Bimorph Cantilever Beam Research Articles

Performance analysis of nonlinear piezoelectric energy harvesting system under bidirectional excitations

In this paper, a cantilever beam piezoelectric energy harvester model of nonlinear partial differential equation based on Hamilton's Principle is established. A piezoelectric device using a bimorph cantilever beam with a fixed is subjected to horizontal and vertical excitation. Based on the Euler-Bernoulli thin beam model assumptions and inextensible deformation, the analysis further includes the effects of geometric nonlinearity and damping nonlinearity. The reduced-order nonlinear partial differential equations of motion with electro-mechanical coupling distributed parameter are derived by using Galerkin method. By using the method of multiple scales and solving the equations of motion, the energy harvester in its fundamental first-order resonance response is analyzed and the amplitudes of fundamental transverse deflection, output voltage and output power are determined. The major influence aspects of excitation amplitude, linear damping coefficient, nonlinear damping coefficient, impedance, nonlinear electro-mechanical coupling coefficient on transverse deflection, voltage and power are analyzed. The result shows that the linear damping coefficient and resistance affect the initial threshold of parametric excitation. The combination of parametric excitation and direct excitation gives full play to the advantages of parametric excitation and improve the energy conversion efficiency of the energy harvesting system.

Uniform Stress Distribution of Bimorph by Arc Mechanical Stopper for Maximum Piezoelectric Vibration Energy Harvesting

To convert as much vibration energy as possible into electrical energy, the design of a high-performance piezoelectric vibration energy harvester (PVEH) has been studied widely in recent years. To overcome the low energy utilization of a traditional piezoelectric cantilever by inhomogeneous strain, a uniform stress distribution of bimorph by an ARC mechanical stopper structure has been designed for maximum piezoelectric vibration energy harvesting. Deflection equations and their simulation at the first-order modal of two classic bimorph cantilever beam models, with transverse tip force and with equal curvature, are derived based on the Euler–Bernoulli beam assumption. Piezoelectric energy from a beam model with equal curvature is four times that of a cantilever beam model with transverse tip force at the theoretical level. The nonlinear frequency response performance of bimorphs by an ARC mechanical stopper and point stopper model could be observed by the numerical simulations of the lumped parameter electromechanical model. PVEH prototypes were manufactured by 3D printing and tested. To verify the high-power generation capacity, PVEH with an ARC stopper has 1.756 times more voltage than that of a PVEH with a point stopper.

Investigating the performance of tri-stable magneto-piezoelastic absorber in simultaneous energy harvesting and vibration isolation

Tri-stable magneto-piezoelastic oscillators exhibit superior performance in terms of broadband resonance frequency and lower excitation threshold, compared to linear and bi-stable systems. Furthermore, inclusion of magnets renders them applicable, tunable, and simple designs. However, the potential of this oscillators for the purpose of simultaneous vibration suppression and energy harvesting has not been investigated. This study aims to investigate simultaneous energy harvesting and vibration isolation through a tri-stable magneto-piezoelastic absorber (TMPA). The absorber comprises a bimorph cantilever beam carrying a magnetic tip mass and two external magnets. The interplay between magnets generates a nonlinear restoring force in the TMPA structure. This absorber is attached to a host vibrating beam, which is under a transient or periodic forcing, in order to reduce its vibrations and harvest electrical energy. The nonlinear magneto-electromechanical equations governing the coupled system are obtained by employing the Hamilton's principle, Euler-Bernoulli beam theory, and a recently proposed magnetic force relationship. First, the mechanisms of tri-stability formation are investigated via bifurcation diagrams. Next the potency of the TMPA in the transient excitation scenario is examined. Furthermore, the performance of the TMPA in the presence of the periodic excitation with different forcing levels is investigated. Specifically, frequency and time domain analyses are carried out to characterize the response of the system and efficiency of the absorber when TMPA performs periodic in-well, aperiodic inter-well and periodic inter-well oscillations. In addition, to provide a better insight regarding the TMPA performance, the kinetic energies, harvested power, and dissipated power for the region of strongly modulated response are also studied. Moreover, the efficacy of the TMPA in periodic snap-through oscillations is examined by the means of the harmonic balance method in conjunction with pseudo-arclength continuation scheme. Finally, the results disclosed that the proposed tri-stable absorber outperforms a linear absorber in vibration annihilation and energy harvesting.

