Bimorph Cantilever Beam Research Articles

Improve efficiency of harvesting random energy by snap-through in a quad-stable harvester

In response to the defects of the bi-stable energy harvester (BEH), we develop a novel quad-stable energy harvester (QEH) to improve the harvesting efficiency. The device is made up of a bimorph cantilever beam having a tip magnet and three external fixed magnets. By introducing the repulsion forces between magnets, the function of potential energy of the QEH is given. It owns four potential wells. It is proved that the quad-stable harvester can cross the barriers and realize snap-through easier. Validation experiments were performed by frequency sweeping and random excitations. Results show that compared to the BEH the frequency bandwidth of snap-through of the novel device is much wider. The QEH can make a dense snap-through in response under random excitation, and give out a large output voltage. This shows that the proposed QEH is more effective in energy harvesting applications.

Energy harvesting in a quad-stable harvester subjected to random excitation

In response to the defects of bi-stable energy harvester (BEH), we develop a novel quad-stable energy harvester (QEH) to improve harvesting efficiency. The device is made up of a bimorph cantilever beam having a tip magnet and three external fixed magnets. By adjusting the positions of the fixed magnets and the distances between the tip magnet and the fixed ones, the quad-stable equilibrium positions can emerge. The potential energy shows that the barriers of the QEH are lower than those of the BEH for the same separation distance. Experiment results reveal that the QEH can realize snap-through easier and make a dense snap-through in response under random excitation. Moreover, its strain and voltage both become large for snap-through between the nonadjacent stable positions. There exists an optimal separation distance for different excitation intensities.

Dynamical Model for an Interharmonic Property of a Piezoelectric Bimorph Cantilever Beam with Self-Sensing Function

A piezoelectric bimorph cantilevered beam is analyzed dynamically by a longitudinal and transverse coupling theory. When a sinusoidal voltage is applied on the actuating layer of the bimorph, the output voltage of the sensing layer appears as interharmonic component signal. The interharmonic frequency is noninteger harmonic frequency of the applied voltage. A dynamic model is proposed to describe the interharmonic property of the piezoelectric bimorph beam. Through some simulations and experiments, the theoretical model is verified effectively to express the nonlinear characteristic. Furthermore, when the piezoelectric bimorph resonance happens, some interharmonic response at low frequency will modulate with the resonance response.

Nonlinear dynamic analyses on a magnetopiezoelastic energy harvester with reversible hysteresis

This paper presents a systematic approach through a series of nonlinear analyses to predict and design the nonlinear resonance characteristics and energy-harvesting performance of a magnetopiezoelastic vibration energy harvester with reversible hysteresis. To this end, a mathematical model of the energy harvester system, composed of a bimorph cantilever beam along with three permanent magnets, is first derived. With this model, frequency response analyses are conducted using the methods of multiple scales and harmonic balance. In the case of weak excitation, the system’s stationary forced response is obtained through multiple-scale analysis (MSA). With this MSA solution, analytical design criteria in terms of the position parameters of the magnets are derived to determine the hysteresis type of the nonlinear resonance (stiffness hardening or stiffness softening). However, in the case of a relatively strong excitation, the high-dimensional harmonic balance analysis (HDHBA) shows that the stiffness-softening effect tends to strengthen for the oscillation amplitude in a specific condition, and this effect can even lead to hysteresis transition or potential well escape. Using the HDHBA, design criteria are set up and evaluated in terms of source vibration strength to detect the hysteresis transition or the condition required to determine the potential well escape. Finally, based on the present systematic analyses, the complicated resonant responses and energy-harvesting performance of the present system are examined with respect to several design parameters, and the results are discussed in detail.

