Bimorph Beam Research Articles

A two-way shape memory alloy-piezoelectric bimorph for thermal energy harvesting

We present an analytical model to analyze the bending of a bimorph beam comprising of piezoelectric material (PM) and shape memory alloy (SMA) thin layers. The model starts from the governing equations of the bending beam based on the Euler-Bernoulli beam theory. The PM and SMA layers are supposed to be perfectly bonded. The linear constitutive equations of PMs are used. Using this approach, we investigate thermal energy conversion into electricity by mean of the SMA-PM bimorph. Particularly, the model takes into account cyclic thermal energy harvesting by coupling the direct piezoelectric effect and the two-way shape memory effect. In this case, the SMA is assumed to be trained prior to assembling the bimorph so that it can deform in a cyclic way upon cyclic thermal loading without applying any external stress. The thermal-to-electrical conversion is achieved from the induced strain within the SMA layer upon heating which induces stress into the PM layer so that it produces an electrical potential.

Electromechanical bending behavior study of soft photocurable ionogel actuator using a new finite element method

The photocurable ionogel actuator (PIA) is one of the most promising driving mechanisms for the future due to its extraordinary features such as its light weight, flexibility, low-energy consumption and ability to work in open air. However, before the benefits of PIA can be effectively exploited for applications, a mathematical model is required to enhance the understanding of the parameters influencing the actuator electromechanical bending behavior. In this work, a model based on the finite element method (FEM) for the electromechanical bending behavior of PIA is established. It is assumed that the PIA consists of one ionogel layer and two activated carbon electrode layers. With reference to its operational principles, an analogy is drawn between thermal strain and induced strain in the PIA due to the volume change of the activated carbon electrode layer, which is a coupled structural/thermal model and can be solved by FEM. The distribution of net charge in the activated carbon electrode layer is mimicked using temperature distribution, and the electromechanical coupling coefficient is mimicked using the thermal expansion coefficient. Compared with the traditional equivalent bimorph beam model, the proposed model can predict the distribution of the induced strain more exactly. On the basis of the model, experiments are carried out to investigate the impact of selected parameters on the tip displacement, electromechanical coupling coefficient and induced strain of the PIA. The voltage of the input signal, and three geometrical parameters, length, width, and thickness, of the PIA are selected in this work. The experimental and simulation results indicate that the voltage, length, and thickness show significant influence on the electromechanical bending behavior of the PIA, but the width does not. As a whole, these results can be beneficial for providing enhanced degrees of understanding, predictability and control of PIA performance.

A novel rate-dependent hysteresis modeling and position control technique for piezo-actuated bimorph beams

Piezoelectric cantilever actuators are widely used in micro/nano-positioning applications due to their relatively accurate response and large operating bandwidth. One of the main obstacles in the way of implementing high-accuracy position tracking in high frequencies is the piezoelectric hysteresis phenomenon. It is known from previous research that piezoelectric materials exhibit a rate-dependent hysteresis loop. The purpose of this article is to obtain a novel hysteresis model that can accurately describe the output of the piezoelectric actuator. This is done by introducing a hysteresis model in the form of an actuated linear dynamic system. This model provides the ability to capture both rate-dependence and magnitude characteristics of the system, and it is simple and easy to implement in real-time. As a result, the proposed method accurately predicts the position of the piezo-actuated beam in a wide range of input frequencies and amplitudes. To demonstrate its effectiveness, the proposed hysteresis model is used along with a robust control loop to track the position of a piezo-actuated beam plant. It is shown using experimental results that utilizing this model leads to accurate position control in a wide range of frequencies.

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.

Characterization of Thermal Expansion Coefficient of LPCVD Polycrystalline SiC Thin Films Using Two Section V-beam Actuators

In this paper we present the characterization of the coefficient of thermal expansion (CTE) of in-situ doped polycrystalline SiC thin films, obtained by low pressure chemical vapor deposition (LPCVD). The material is characterized using V-beam actuators on which the temperature coefficient of resistance (TCR) and the in-plane displacement versus current are measured. A CTE value of 4.3 ± 0.4 ppm/K is obtained in the temperature region of 20°C to 300°C. This value is used in a finite element modeling (FEM) simulation of vertical SiC-SiO2 bimorph beams. For an actuator length of 700 μm, width of 100 μm and layer thickness of 2 μm, a displacement up to 200 μm can be obtained.