Analysis of Circular Disc and Bimorph Cantilever Beam Energy Harvesters Under Various Constraint Conditions

Analysis of Circular Disc and Bimorph Cantilever Beam Energy Harvesters Under Various Constraint Conditions

Exploiting bi-stable magneto-piezoelastic absorber for simultaneous energy harvesting and vibration mitigation

This paper investigates efficient simultaneous energy harvesting and vibration suppression utilizing a tunable bi-stable magneto-pieozelastic absorber (BMPA). The absorber comprises a bimorph cantilever beam exposed to a magnetic field. Furthermore, it is attached to a primary simply supported beam which is under an external excitation. The nonlinear magneto-electromechanical equations governing the coupled continuous system are derived utilizing the Hamilton's principle. First, the nonlinear magnetic force and its bifurcations are explored. Next, using numerical approaches, the efficacy of the absorber under a transient excitation from energy harnessing and vibration annihilation viewpoints is assessed. Furthermore, the efficiency of the BMPA in a steady-state harmonic excitation is investigated, both in time and frequency domains. Bifurcation diagrams disclosed that, based on magnets gap, the absorber performs periodic in-well low-amplitude oscillations, chaotic inter-well large-amplitude vibrations, or periodic high-amplitude motions. However, it is observed that in inter-well oscillations, chaotic strongly modulated response occurs and efficiency of the BMPA in vibration mitigation and energy harvesting markedly improves, compared to a linear absorber. Moreover, perfection rate examinations disclosed that when vibration suppression and energy harvesting are of the same importance, the bistable PZT absorber performance is 46.5% better than the corresponding linear absorber. Furthermore, when energy harvesting has priority, the BMPA performance is 158% higher than the linear absorber. Finally, harmonic balance method along with pseudo-arclength scheme are exploited to investigate the efficacy in large-amplitude inter-well scenario. It is illustrated that the system solutions are nonlinear and experience various cyclic fold and Hopf bifurcations. Further, the frequency response curves revealed that the BMPA decreases the host structure vibrations. Moreover, in this scenario, a considerable level of voltage is generated over a wide frequency range.

Performance analysis of bimorph cantilever beam using piezoelectric materials and MEMS technology

This research paper is an attempt to present an insight into the use of micro electromechanical systems (MEMS) technology harvesting of green energy. One of the common examples of MEMS technology is by utilizing bimorph cantilever beams. Subsequently, it has also been discussed that Bimorph cantilever beam based sensors with high sensing ability could be used for harvesting energy from the physical environment. In this paper, we concentrate on the comparative analysis of the MEMS and piezoelectric materials which are used to design bimorph cantilever beams and convert mechanical energy into electrical energy. Detailed performance analysis of bimorph cantilever beams made of different materials has been carried out through various simulation models. Design and the simulation of bimorph cantilever beam is performed using Comsol multiphysics 5.2. state of art software. Comparative analysis of Lead zirconate (PZT-4D) and Lead zirconate (PZT-7A) has been done in this research to find more suitable material for fabrication of bimorph cantilever beams. PZT-7A is found to provide better electrical output for various analysis performed.

Analytical evaluation and experimental validation of energy harvesting using low-frequency band of piezoelectric bimorph actuator