A New Motor of Stick Type with Coupled Mechanical Vibration of Bimorph Beam and Frictional Force

This paper proposes a new non-magnetic motor with a rotor rotated by using the resonance energy of a bimorph cantilever beam excited by electrostatic force. The use of flexible material enables conversion of translational vibration to rotary movement in one direction. Basic characteristics of a prototype motor with two bimorph cantilever beams, such as rotational speed, output torque, and efficiency were determined experimentally. Results show that a maximum rotational speed of 2800 rpm was obtained without a load torque. It is also observed that this motor produces the output torque of 98 μNm when the rotational speed was 980 rpm. The maximum efficiency was 24% when the input power was 0.065 W.

Performance Analysis of Wind-Induced Piezoelectric Vibration Bimorph Cantilever for Rotating Machinery

Harvesting the energy contained in the running environment of rotating machinery would be a good way to supplement energy to the wireless sensor. In this paper, we take piezoelectric bimorph cantilever beam with parallel connection mode as energy collector and analyze the factors which can influence the generation performance. First, a modal response theory model is built. Second, the static analysis, modal analysis, and piezoelectric harmonic response analysis of the wind-induced piezoelectric bimorph cantilever beam are given in detail. Finally, an experiment is also conducted. The results show that wind-induced piezoelectric bimorph cantilever beam has low resonant frequency and stable output under the first modal mode and can achieve the maximum output voltage under the resonant condition. The output voltage increases with the increase of the length and width of wind-induced piezoelectric bimorph cantilever beam, but the latter increasing amplitude is relatively smaller. In addition, the output voltage decreases with the increase of the thickness and the ratio of metal substrate to piezoelectric patches thickness. The experiment showed that the voltage amplitude generated by the piezoelectric bimorph cantilever beam can reach the value simulated in ANSYS, which is suitable for actual working conditions.

A multi-stable energy harvester: Dynamic modeling and bifurcation analysis

A theoretical investigation is conducted on the dynamic and energetic characteristics of a multi-stable bimorph cantilever energy harvester that uses magnetic attraction effect. The multi-stable energy harvester under study is composed of a bimorph cantilever beam with soft magnetic tip and two externally fixed permanent magnets that are arranged in series. With this configuration, the magnetic force and the moment that are exerted on the cantilever tip tend to be highly dependent on the magnetic field induced by the external magnets. Such an energy harvester can possess multi-stable potential functions, ranging from mono-stable to penta-stable. The mechanism that governs the formation of this multi-stability is thoroughly identified and examined thorough a bifurcation analysis performed on the system׳s equilibrium solutions. From this analysis, it is found that the transitions between these multi-stable states occur through very complicated bifurcation scenarios that include degenerate pitchfork bifurcations and mergers of pitchfork bifurcations or saddle-node bifurcations. Bifurcation set diagram is obtained, which is composed of five separate parametric regions, from mono- to penta-stability. The resulting stability map satisfactorily describes the multi-stable characteristics of the present energy harvester. In addition, the dynamic and energetic characteristics of the present multi-stable energy harvester are more thoroughly examined using its potential energy diagrams and a series of numerical simulations, and the obtained results are compared with those for the equivalent bi-stable cases.

Investigation of Piezoelectric Energy Harvesting at Elevated Temperatures

Due to their capability to convert mechanical energy directly to electrical energy, piezoelectric energy harvesters have become a new powering choice for many electronic devices. This work demonstrates piezoelectric energy harvester systems operating in environments ranging from room temperature up to 82°C and compares their performance using different piezoelectric materials. The systems are structured with a PMN-PT (lead magnesium niobate-lead titanate) single crystal patch bonded to an aluminum cantilever beam, PIN-PMN-PT (lead indium niobate-lead magnesium niobate-lead titanate) single crystal patch bonded to an aluminum cantilever beam and a bimorph cantilever beam which is made by lead zirconate titanate (PZT). The results show that temperature has affected the output power of the energy harvesting system in a complex way and shifted the resonance frequency to a lower value. The results provide an invaluable reference for energy harvesting in harsh environments.