A Broadband Vibration-Based Energy Harvester Using an Array of Piezoelectric Beams Connected by Springs

Piezoelectric cantilevered beams have been widely used as vibration-based energy harvesters. Nevertheless, these devices have a narrow frequency band and if the excitation is slightly different there is a significant drop in the level of power generated. To handle this problem, the present investigation proposes the use of an array of piezoelectric cantilevered beams connected by springs as a broadband vibration-based energy harvester. The equations for the voltage and power output of the system are derived based on the analytical solution of the piezoelectric cantilevered energy harvester with Euler-Bernoulli beam assumptions. To study the advantages and disadvantages of the proposed system, the results are compared with those of an array of disconnected beams (with no springs). The analytical model is validated with experimental measurements of three bimorph beams with and without springs. The results show that connecting the array of beams with springs allows increasing the frequency band of operation and increasing the amount of power generated.

Analytical analysis of a beam flexural-mode piezoelectric actuator for deformable mirrors

A beam flexural-mode piezoelectric bimorph actuator is analyzed based on linear piezoelectricity, and the performance of the actuator is studied. The beam bimorph piezoelectric actuator (BBPA), which is a sand- wich compound consisting of a lower and an upper piezoelectric ceramic surface layer and a middle layer made of metal, is driven to flexural deformation. The statistical analytical solution and dynamical solutions from the three-dimensional equations of linear piezoelectricity are derived, and the dependence of the performance upon the physical parameters of the BBPA is evaluated. Numerical results illustrate the strengthened performance achieved by adjusting the geometrical and material parameters of the BBPA.©2015SocietyofPhoto-OpticalInstrumentation

Dynamic behavior of piezoelectric bimorph beams with a delamination zone

The First Order Shear Deformation Theory (FOSDT) is considered to study the dynamic behavior of a bimorph beam. A delamination zone between the upper and the lower layer has been taken into consideration; the beam is discretised using the finite elements method (FEM). Several parameters are taken into consideration like structural damping, the geometry, the load nature and the configurations of the boundary conditions. Results show that the delamination between the upper and the lower layer affects considerably the actuation.

Nonlinear Vibration of PZT4/PZT-5H Monomorph and Bimorph Beams with Graded Microstructures

Monomorph and bimorph actuators made of piezoelectric materials are widely used in smart materials and structural control. Recent studies show that their performances can be remarkably improved by the use of functionally graded piezoelectric materials (FGPMs) whose compositional profile and effective material properties are graded along the thickness direction. This paper investigates the linear and nonlinear vibration behaviors of monomorph and bimorph made from a mixture of PZT4 and PZT-5H with material composition following a power law distribution. Theoretical formulations are based on von Kármán kinematic relationships and Timoshenko beam theory to account for the effect of transverse shear deformation. The differential quadrature method (DQM) and the second-order backward difference scheme are employed to obtain the linear and nonlinear vibration frequencies. A parametric study is conducted to investigate the influences of volume fraction index, slenderness ratio, nonlinear deformation and different loading conditions.

Developing an active artificial hair cell using nonlinear feedback control

The hair cells in the mammalian cochlea convert sound-induced vibrations into electrical signals. These cells have inspired a variety of artificial hair cells (AHCs) to serve as biologically inspired sound, fluid flow, and acceleration sensors and could one day replace damaged hair cells in humans. Most of these AHCs rely on passive transduction of stimulus while it is known that the biological cochlea employs active processes to amplify sound-induced vibrations and improve sound detection. In this work, an active AHC mimics the active, nonlinear behavior of the cochlea. The AHC consists of a piezoelectric bimorph beam subjected to a base excitation. A feedback control law is used to reduce the linear damping of the beam and introduce a cubic damping term which gives the AHC the desired nonlinear behavior. Model and experimental results show the AHC amplifies the response due to small base accelerations, has a higher frequency sensitivity than the passive system, and exhibits a compressive nonlinearity like that of the mammalian cochlea. This bio-inspired accelerometer could lead to new sensors with lower thresholds of detection, improved frequency sensitivities, and wider dynamic ranges.

Study of the Delamination in the Case of Piezoelectric Bimorph Beams “Static Behavior”

The first-order shear deformation theory is used to study the static behavior of a piezoelectric bimorph beam with delamination between its layers. This delamination is taken with several lengths and locations along the beam with different boundary conditions. The results show that the shape of the axial displacement field is not affected by either the length of the debonded zone or the variation in the ambient. However, this shape is deformed when an electrical field is applied.