The present article reports the feasibility of the electrical energy generation from ambient low-frequency vibration using a piezoelectric material mounted on a bimorph cantilever beam actuator. A corresponding higher-order analytical model is developed using MATLAB in conjunction with finite element method under low-frequency with both damped and undamped conditions. An alternate model is also developed to check the material and dimensional viability of both piezoelectric materials (mainly focussed to PVDF and PZT) and the base material. Also, Genetic Algorithm is implemented to find the optimum dimensions which can produce the higher values of voltage at low-frequency frequencies (≤ 100 Hz). The delamination constraints are employed to avoid inter-laminar stresses and to increase the fracture toughness. The delamination has been done using a Teflon sheet sandwiched in between base plates and the piezo material is stuck to the base plate using adhesives. The analytical model is tested for both homogenous and isotropic material characteristics of the base material and extended to investigate the effect of the different geometrical parameters (base plate dimensions, piezo layer dimensions and placement, delamination thickness and placement, excitation frequency) on the model responses of the bimorph cantilever beam. It has been observed that when the base material characteristics are homogenous, the efficiency of the model remains higher when compared to the condition when it is of isotropic material. The necessary convergence behaviour of the current numerical model has been established and checked for the accuracy by comparing with available published results. Finally, using the results obtained from the model, a prototype is fabricated for the experimental validation via a suitable circuit considering Glass fibre and Aluminium as the bimorph material.

Design of a Unique Unimorph and Bimorph Cantilever Energy Harvesting System

Piezoelectric energy conversion has received considerable attention for vibration-to-electric energy conversion over the past decade. A typical piezoelectric energy harvester is a unimorph or a bimorph cantilever located on a vibrating host structure. This paper presents a comparison between unimorph and bimorph cantilever beam having a number of segmented PMN-PT piezo-elements on the input and output power. The numerical simulation was carried out by applying the finite element analysis (FEA) using COMSOL multi-physics software in order to predict output voltage and power over a frequency range of 60–200 Hz for the first resonant frequencies. The simulation results show maximum output voltage and power harvested of 7.38 V and 135.73 μW, respectively, by the unimorph piezoelectric energy harvester at resonant frequency value of 84 Hz with electromechanical coupling factor (ke) of 77.29%. These results highlight that the highest value of the output electrical power can be obtained when the piezoelectric element is attached on the top of a clamped end of a cantilever piezoelectric beam. Moreover, in an unimorph or bimorph cantilever beam system, increasing the number of piezoelectric elements results in a higher resonant frequency shift and significantly decreasing in the harvested power.

Modeling and analysis of dynamic structure with macro fiber composite for energy harvesting

In this investigation the modeling and analysis of dynamic structured Macro-Fiber Composite (MFC) for ambient power has been composed to unimorph and bimorph cantilever beam. The dimensions of the beam and its properties were investigated in order to tip displacement across its length with active and inactive piezoelectric layers of MFC. To optimize structure of a cantilever beam with respect to natural frequency, more effective vibration control that can be achieved with minimum control input. The results show that the dynamic model of the cantilever beam is validated with comparisons of experimental, theoretical data and analytical investigation by using ANSYS Simulation.

Particle swarm approach to the optimisation of trenched cantilever‐based MEMS piezoelectric energy harvesters

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.

Topology Optimization of the Thickness Profile of Bimorph Piezoelectric Energy Harvesting Devices

Due to developments in additive manufacturing, the production of piezoelectric materials with complex geometries is becoming viable and enabling the manufacturing of thicker harvesters. Therefore, in this study a piezoelectric harvesting device is modelled as a bimorph cantilever beam with a series connection and an intermediate metallic substrate using the plain strain hypothesis. On the other hand, the thickness of the harvester’s piezoelectric material is structurally optimized using a discrete topology optimization method. Moreover, different optimization parameters are varied to investigate the algorithm’s convergence. The results of the optimization are presented and analyzed to examine the influence of the harvester's geometry and its different substrate materials on the harvester’s energy conversion efficiency.

A Self-Powered Engine Health Monitoring System Based on L-Shaped Wideband Piezoelectric Energy Harvester.