Modeling and experimental investigation of an impact-driven piezoelectric energy harvester from human motion

An impact-driven piezoelectric energy harvester from human motion is proposed in this paper. A high-frequency PZT-5A bimorph cantilever beam with attached proof mass at the free end was selected. A frequency up-conversion strategy was realized using impulse force generated by human motion. An aluminum prototype was attached to the leg of a person on a treadmill and measurements taken of the dissipated electric energy across multiple resistances over a range of walking speeds. The outer dimensions of this prototype are 90 mm × 40 mm × 24 mm. It has been shown that the average output voltage generated by the piezoelectric bimorph increases sequentially with a faster walking speed, the power varies with the external resistances and maximum levels occur at the optimal resistance, which is consistent with the simulation result. An open circuit voltage of 2.47 V and maximum average power of 51 μW can be achieved across a 20 kΩ external load resistance and 5 km h−1 walking speed. Experimental results reveal that the impact-driven piezoelectric energy harvesting system mounted on a person’s leg has the potential for driving wearable devices.

Nonlinear stochastic controllers for power-flow-constrained vibratory energy harvesters

This study addresses the formulation of nonlinear feedback controllers for stochastically excited vibratory energy harvesters. Maximizing the average power generated from such systems requires the transducer current to be regulated using a bi-directional power electronic converter. There are many applications where the implementation of these types of converters is infeasible, due to the higher parasitic losses they must sustain. If instead the transducer current is regulated using a converter capable of single-directional power-flow, then these parasitic losses can be reduced significantly. However, the constraint on the power-flow directionality restricts the domain of feasible feedback laws. The only feasible linear feedback law imposes a static relationship between current and voltage, i.e., a static admittance. In stochastic response, the power generation performance can be enhanced significantly beyond that of the optimal static admittance, using nonlinear feedback. In this paper, a general approach to nonlinear control synthesis for power-flow-constrained energy harvesters is presented, which is analytically guaranteed to outperform the optimal static admittance in stationary stochastic response. Simulation results are presented for a single-degree-of-freedom resonant oscillator with an electromagnetic transducer, as well as for a piezoelectric bimorph cantilever beam.

Highly Reliable MEMS Temperature Sensors for 275 $^{ \circ}\hbox{C}$ Applications—Part 2: Creep and Cycling Performance

The second part of this paper presents an experimental reliability assessment of microelectromechanical-system bimorph cantilever beams for high-temperature sensing applications. The sensor, presented in Part I, is shown to operate up to 275 °C and to have a quality factor of over 5000 at room temperature, a response time of under 600 μ s, and an inherent capacitance uncertainty of under 0.13 fF. In this part, the reliability of the bimorph component of the sensor is tested at sustained high temperatures (up to 275 °C), as well as throughout thermal cycling. The cantilevers are initially thermally annealed to relax the film stresses. During the anneal of the device, there is a decrease in room-temperature tip displacement from 120 to 70 μm and a decrease in the high-temperature tip displacement from 40 to 10 μm. After the thermal anneal, the devices show less than 3 μm of further creep after three months (over 2000 h) at 200 °C and over 120 h at 275 °C. Over 20 samples have been successfully tested up to 100 million cycles without failure. Record results are demonstrated to over 1.2 billion thermal cycles from fully relaxed to fully deflected states. Consisting of over 1000 beam profile measurements and dozens of individual fabricated chips, this represents one of the largest reliability studies of bimorphs to date.

Modeling and Analysis of Piezoelectric Bimorph Cantilever for Vibration Energy Harvesting

The vibration energy can be converted to electrical energy directly and efficiently using piezoelectric cantilever beam based on piezoelectric effect. Since its structure is simple and its working process is unpoisonous to the environment, the piezoelectric cantilever beam can be used in various fields comprehensively. The present paper perform an analysis on the vibration energy harvesting problem of piezoelectric bimorph cantilever beam. The piezoelectric cantilever model has been formulated using the theory of elasticity mechanics and piezoelectric theory. A prototype of piezoelectric power generator is set up to do vibration test, and the electromechanical coupling FEA model under vibration load is built to simulate its output displacement, stress and voltage. The present numerical results of piezoelectric bimorph cantilever coincide well with our related experimental results, which shows the validity of the present FEA model and the relate results.

