Bimorph Cantilever Research Articles

Investigation and Numerical Simulation of Different Piezoelectric Bimorph Cantilever Designs for Energy Harvesting

The study investigates the dynamic performance and energy harvesting efficiency of different cantilever configurations using numerical simulations. It examines factors such as material properties, geometrical parameters, and excitation conditions to optimize the design for enhanced energy harvesting capabilities. The research contributes to understanding how different cantilever designs affect the overall performance and efficiency of piezoelectric energy harvesters. Vibrational energy harvesters, also known as MEMS, have become popular due to their efficiency and ease of inclusion in microsystems. COMSOL Multiphysics was used to simulate six different forms of piezoelectric bimorph cantilevers for energy harvesting. Designs were analyzed, with each design having a distinct arrangement of proof masses. Design 01 had a rectangular cantilever with a proof mass connected to its top surface, Design 02 used a rectangular cantilever, Design 03 used a novel approach, Design 04 used a trapezoidal cantilever, and Design 05 preserved the trapezoidal form but moved the proof mass to the structure's base. Design 06 successfully completed the trapezoidal cantilever. The study found that design 04 had a significant advantage in power production efficiency at higher resistor values, surpassing design 01 in power output. The use of these varied designs allows for an exhaustive examination of piezoelectric bimorph cantilever configurations, potentially leading to insights that may enhance energy harvesting effectiveness in various applications.

Pulsed heating of the self-actuated cantilever: a one-dimensional exact solution investigation of non-axial temperature gradients

Self-actuated bimorph cantilevers are implemented in a variety of micro-electro-mechanical systems. Their tip deflection relies on the unmatched coefficients of thermal expansion between layers. The thermal bimorph phenomenon is dependent on the temperature rise within the cantilever and, while previous studies have investigated variations in the thermal profile along the cantilever length, these have usually neglected variations in the thermal profile along the cantilever thickness. The current study investigates the thermal distribution across the thickness of the cantilever. The exact closed form solution to the one-dimensional problem of heat conduction in the composite (layered) domain subjected to transient volumetric heating is developed using the appropriate Green’s function. This solution is applied to a one-dimensional case study of a 3-layer cantilever with an Aluminium heater, a silicon dioxide resistive layer, and a silicon base layer. The aluminium heater experiences volumetric heating at a rate of 0.2 mW/μm3 of 5 μs duration at 100 μs intervals (10 kHz with a 1/20 duty cycle). Benchmark solutions of the temperature at select times and positions are provided. It is shown that there are negligible temperature gradients across the cantilever thickness during the heating and the first ~ 5 μs afterward. These short-lived temperature differences are positively biased with the unmatched thermal expansion coefficients between the layers, though their relative influence on bending is not clear. A simple parametric analysis indicates that the relative magnitude of the temperature differences across the cantilever (compared to the overall temperature) decreases substantially with increasing duty cycle.

BaHf0.05Ti0.95O3 Ceramics from Sol-Gel and Solid-State Processes: Application to the Modelling of Piezoelectric Energy Harvesters.

A typical piezoelectric energy harvester is a bimorph cantilever with two layers of piezoelectric material on both sides of a flexible substrate. Piezoelectric layers of lead-based materials, typically lead zirconate titanate, have been mainly used due to their outstanding piezoelectric properties. However, due to lead toxicity and environmental problems, there is a need to replace them with environmentally benign materials. Here, our main efforts were focused on the preparation of hafnium-doped barium titanate (BaHfxTi1-xO3; BHT) sol-gel materials. The original process developed makes it possible to obtain a highly concentrated sol without strong organic complexing agents. Sol aging and concentration can be controlled to obtain a time-stable sol for a few months at room temperature, with desired viscosity and colloidal sizes. Densified bulk materials obtained from this optimized sol are compared with a solid-state synthesis, and both show good electromechanical properties: their thickness coupling factor kt values are around 53% and 47%, respectively, and their converse piezoelectric coefficient d33∗ values are around 420 and 330 pm/V, respectively. According to the electromechanical properties, the theoretical behavior in a bimorph configuration can be simulated to predict the resonance and anti-resonance frequencies and the corresponding output power values to help to design the final device. In the present case, the bimorph configuration based on BHT sol-gel material is designed to harvest ambient vibrations at low frequency (<200 Hz). It gives a maximum normalized volumetric power density of 0.03 µW/mm3/Hz/g2 at 154 Hz under an acceleration of 0.05 m/s2.