Engine health monitoring is very important to maintain the life of engines, and the power supply to sensor nodes is a key issue that needs to be solved. The piezoelectric vibration energy harvester has attracted much attention due to its obvious advantages in configuration, electromechanical conversion efficiency, and output power. However, the narrow bandwidth has restricted its practical application. A self-powered engine health monitoring system was proposed in this paper, and an L-shaped wideband piezoelectric energy harvester was designed and implemented. The L-shaped beam-mass structure and the piezoelectric bimorph cantilever beam structure was combined to form the wideband piezoelectric energy harvester configuration, which realized effective output at both resonance points. The theoretical model and finite element simulation analysis of the wideband piezoelectric energy harvester were proposed and the parameters were optimized based on that to meet the requirement of the vibration frequency of the engine. The experimental results show that the proposed energy harvester can be applied into the automobile engine health monitoring system. Engine signal analysis results also demonstrate that the proposed system can be used for engine health monitoring.

A novel composite multi-layer piezoelectric energy harvester

A typical linear piezoelectric energy harvester (PEH) is represented by a unimorph or bimorph cantilever beam. To improve the efficiency of linear PEHs, classical strategies involve the increase of the beam length, tapering or adding additional cantilever beams to the free end. In this work we discuss the design of novel type of composite linear multi-layer piezoelectric energy harvester (MPEH). MPEHs here consist of carbon fibre laminates used as conducting layers, and glass fibre laminas as insulating components. We develop first a electromechanical model of the MPEH with parallel connection of PZT layers based on Euler-Bernoulli beam theory. The voltage and beam motion equations are obtained for harmonic excitations at arbitrary frequencies, and the coupling effect can be obtained from the response of the system. A direct comparison between MPEH and PEH configurations is performed both from the simulation (analytical and numerical) and experimental point of views. The experiments agree well with the model developed, and show that a MPEH configuration with the same flexural stiffness of a PEH can generate up to 1.98–2.5 times higher voltage output than a typical piezoelectric energy harvester with the same load resistance.

Optimisation of hybrid energy harvesting using finite element method based on vibration excitation

The main objective of this paper is to optimise energy harvesting design of piezoelectric and magnetic based on vibration excitation; an alternate method for predicting the power output of a bimorph cantilever beam using finite element method with harmonic analysis solver. Both power output generated from the electromagnetic and the piezoelectric were combined to form one unit of energy. In addition, the optimum model was analysed using parametric optimisation analysis solver in finite element analysis to produce an optimum power output. The result showed a maximum power output of 56.66 μW from 47.94 Hz, 4.905 m/s2, and 0.18 cm3 generated for resonance frequency with acceleration and volume. The decreasing size of the harvester with a low natural frequency produces a high-power output.

Finite Element Study on Performance of Piezoelectric Bimorph Cantilevers Using Porous/Ceramic 0–3 Polymer Composites

Finite element analysis of 0–3 composites made of piezoceramic particles and pores embedded in polyvinylidene difluoride (PVDF) has been carried out. The representative volume element (RVE) approach was used to calculate the effective elastic and piezoelectric properties of the periodic isotropic 0–3 piezoelectric composites. It was observed that the elastic and piezoelectric properties increased with the volume fraction of \({\hbox{K}}_{0.475} {\hbox{Na}}_{0.475} {\hbox{Li}}_{0.05} \left( {{\hbox{Nb}}_{0.92} {\hbox{Ta}}_{0.05} {\hbox{Sb}}_{0.03} } \right){\hbox{O}}_{3}\) (KNLNTS) particles but decreased for the porous composites. These effective properties were further used to analyze the potential use of such bimorph cantilever beams in sensing and energy harvesting applications. Sensing voltage continuously increased for KNLNTS filled composites while for porous materials it increased up to 15% volume fraction porosity and then decreased. The same trend was also observed for the power produced by the harvester. However, the sensing voltage and power produced by harvesters made of porous composites were lower than for harvesters made of pure PVDF.

Motor Using Mechanical Vibration of Multiple Bimorph Beams

The present paper proposes a non-magnetic motor with a rotor rotated by the mechanical resonance energy of four bimorph cantilever beams excited by an electrostatic force. The use of a flexible material such as silicon rubber enables conversion of translational vibration to rotary movement in one direction. The rotational speed of the proposed motor increases in proportion to the input voltage when two bimorph beams are used, and the maximum rotational speed was found to be 6,804 rpm when the input voltage was set to 24.6 V. Next, the basic characteristics of a prototype motor with four bimorph cantilever beams, including rotational speed, output torque, and efficiency, were determined experimentally. The experimental results revealed that a maximum rotational speed of 6,370 rpm was obtained when the output torque was 19.6 uNm. The proposed motor was also observed to produce an output torque of 63.7 uNm when the rotational speed was 1,491 rpm. The maximum efficiency was 6.2% when the input power was 0.3 W. For the proposed motor, the volume and weight were reduced by approximately 35%, as compared with a motor from a previous study.