A retrofitted energy harvester for low frequency vibrations

Piezoelectric-based energy harvesting is an efficient way to convert ambient vibration energy into usable electric energy. However, its output power drops steeply with reducing excitation frequency. To improve the harvesting performance at low frequencies, a multi-impact harvester is proposed in this paper. The proposed design consists of a hung mass and two stiff piezoelectric cantilever beams. A series of impacts between the mass and cantilever beams are involved during the vibration of the mass, which triggers high frequency vibrations on the cantilever beams. Four equations of motion corresponding to different system statuses are presented to simulate the vibration of the harvester. Based on the linear piezoelectric theory, a distributed-parameter electromechanical model is used for the bimorph cantilever beam and its output power is calculated. For comparison, a conventional cantilever-beam-based harvester and a single-impact harvester are introduced and their output powers are also calculated. Under the same sinusoidal excitation, the modeling result shows that the power of the proposed harvester is more than three times larger than the ones from the conventional cantilever beam harvester and the single-impact harvester. The multi-impact harvester also occupies less space than the conventional one. A parametric study is presented in this paper for the multi-impact harvester considering different external resistances, hung masses, cantilever beam thicknesses and excitation frequencies.

Implementation of a user defined piezoelectric shell element for analysis of active structures

This paper presents the results of the structural behavior analysis, which was performed using a special type of the user defined finite element incorporated within commercial finite element software. As a basis for the user element implementation, a Mindlin-type nine-node shell element is used, which was developed for the application with piezoelectric materials and composite structures. For the element implementation purposes the FORTRAN user subroutine was developed and incorporated within the ABAQUS finite element software. The analysis is conducted through several examples regarding the piezoelectric bimorph cantilever beam. Results of the analysis document a very good agreement between the user element and analytical and other standard results, confirming thus a successful implementation of the developed user element subroutine. Furthermore, the analysis was extended to show the robustness of the user element to mesh distortion.

Optimization of partial-state feedback for vibratory energy harvesters subjected tobroadband stochastic disturbances

In many applications of vibratory energy harvesting, the external disturbance is mostappropriately modeled as a broadband stochastic process. Optimization of the averagepower generated from such disturbances is a feedback control problem, and solvable viaLQG (linear–quadratic–Gaussian) control theory. Implementing the optimal feedbackcontroller requires a power electronic drive capable of two-way power flow, which canimpose dynamic relationships between the voltage and current of the transducer.Determining the optimal energy harvesting current control is accomplished by solving anonstandard Riccati equation. In this paper we show that appropriate tuning of thepassive parameters in the harvesting system results in a decoupled solution to theRiccati equation and a corresponding controller that only requires half of the statesfor feedback. However, even when such tuning methods are not used and thesolution to the Riccati equation does not decouple, it is possible to determinethe states in the feedback law that contribute the most to the average powergenerated by the harvester. As such, partial-state feedback gains can be optimizedusing a gradient descent method. Two energy harvesting examples are presented,including a single-degree-of-freedom oscillator with an electromagnetic actuatorand a piezoelectric bimorph cantilever beam, to demonstrate these concepts.

Modeling and Analysis of a Piezoelectric Energy Scavenger for Rotary Motion Applications

This paper presents modeling and analysis of a piezoelectric mounted rotary flexible beam that can be used as an energy scavenger for rotary motion applications. The energy harvester system consists of a piezoelectric bimorph cantilever beam with a tip mass mounted on a rotating hub. Assuming Euler–Bernoulli beam equations and considering the effect of a piezoelectric transducer, equations of motion are derived using the Lagrangian approach followed by relationships describing the harvested power. The equations provide a quantitative description of how the hub acceleration and gravity due to the tip mass contribute power to the energy harvester. In particular, expressions describing optimum load resistance and the maximum power that can be harvested using the proposed system are derived. Numerical simulations are performed to show the performance of the harvester by obtaining tip velocities and electrical output voltages for a range of electrical load resistances and rotational speeds. It is shown that by proper sizing and parameter selection, the proposed system can supply enough energy for operating wireless sensors in rotating mechanisms such as tires and turbines.