A vibration-based energy harvester suitable for low-frequency, high-amplitude environments: Theoretical and experimental investigations

This article presents theoretical and experimental investigations of a vibration-based energy harvester which is suitable to extract energy from low-frequency, high-amplitude environments. The proposed device consists of a rotating proof mass and eight piezoelectric bimorph beams. A magnet, mounted on the rotating pendulum, actuates the tips of the piezoelectric beams due to magnetic interaction. The free oscillations of the piezoelectric beam generate energy each time the pendulum passes over the beams. Based on energy principles, the nonlinear ordinary differential equations governing the electromechanical behavior of the system are derived and solved numerically. Using the proposed model, the effects of angular velocity of the rotating mass on the generated voltage are investigated. It is shown that the harvester with a relatively high angular velocity generates more voltage than the one with a low angular velocity. The performance of the proposed device in the attractive and the repulsive cases is compared to each other and it is concluded that the generated voltage of the attractive case is more than that of the repulsive case. The overall generated power of the harvester under harmonic external excitations is investigated for various amplitudes and frequencies. Using theoretical model, it is shown that the proposed device can be used for harvesting the out-of-plane vibrational energy. A model of the system has been devised and tested. The obtained experimental results show good qualitative agreements with the theoretical ones.

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.

Resonance-type bimorph-based high-speed atomic force microscopy: real-time imaging and distortion correction

Resonance-type bimorph-based high-speed atomic force microscopy (HSAFM) capable of operating in the sample-scan and tip-scan modes is presented in this paper. The working principle of the high-speed scanner, the experimental setup, and the data collection system are described in detail. The main characteristic of the high-speed scanner is the use of a piezoelectric bimorph, where one of the piezoelectric layers is used to drive the bimorph beam to scan at a high speed and the other monitors the bimorph vibration. Image distortions due to the phase-lag and sinusoidal scanning are analyzed and simulated. The correction methods for the compensation of the phase-lag and nonlinear movement are proposed based on data shift and nonlinear mapping relations, respectively. The HSAFM imaging at the maximum rate of ~30 frames per second is demonstrated with our data collection and correction program. The image distortions caused by the phase-lag and sinusoidal scanning are effectively eliminated in real-time. This work would provide useful methods for the development of HSAFM and applications in the observation of dynamic processes at nanoscale.

Theoretical analysis of energy harvesting performance for clamped–clamped piezoelectric beam

The clamped---clamped beam has attracted increasing attention in the area of piezoelectric energy harvesting and transducer. In this paper, we present the theoretical models of clamped---clamped piezoelectric unimorph and bimorph beams with a quasi-static force in the middle. Based on the models, numerical studies are carried out to compare the generated charge, open-circuit voltage and generated energy of the piezoelectric beams under different condition. The simulation results demonstrate that the output performance of the beams are depended on the bonding position and electromechanical properties of the piezoelectric layer, and the length ratio, thickness ratio and the Young's modulus ratio (YMR) of the piezoelectric layer and substrate. Specifically, the unimorph and bimorph beams share the same optimal length ratio while their optimal width ratio and thickness ratio are different. The YMR imposes a great impact on the performance of the beam both in the unimorph and bimorph cases. As a generalization, the models are not only suitable for the beam with a non-uniform cross-section but also applicable for the beam with uniform cross-section. The analyses can be used to improve the performance of the clamped---clamped beam working as an energy harvester and transducer.

SMART MATERIALS USED FOR AERO ENGINE VIBRATION CONTROL

ABSTRACTThe new generation of smart materials and structure technologies featuring at the most sophisticated level a network of sensors and actuators, real time control capabilities, computational capabilities and a host structural material. Smart materials are usually attached or embedded into structural systems to enable these structures to sense disturbances, process the information and evoke reaction at the actuators, possibly to negate the effect of the original disturbance. For active vibration reduction tasks in smart structures technology, piezoelectric ceramics are the first choice. They generate large forces, have fast response times, are commercially available as fibers, patches and stacks, and allow integration into structural components. Piezoelectric extension actuators are bonded to the surface or embedded within the structure. Resonant vibrations of aero engine blades cause blade fatigue problems in engines, which can lead to thicker and aerodynamically lower performing blade designs, increasing engine weight, fuel burn, and maintenance costs. In order to suppress undesirable blade vibration levels, active piezoelectric vibration control are used, potentially enabling thinner blade designs for higher performing blades and minimizing blade fatigue problems. Thus, this paper gives an overview of smart materials, piezoelectric materials and their applications in vibration damping and a finite element ANSYS model analysis for piezoelectric bimorph beam including resistor capacitor (RC) circuit to study the effect of resistance (R) and capacitance (C) values change in vibration damping control.