A Preliminary Study on the IoT-Based Pavement Monitoring Platform Based on the Piezoelectric-Cantilever-Beam Powered Sensor

Green and sustainable power supply for sensors in pavement monitoring system has attracted attentions of civil engineers recently. In this paper, the piezoelectric energy harvesting technology is used to provide the power for the acceleration sensor and Radio Frequency (RF) communication. The developed piezoelectric bimorph cantilever beam is used for collecting the vibrational energy. The energy collection circuit is used to charge the battery, where the power can achieve 1.68 mW and can meet the power need of acceleration sensor for data collection and transmission in one operation cycle, that is, 32.8 seconds. Based on the piezoelectric-cantilever-beam powered sensor, the preliminary study on the IoT-based pavement monitoring platform is suggested, which provides a new applicable approach for civil infrastructure health monitoring.

A broadband quad-stable energy harvester and its advantages over bi-stable harvester: Simulation and experiment verification

This paper presents a novel quad-stable energy harvester (QEH) to harvest vibration energy. The QEH is composed of a piezoelectric bimorph cantilever beam with a tip magnet and three external fixed magnets. The potential energy of the QEH is derived, which has four potential wells and three low barriers. This implies that the QEH needs relatively lower excitation energy to cross the barriers than the bi-stable energy harvester (BEH). Simulations are carried out for the BEH and QEH at different levels of excitations. Results show that the QEH owns a smaller threshold and a wider range of frequencies for occurrence of snap-through than the BEH. Thus the QEH can give out a large output voltage. Corresponding experiments were performed for validation. The experimental results are in agreement with the simulations, which means that the QEH can improve the harvesting efficiency considerably.

Numerical modeling of shape and topology optimisation of a piezoelectric cantilever beam in an energy-harvesting sensor

Piezoelectric materials are excellent transducers for converting mechanical energy from the environment for use as electrical energy. The conversion of mechanical energy to electrical energy is a key component in the development of self-powered devices, especially enabling technology for wireless sensor networks. This paper proposes an alternative method for predicting the power output of a bimorph cantilever beam using a finite-element method for both static and dynamic frequency analyses. A novel approach is presented for optimising the cantilever beam, by which the power density is maximised and the structural volume is minimised simultaneously. A two-stage optimisation is performed, i.e., a shape optimisation and then a topology hole opening optimisation.

Thermal Management Using MEMS Bimorph Cantilever Beams

This paper examines a passive cooling technique using microelectromechanical systems (MEMS) for localized thermal management of electronic devices. The prototype was designed using analytic equations, simulated using finite element methods (FEM), and fabricated using the commercial PolyMUMPs™ process. The system consisted of an electronic device simulator (EDS) and MEMS bimorph cantilever beams (MBCB) array with beams lengths of 200, 250, and 300 μm that were tested to characterize deflection and thermal behavior. The specific beam lengths were chosen to actuate in response to heating associated with the EDS (i.e. the longest beams actuated first corresponding to the hottest portion of the EDS). The results show that the beams deflected as designed when thermally actuated and effectively transferred heat away via thermal conduction. The temperature when the beams reached “net-zero” deflection (i.e. uncurled and flat) was related to the initial deflection distance while the contact deflection temperature and rate of actuation was related to beam length. Initial beam deflections, after release, and contact temperatures, when fully actuated, were approximately 5.05, 9.45, 14.05 μm, and 231, 222, 216 °C, respectively with the longer beams making contact first. This innovative passive thermal management system enables selective device cooling without requiring active control or forced convection to maintain steady-state operating temperatures for sensitive microelectronic devices.