voltage generated by a painted FPED excited by various wave forces, heights and periods. Moreover, a theoretical model was proposed, and the results were in good agreement with the experimental results under several wave conditions. The electrical power in real sea states was estimated by the theoretical model. The electric power could be stored in batteries, and both the monitoring sensors and ocean environmental devices could be triggered and activated to work for practical applications in real sea states.

This paper proposes a bimorph piezoelectric vibration energy harvester (PVEH) with a flexible 3D meshed-core elastic layer for improving the output power while lowering the resonance frequency. Owing to the high void ratio of the 3D meshed-core structure, the bending stiffness of the cantilever can be lowered. Thus, the deflection of the harvester and the strain in the piezoelectric layer increase. According to vibration tests, the resonance frequency is 15.8% lower and the output power is 68% higher than in the conventional solid-core PVEH. Compared to the solid-core PVEH, the proposed meshed-core PVEH (10 mm × 20 mm × 280 μm) has 1.3 times larger tip deflection and the maximum output power is 24.6 μW under resonance condition at 18.7 Hz and 0.2G acceleration. Hence it can be used as a power supply for low-power-consumption sensor nodes in wireless sensor networks., Graphical Abstract

In this paper, we demonstrate a multi-membranes piezoelectric micromachined ultrasonic transducer (pMUT) device devoted to air-borne pulse-echo measurement with an angular resolution of 18 degrees. The setup includes a one-dimensional pMUT array of 5 bimorph AlN-based membranes working at 113.6 kHz for reception and a single pMUT membrane for emission. Pulse-echo measurement are achieved on an acoustic target located at 40 cm from the device. A beamforming strategy is implemented to achieve spatial filtering of the signal. The angle of the acoustic beam is manually defined and clearly evidenced by signal processing, confirming experimentally the potential of pMUT device for air-borne beamforming-based system.

This paper focuses on the energy generating capacity of polyvinylidene difluoride (PVDF) piezoelectric material through a number of prototype sensors with different geometric and loading characteristics. The effect of sensor configuration, surface area, dielectric thickness, aspect ratio, loading frequency and strain on electrical power output was investigated systematically. Results showed that parallel bimorph sensor was found to be the best energy harvester, with measured capacitance being reasonably acceptable. Power output increased with the increase of sensor’s surface area, loading frequency, and mechanical strain, but decreased with the increase of the sensor thickness. For all scenarios, sensors under flicking loading exhibited higher power output than that under bending. A widely used energy harvesting circuit had been utilized successfully to convert the AC signal to DC, but at the sacrifice of some losses in power output. This study provided a useful insight and experimental validation into the optimization process for an energy harvester based on human movement for future development. Refereed/Peer-reviewed

In order to improve the acoustic radiation capability of piezoelectric ultrasonic transducer in gas, a bimorph rectangular transducer based on type 2-2 piezoelectric composites is proposed in this paper, which is composed of two piezoelectric composite rectangular slices with thickness polarization. First, the bending vibration of the rectangular transducer is divided into two bending vibrations of the thin rods in the x and y directions using the equivalent elastic method. When the mechanical coupling coefficient is introduced and combined with the anisotropic piezoelectric equations, the resonance frequency equations of the thickness-polarized transducer are derived with simply supported boundary conditions. Then the bending vibration of the transducer is numerically simulated. The results show that the resonance frequency obtained by the analytical method is in good agreement with the numerical simulation results. Finally, the influence of geometrical size and two-phase volume ratio on the bending vibration performance of the transducer is analyzed. Compared with the piezoelectric bimorph transducer, the piezoelectric composite bimorph transducer has a larger bending vibration displacement amplitude, a larger transmitting voltage response, a lower resonant frequency and better acoustic radiation capability.

The development of an untethered soft actuator that can perform complex task under external control is highly desirable. In this work, we present an ultrasonically actuated programmable polymorphic soft actuator scheme and demonstrate the untethered polymorphic actuation of the proof-of-concept device. The ultrasonic actuation is enabled through converting the incoming ultrasonic energy to thermal energy by the Joule heating. The temperature increase triggers shrinking of the thermally responsive hydrogel/polymer bimorph. By employing two ultrasonic receivers with different resonant frequencies (frequency coding), we demonstrated 4 different motions of the actuator.