Dynamic response of auxetic and functionally graded piezoelectric energy harvester using PVDF polymer

Piezoelectric energy harvesting has garnered greater interest in the past two decades than other vibration energy harvesting techniques for wireless power sensors and portable electronics. This work initially considers a bimorph cantilever with a solid substrate for analysis, keeping the first eigenfrequency below 100 Hz for environmental energy harvesting. Polyvinylidene fluoride (PVDF)-polymer is used as piezoelectric material due to its higher flexibility and brass is used as a substrate. The cantilever beam of length (L), width (B), the thickness of the substrate (t s) and piezoelectric layer (t p) are 50, 12.5, 0.14, and 0.25 mm, respectively, considered for analysis and having an eigenfrequency of 44 Hz. Further, an auxetic substrate (elliptical structure) and functionally graded piezoelectric material are incorporated to enhance power output. The maximum power is obtained as 8.33, 8.97 and 3.3 mW for conventional (solid) substrate, auxetic substrate and functionally graded piezoelectric layer under 3.5g excitation. The auxetic design has enhanced power output, whereas functionally graded materials have better surface bonding.

Design, tuning and in-field validation of energy harvesters for railway bridges

Energy harvesters are a promising technology for powering infrastructure condition monitoring systems without batteries. When deployed on railway bridges they are typically tuned to the bridge’s natural frequency, however due to the dominance of train-induced forced vibration of the structure, this results in sub-optimal energy harvesting. As a solution, this paper presents a novel tuning strategy for energy harvesters on railway bridges. The strategy is based on a statistical analysis of the mechanical energy generated in the bridge during train passage and involves four steps: (i) measurement of bridge response due to train traffic, (ii) calculation of mechanical energy during train passage, (iii) statistical characterisation of the energy distribution, and finally, (iv) calculation of the tuning frequency. A case study is presented to compare the potential of the proposed strategy against tuning based upon the bridge natural frequency. First, an in-service railway bridge is monitored to determine its natural frequency and response to train traffic. Combining the field data with the proposed tuning strategy, the design of energy harvesters for the bridge is optimised. The design of harvesters tuned to natural frequencies is also studied. The underlying harvester type is a cantilever bimorph beam with a mass at the tip and load resistance. Additive manufacturing is used for the substructure, which is formed from PAHT-CF15 (High Temperature Polyamide carbon fibre reinforcement). The harvesters are manufactured and deployed on the bridge subject to live railway traffic. Field results show the devices designed using the new tuning strategy harvest up to 300% more energy. The energy harvested in a time window of three hours (18 train passages) is 7.65mJ.

Investigation and hybrid deep belief neural network-based validation of piezoelectric bimorph cantilever composites assisted with tip mass

This work fabricated the piezoelectrical material using PMMA (polymethyl methacrylate) and Ce-doped ZnO nano-powders. The study was conducted to validate the piezoelectric performance of the proposed material and its suitability for the cantilever structure. The PMMA/Ce-ZnO makes the cantilever structure more flexible and performs better. The frequency response is applied to the beam using an electrical circuit to analyze the power and voltage output. The acceleration is given to the cantilever beams to analyze their resonant frequencies. The change in resonant frequencies results in a high voltage and power output. The resistive loads are used in the circuit to find the electrical load. The frequency response is analyzed in three different inner (18 mm, 20 mm, 22 mm) and outer (23 mm, 25mm, 27 mm) active layer lengths of beams. As a result, the maximum voltage of 21.94 V with 13.67 mW power and 2.9 mA current is obtained at a resonant frequency of 51.06 Hz and 1 g acceleration amplitude, which are approximately 42%, 45% and 15% higher voltage, power and current obtained from the lowest performer of proposed piezoelectric cantilevers. The experiment results are validated using the hybrid DBN-SSO (Deep Belief Network based Salp Swarm Optimization) machine learning technique. The proposed DBN-SSO achieved 0.9998 and 0.9966 regression coefficients for voltage and power outputs, thus proving the fitness of predicted results with the experiments. As per findings, a 27 mm inner and 18 mm outer active layer based energy harvesting system is suggested as a suitable energy source where ever 10-12 mW power, 2.5-2.9 mA current and 20-21.94 V voltage are applicable.