Improving the performance of a piezoelectric energy harvester using a variable thicknessbeam

In recent years, researchers have shown a growing interest in the possibility of harvestingmechanical energy from vibrating structures. A common way to proceed consists ofusing the direct piezoelectric effect of a bimorph cantilever beam with integratedpiezoelectric elements. Several studies focused on the development of analytical modelsdescribing the electromechanical coupling. Historically, most of these models havebeen limited to simple structures such as a constant cross-section cantilever beamharvester. This paper studies the effect of a variable thickness beam harvester on itselectromechanical performance. A semi-analytical mechanical model was developed usingRayleigh–Ritz approximations with a trigonometric functions set. The model was nextvalidated by a finite element (FE) modeling. Numerical simulations were thenperformed for different beam slope angles in order to find the optimum for a givenmaximal strain across the piezoelectric elements. For the case under study, it isshown that tapered beams lead to a more uniform strain distribution across thepiezoelectric material and increase the harvesting performance by a factor of 3.6.

Design and simulation of a thermally actuated MEMS switch for microwave circuits

The design, modeling, and optimization of a novel, thermally actuated CMOS-MEMS switch are presented in this article. This series capacitive MEMS switch solves the substrate loss and down-state capacitance degradation problems commonly plaguing MEMS switches. The switch uses finger structure for capacitive coupling. The vertical bending characteristic of bimorph cantilever beams under different temperatures is utilized to turn the switch on and off. A set of electrical, mechanical, and thermal models is established, and cross-domain electro-thermo-mechanical simulations are performed to optimize the design parameters of the switch. The fabrication of the switch is completely CMOS-process compatible. The design is fabricated using the AMI 0.6 μm CMOS process and a maskless reactive-ion etching process. The measured results show the insertion loss and isolation are 1.67 and 33 dB, respectively, at 5.4 GHz, and 0.36 and 23 dB at 10 GHz. The actuation voltage is 25 V and the power consumption is 480 mW. This switch has a vast number of applications in the RF/microwave field, such as configurable voltage control oscillators, filters, and configurable matching networks. © 2009 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.

An optimal stochastic control theory for distributed energy harvesting networks

A new approach, based on H 2 optimal control theory, is presented for the design of feedback controllers for energy harvesting systems for maximal power generation. The theory applies to stochastically excited vibratory systems in broadband stationary response, and allows for harvested power to be explicitly optimized. It is applicable to both single-transducer systems as well as coupled networks of many transducers. The theory accounts for the influence of energy harvesting on the dynamics of the structure to which the transducers are attached. It also accounts for resistive and semiconductor dissipation in the power-electronic network interfacing the transducers with energy storage. Due to its predominance in the literature, a piezoelectric bimorph cantilever beam is used as the context for the theory, and simulation examples are used to illustrate various aspects of the optimal controllers.

Nanoparticle-embedded actuator based on localized surface plasmon resonance

The bimorph cantilever beams of high photothermal efficiency based on LSPR (localized surface plasmon resonance) of silver–NPs (silver–nanoparticles) were demonstrated. The silver–NPs converted absorbed optical energy of 14% into heat at maximum of 530 nm. The beams had a length of 350 µm, a width of 40 µm and the total thickness of 770 nm. They were composed of 400 nm thick PVP (poly(vinylpyrrolidone)) embedded with silver–NPs and 370 nm thick silicon nitride. The beams bent up vertically by a deflection of 30 µm under an optical intensity of 500 W cm−2 using a green laser. The corresponding mechanical and thermal response times were 0.25 ms and 10 ms, respectively.