This work presents the sense of touch via non-contact ultrasonic waves by a dual-electrode bimorph piezoelectric micromachined transducer (pMUT) array. The prototype device has 12×12 elements with circular diaphragms of 415μm in radius made of 2 μm-thick AlN. They are fabricated by a CMOS compatible micromachining process resulting a resonant frequency at 109.4 kHz. Experimentally, a best haptic sensation on human fingers is found when emitting high frequency ultrasonic waves to emulate 100 Hz signals by means of pulse width modulation with a 50% duty cycle. Strong haptic sensations are reported by volunteers under an AC peak-to-peak amplitude of 12 V up to 10 cm away from the transducers. Applications as the human-machine interfaces in biomedical, gaming, and AR/VR are a few of the MEMS uses; we present results by transmitting a series of Morse codes remotely to the skins of volunteers.

This paper reports a highly directional air-coupled parametric loudspeaker using a single chip of piezoelectric micromachined ultrasonic transducers (pMUTs). Compared with the state-of-art technologies, three distinctive advancements have been achieved: (1) a micromachined parametric array based on CMOS-compatible bimorph AlN pMUTs; (2) generation of highly directional audible sound with a half power beam width less than 5 degrees; and (3) generation of multiple audible frequency using a single chip with 246 pMUT elements in a footprint of 13mm by 13mm. As such, the proposed AlN pMUT parametric array could open up a new class for low-power portable directional loudspeakers for private communication and so on.

This paper reports an ultrasonic 3D object detector with > 1 meter range based on an AlN piezoelectric micromachined ultrasonic transducers (pMUTs) chip. Compared with the state-of-art technologies, three distinctive advancements have been achieved: (1) more than 1-meter in sensing distance enabled by a bimorph dual electrode pMUT design; (2) small form factor (6×6 mm2) and a more than 135° field of view; (3) capability of real time 3D object detection with up to 125 fps (frames per second) based on the scheme of ultrasound beamforming. As such, this work could open up a new class of miniaturized, low-power, real-time 3D object detections for applications such as drone navigation, machine vision and so on.

This study investigates the resonant and energy harvesting characteristics of a piezoelectric fiber composite bimorph by using theoretical and experimental techniques, including the full-field optical technique, for the purpose of getting a new perspective on the mechanical and electrical energy transformation ability of piezoelectric composites. A laser Doppler vibrometer, impedance analysis, fotonic sensor, and polyvinylidene fluoride sensor are used in the experiments. Furthermore, an full-field optical technique is also used to measure the resonant frequencies and mode shapes of in-plane and out-of-plane vibrations. Finally, the electrical voltage of the piezoelectric fiber composite bimorph with shaker excitation is measured and used for a light-emitting diode. The shaker input voltage, output voltage of the piezoelectric structure, and light intensity are all measured to find out the power generation capacity of piezoelectric composite. The relationship between the energy harvesting ability and excitation methods, the input voltage value, and frequency are obtained through analyses. From the experiment results, it is indicated that the most efficient modes are affected by the excitation method and the location of an excitation point of the shaker. This study helps in understanding the resonant characteristics as well as the energy harvesting capability of piezoelectric composite.

This paper presents the modeling of electrothermally actuated bimorph actuator for out-of-plane actuation application. Al-Si bimorph was optimized for higher displacement applications. Temperature distribution analysis of the Al-Si bimorph combination was chosen due to their larger displacement range. The modeling of Al-Si was performed with FEM and analytical analysis. Temperature distribution across the bimorph actuator with respect to length and applied voltage was optimized using FEM, lumped, and analytical analysis. The maximum temperature across Al-Si bimorph was achieved around 106 °C without convection and 85 °C with convection.

This paper presents the design and analysis of a piezoelectric cantilever beam with tip mass under ambient mechanical vibration energy source. The ambient mechanical vibration energy generates stress and strain in the piezoelectric materials, which is converted into electrical energy by the principle of piezoelectric effect. The generated energy can be used for low power electronic devices. The geometry of the cantilever beam structure was designed by using SolidWorks. The structure consists of a bimorph piezoelectric layer, Aluminium substrate, and a tungsten proof mass. The cantilever beam was simulated using the Finite Element Method (FEM) in COMSOL Multiphysics. During FEM simulation, a vibration source of 1g acceleration was applied on the beam. As a result, the maximum displacement of the beam was obtained 2.4 µm at a resonant frequency of 192.25 Hz. Stress generation on the beam was analyzed because the piezoelectric energy harvesting from vibration depends on stress generation in piezoelectric materials. The maximum amount of stress was found 1.11×105 N/m2 at the clamped end of the beam during resonance. A voltage output of 4.4mV has been obtained from the harvester. The designed beam can be operated in low-frequency ambient vibration sources.