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.

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

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

Cost-effective measurement of magnetostriction in nanoscale thin films through an optical cantilever displacement method

A cost-effective method for the quantitative characterization of the magnetostrictive effect in thin films is presented. In this method, a sample's magnetostriction is extrapolated from the tip displacement of a thin-film magnetostrictive cantilever. The tip displacement is measured by monitoring the position of a reflected laser beam using two differentially coupled photodiode positioning sensors. In contrast with alternative optical deflection-angle devices designed for educational purposes, the detection limit of our setup resolves submicron-level displacements from nanoscale thin films. The efficacy of the system is demonstrated through measurements using amorphous 200-nm thick Terfenol-D/Si (100) bimorph cantilevers. In these measurements, magnetostriction values of 106 ± 3.5 ppm at ±4300 Oe applied field were attained, where the voltage noise floor was ±0.05 V (a cantilever displacement uncertainty of ±70 nm). In-plane (IP) and out-of-plane (OOP) magnetization curves and crystallographic x-ray diffraction (XRD) were performed to determine the magnetic behavior and confirm the amorphous nature of the films, respectively. The experimental methods and material characterization systems demonstrated here enhance the understanding of complex magnetic phenomena and introduce common measurement techniques to better equip students with the skills for insightful analysis of fundamental magnetic physics.

Parametric excitation analysis for system performance of piezoelectric energy harvesters

Capitalizing on the advantages of parametric excitation and real-life low frequency vibration, the steady-state response of piezoelectric energy harvesting system composing of a cantilever beam with a tip mass and horizontal excitation at the fixed end is investigated. By applying Hamilton's principle, the nonlinear partial differential equation of a cantilever bimorph piezoelectric energy harvesting system with an additional tip mass is derived and analyzed. The cantilever is modeled as an axially non-elongated Euler Bernoulli beam with geometric and damping nonlinearities. By using the Galerkin method, the nonlinear partial differential equation is reduced to an electromechanical coupling system that governs a cantilever piezoelectric energy harvesting system with a tip mass under parametric excitation. The first-order resonance response of this harvesting system is studied by using the method of multiple scales. The analytical response expressions and first-order amplitude functions for vertical displacement, output voltage and output power are derived and analyzed. The influence of different impedance and tip mass on the piezoelectric energy harvesting system performance is summarized and concluded. For the parametric excitation system, the load resistance shows significant influence on the initial threshold of the piezoelectric energy harvesters under parametric excitation. For a short circuit, the initial threshold increases with increasing load resistance. For an open circuit, the initial threshold decreases with increasing load resistance. For an open circuit resistance or a short circuit resistance under parametric excitation, an increase in the end block mass effectively reduces the resonance frequency of the piezoelectric energy harvesters. Consequently, the energy harvesting bandwidth is increased, and the harvesting effect of the piezoelectric energy harvesters is enhanced. In this paper, a more accurate and practical theoretical model is established to predict the electromechanical coupling behavior of cantilever piezoelectric energy harvester under parametric excitation. Using this approach, it is possible to complement parametric and direct excitation such that the advantages of parametric excitation can be achieved. It is also significant to improve the energy conversion efficiency of energy harvesting system.

Design and testing of ultraminiature microelectromechanical systems middle ear accelerometers

Moderate to severe hearing loss is a debilitating condition that affects over 5% of the world’s population. Hearing aids and cochlear implants positively impact the lives of those who suffer from sensorineural hearing loss. However, both display numerous limitations that affect their adoption and use rates, notably including those associated with the external elements of these devices (e.g., microphone and signal processor). These external components impact device safety, appearance, acoustic performance, and ease-of-use. A totally implantable auditory prosthesis would help to address these issues by eliminating external components. A major barrier to progress toward this goal is the lack of a completely implantable acoustic sensor capable of matching or exceeding the performance of commercial external microphones. Our previous studies have indicated that piezoelectric microelectromechanical systems (MEMS) accelerometers have the potential to function as implantable sensors within the middle ear meeting a 20-phon noise floor over a 100–8 kHz range. In this paper, we describe a process to design and fabricate dual and tri-resonance devices that are comprised of piezoelectric cantilever bimorph beams tip-loaded by a proof mass, can meet or exceed the 20-phon noise floor, and can produce a measurable voltage output when deflected by sound-induced ossicular vibrations.