Resonance Tuning of a Multi-piezoelectric Bimorph Beams Energy Harvester Connected by Springs

Piezoelectric energy harvesters are ideal for capturing energy from mechanical vibrations in the ambient environment. Numerous studies have been made of this application of piezoelectric energy conversion; however, thus far researchers have encountered limitations in the amount of power that can be captured. In this paper, a frequency- adjustable energy harvester with an array of piezoelectric bimorphs connected by springs has been designed and analyzed based on the 1D piezoelectric beam equations. The result shows that the energy harvester is capable of operating in multiple frequencies, and the operating frequencies can be adjusted by changing the small end masses and spring stiffness. An optimal selection of the load impedance to realize the maximum power output is discussed. The power efficiency of the energy harvester has been analyzed as well.

A piezoelectric energy harvester with increased bandwidth based on beam flexural vibrations in perpendicular directions

We propose a new structure for piezoelectric energy harvesters. It consists of an elastic beam with two pairs of piezoelectric films operating with the fundamental flexural modes in perpendicular directions. A one-dimensional model is developed and used to analyze the proposed structure. The output power density is calculated and examined. Results show that, with simultaneous flexural motions in two perpendicular directions, the output power has two peaks close to each other resulting from the two fundamental flexural resonances. The distance between the two peaks can be adjusted through design to make the two peaks merge into one wide peak. Hence, the frequency bandwidth through which energy can be harvested is roughly doubled when compared with conventional beam bimorph energy harvesters operating with flexural motion in one direction and one resonance only.

Response of duffing-type harvesters to band-limited noise

This paper aims to experimentally investigate the influence of stiffness-type nonlinearities on the transduction of vibratory energy harvesters (VEHs) under band-limited noise. For the purpose of the study, an energy harvester consisting of a clamped–clamped piezoelectric beam bi-morph is considered. The shape of the harvester's potential function is altered by applying a static compressive axial load at one end of the beam. The axial load permits the harvester to operate with different potential energy characteristics, namely, the mono-stable (pre-buckling) and bi-stable (post-buckling) configurations. The performance of the harvester in both the configurations is investigated and compared by tuning the harvester's oscillation frequencies around the static equilibria such that they have equal values in both scenarios. The harvester is then subjected to random base excitations of different levels, bandwidths, and center frequencies. The variance of the output voltage is measured across an arbitrary, purely resistive load and used for the purpose of performance comparison. Critical conclusions pertinent to the influence of the nonlinearity and relative performance in both configurations are presented and discussed.

Highly Reliable MEMS Temperature Sensors for 275 $^{ \circ}\hbox{C}$ Applications—Part 1: Design and Technology

This paper presents the design, fabrication, packaging, and experimental characterization of the first temperature-sensitive MEMS capacitors for health monitoring applications up to 275 °C. The capacitive sensor chip is 2 × 2 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> fabricated on a 500-μm -thick Si wafer and comprises an array of 220 individual 10 × 250 μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> inherently robust bimorphs. This first part focuses on the fabrication and packaging, thermomechanical design, electromagnetic modeling, and technology of the unpackaged and packaged bimorph beams. On the thermomechanical part, the measured profiles match theoretically predicted profiles from 20 °C to 250 °C within 4% and 3% at the beam midpoints and tips, respectively. Similarly, experimentally obtained capacitance changes for five separate packaged devices show a mean error of less than 3% and a maximum error of less than 5% from the theoretical model up to 165 °C. The packaged sensors simultaneously achieve for the first time: 1) high temperature operation; 2) monotonic capacitance-temperature response from 20 °C to 300 °C; 3) hermetic sealing; 4) miniature size of 5.4 × 5.4 × 3.6 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ; and 5) capacitance quality factor of over 5000 at 20 °C and 1000 at 160 °C. Experimental results underline the tradeoffs between beam arrangement, attachment method to the package, and package to the quality factor of the device.