In this paper, we discuss the use and design of a bimorph cantilever shaped energy harvester for pacemaker application. The basis of this approach is to find an alternative way to power pacemakers using novel energy harvesters. Different energy harvester geometries such as the cantilever, triangular and rectangular based harvesters were studied. PZT-5A material was chosen as an active piezoelectric material, it was then designed and simulated on COMSOL Multiphysics package. After simulating various designs, it was found that an energy harvester with dimensions of 21mm width, 0.16 mm thickness and 10mm out of plate dimension. At resonance, it yielded 10.7 Volts and 4.77 mW electrical power for an input of 4.88 mW of mechanical power.

Inspired by bells, a kinetic energy harvester was designed to scavenge energy from ambient vibrations and winds in different directions. It is constructed by supporting a bracket, surrounded by six cantilevered bimorphs, with a spring. Under excitations of base movements and airflows, the bracket vibrates and causes a steel bead in it to roll and to strike the bimorphs, making the bimorphs vibrate and produce electricity. A prototype was tested on an electromagnetic shaker and the experimental results showed that the prototype is good at scavenging two dimensional vibrations, with the minimum total output power of about 0.85 times the maximum value when the vibration direction changes in the horizontal plane. In addition, the prototype was tested in a small wind tunnel and the experiments verified that the device can collect wind energy effectively when a cardboard cover is added onto it. With the increase of the wind speed, it experienced the transverse vibrations, the rotational vibrations and the back-and-forth vibrations, respectively. The output power of one bimorph is about 109.4 μW when wind speed is 10 m/s.

Converting the mechanical energy of human body to electrical energy became promising alternative to ensure power supply of nomadic devices. This approach has great potential innovation and respect for environmental issue and falls under the termed of renewable energy. In this work, the design and simulation of a transducer that can convert the mechanical availed energy due to knee flexion during gait cycle into electrical energy are studied. This transducer consists of bimorph piezoelectric cantilever beam with a tip mass at the end. This beam is designed to be positioned in the back side of knee to transfer the mechanical excitation due the knee flexions. Using Comsol Multiphysics, simulations were performed to expose the output power that can generate since a single transducer and two transducers although phases of walking cycle. In full stride at naturel walking speed of l m/s has a frequency of IHZ (two steps per second) the maximum power that can be stored is 36 mW from a single transducer at 10° angle of knee flexion. This value was observed decrease to 2. 5mW at loading response phase of two transducers. The level of power attained with two transducers is lower than single transducer in each angle of knee flexion. This evaluation of output energy demonstrates that energy harvesting from knee motion during walking can supply autonomous systems.

Kinetic piezoelectric energy harvesters are used to power up ultra-low power devices without batteries as an alternative and eco-friendly source of energy. This paper deals with a novel design of a lead-free multilayer energy harvester based on BaTiO3 ceramics. This material is very brittle and might be cracked in small amplitudes of oscillations. However, the main aim of our development is the design of a crack protective layered architecture that protects an energy harvesting device in very high amplitudes of oscillations. This architecture is described and optimized for chosen geometry and the resulted one degree of freedom coupled electromechanical model is derived. This model could be used in bistable configuration and the model is extended about the nonlinear stiffness produced by auxiliary magnets. The complex bistable vibration energy harvester is simulated to predict operation in a wide range of frequency excitation. It should demonstrate typical operation of designed beam and a stress intensity factor was calculated for layers. The whole system, without presence of cracks, was simulated with an excitation acceleration of amplitude up to 1g. The maximal obtained power was around 2 mW at the frequency around 40 Hz with a maximal tip displacement 7.5 mm. The maximal operating amplitude of this novel design was calculated around 10 mm which is 10-times higher than without protective layers.

A novel feedback control technique for the local oscillation amplitude in an artificial cochlear sensory epithelium that mimics the functions of the outer hair cells in the cochlea is successfully developed and can be implemented with a control time on the order of hundreds of milliseconds. The prototype artificial cochlear sensory epithelium was improved from that developed in our previous study to enable the instantaneous determination of the local resonance position based on the electrical output from a bimorph piezoelectric membrane. The device contains local patterned electrodes deposited with micro electro mechanical system (MEMS) technology that is used to detect the electrical output and oscillate the device by applying local electrical stimuli. The main feature of the present feedback control system is the principle that the resonance position is recognized by simultaneously measuring the local electrical outputs of all of the electrodes and comparing their magnitudes, which drastically reduces the feedback control time. In this way, it takes 0.8 s to control the local oscillation of the device, representing the speed of control with the order of one hundred times relative to that in the previous study using the mechanical automatic stage to scan the oscillation amplitude at each electrode. Furthermore, the intrinsic difficulties in the experiment such as the electrical measurement against the electromagnetic noise, adhesion of materials, and fatigue failure mechanism of the oscillation system are also shown and discussed in detail based on the many scientific aspects. The basic knowledge of the MEMS fabrication and the experimental measurement would provide useful suggestions for future research. The proposed preliminary prototype high-speed feedback control can aid in the future development of fully implantable cochlear implants with a wider dynamic range.

Due to its multidisciplinary nature, the power behavior of a piezoelectric vibration energy harvester depends on system properties in multiple domains such as material, mechanical and electrical. This paper presents a dimensionless maximum power equation that integrates these effects into a simple model, which serves as a convenience tool for the design and analysis of piezoelectric vibration energy harvesters. The model is given as a closed-form relationship between the dimensionless maximum power (maximum power normalized by the power limit) and the normalized electromechanical coupling coefficient with respect to the critical coupling coefficient, which is the minimum coupling to reach the power limit of a system. In addition, this integrated design equation can be applied to different energy harvesting interface circuit types such as resistive and standard AC-DC with a simple change of the critical coupling expression in the equation. The application of this equation is illustrated by a detailed design example of a bimorph beam harvester for fixed target natural frequency and length given a base motion excitation. It is found that under the same level of excitation, there is an optimal PZT thickness for maximum power. In addition, overall, it is beneficial to make the system of low damping to yield a larger structural response and more power. However, this also leads to a higher bending stress, which is an important design consideration due to the relatively brittle nature of PZT materials.

Piezoelectric actuators have achieved remarkable progress in many fields, being able to generate forces or displacements to perform scanning, tuning, manipulating, tactile sensing or delivering functions. In this work, two piezoelectric PZT (lead zirconate titanate) bimorph actuators, with different tip contact materials, were applied as tactile sensors to estimate the modulus of elasticity, or Young&acute, s modulus, of low-stiffness materials. The actuators were chosen to work in resonance, taking advantage of a relatively low resonant frequency of the out-of-plane vibrational modes, associated with a convenient compliance, proven by optical and electrical characterization. Optical measurements performed with a scanning laser vibrometer confirmed that the displacement per applied voltage was around 437 nm/V for the resonator with the lower mass tip. In order to determine the modulus of elasticity of the sensed materials, the stiffness coefficient of the resonator was first calibrated against a force sensor, obtaining a value of 1565 &plusmn, 138 N/m. The actuators were mounted in a positioning stage to allow approximation and contact of the sensor tip with a set of target materials. Electrical measurements were performed using the resonator as part of an oscillator circuit, and the modulus of elasticity of the sample was derived from the contact resonant frequency curve of the cantilever&ndash, sample system. The resulting sensor is an effective, low-cost and non-destructive solution compared to atomic force microscopy (AFM) techniques. Materials with different modulus of elasticity were tested and the results compared to values reported in the literature.

International audience; Experimental and theoretical results on the nonlinear dynamics of a homogeneous thin beam equipped with piezoelectric patches, presenting internal resonances, are provided. Two configurations are considered: a unimorph configuration composed of a beam with a single piezoelectric patch and a bimorph configuration with two collocated piezoelectric patches symmetrically glued on the two faces of the beam. The natural frequencies and mode shapes are measured and compared with those obtained by theoretical developments. Ratios of frequencies highlight the realization of 1:2 and 1:3 internal resonances, for both configurations, depending on the position of the piezoelectric patches on the length of the beam. Focusing on the 1:3 internal resonance, the governing equations are solved via a numerical harmonic balance method to find the periodic solutions of the system under harmonic forcing. A homodyne detection method is used experimentally to extract the harmonics of the measured vibration signals, on both configurations, and exchanges of energy between the modes in the 1:3 internal resonance are observed. A qualitative agreement is obtained with the model.

With the aim of providing the larger frequency band and progress the energy harvesting proficiency of the bistable piezoelectric energy harvester (BPEH), a 2-DOF nonlinear distributed parameter model of BPEH with an elastic magnifier is considered in this paper. This study deals with bimorph beam with functionally graded piezoelectric (FGP) layers carrying concentrated mass at tip while taking into account the geometrical nonlinear terms and the nonlinear magnetic force to enhance energy harvesting performance. By presenting the magnifier, oscillations of the tip are inspired into high-energy orbits. Mathematical model of BPEH with a dynamic magnifier has been developed, then the nonlinear coupled equation of motion derived using Hamilton principle. Initially, frequency response of harvester derived according to harmonic balance method and the adjusted model has been confirmed by parametric studies of earlier lumped parameter model. Analytical results show that the harvesting voltage can be improved with correct selection of design parameters of the magnifier. The proposed 2-DOF harvester system can provide higher output over a wider frequency band and may cause a considerable change in harvester performance. A parametric study is consummated to expose the effects of power law index of FGP on the output voltage and dynamic characteristic.