3D printed energy harvesters for railway bridges-Design optimisation

This paper investigates the optimal design of 3D printed energy harvesters for railway bridges. The type of harvester studied is a cantilever bimorph beam with a mass at the tip and a load resistance. These parameters are adjusted to find the optimal design that tunes the harvester to the fundamental frequency of the bridge. An analytical model based on a variational formulation to represent the electromechanical behaviour of the device is presented. The optimisation problem is solved using a genetic algorithm with constraints of geometry and structural integrity. The proposed procedure is implemented in the design and manufacture of an energy harvesting device for a railway bridge on an in-service high-speed line. To do so, first the methodology is validated experimentally under laboratory conditions and shown to offer strong performance. Next the in-situ railway bridge is instrumented using accelerometers and the results used to evaluate energy harvesting performance. The results show the energy harvested in a time window of three and a half hours (20 train passages) is E=109.32mJ. The proposed methodology is particularly useful for bridges with fundamental mode shapes above 4.5Hz, however optimal design curves are also presented for the most common railway bridges found in practice. A novelty of this work is the use of additive manufacturing to 3D print energy harvesters, thus maximising design flexibility and energy performance.

Importance of Three-Dimensional Piezoelectric Coupling Modeling in Quantitative Analysis of Piezoelectric Actuators

This paper demonstrates the importance of three-dimensional (3-D) piezoelectric coupling in the electromechanical behavior of piezoelectric devices using three-dimensional finite element analyses based on weak and strong coupling models for a thin cantilevered piezoelectric bimorph actuator. It is found that there is a significant difference between the strong and weak coupling solutions given by coupling direct and inverse piezoelectric effects (i.e., piezoelectric coupling effect). In addition, there is significant longitudinal bending caused by the constraint of the inverse piezoelectric effect in the width direction at the fixed end (i.e., 3-D effect). Hence, modeling of these effects or 3-D piezoelectric coupling modeling is an electromechanical basis for the piezoelectric devices, which contributes to the accurate prediction of their behavior.

Evaluation of shear piezoelectric coefficients by a bimorph cantilever technique for extruded and oriented poly(l‐lactide) films

AbstractUniaxially stretched poly(l‐lactide) (US‐PLA) films display shear piezoelectric properties of interests for smart applications. However, the measurement of these properties is quite challenging and a simple technique based on bimorph cantilevers is here used. This technique is validated with commercial piezoelectric poly(vinylidene fluoride) (PVDF) films. A piezoelectric coefficient d31 close to 19 pm/V is then obtained with a precision close to 5% and a good accuracy to expected values. For US‐PLA films made by extrusion—machine‐direction orientation, shear piezoelectric coefficients d14 up to 5.9 pm/V are found. Relevant trends can be captured but a low precision on d14, close to 10%, is highlighted. This behavior is probably related to film thickness heterogeneities arising from the extrusion processing at the laboratory scale. Piezoelectric voltage coefficients (g14) and electromechanical coupling coefficients could be also easily obtained with additional measurements of the dielectric permittivity and mechanical compliance. Outstanding g14 coefficients up to 320 mV.m/N are confirmed for US‐PLA films with a precision close to 20%. The bimorph cantilever technique consequently represents a simple and reliable technique to evaluate piezoelectric properties of soft materials, in particular shear piezoelectric properties of US‐PLA films for future developments and optimizations at the pilot scale.

Comparative Study of Tapered Shape Bimorph Piezoelectric Energy Harvester via Finite Element Analysis

We report the power efficiency comparison of two tapered shape bimorph piezoelectric energy harvesters. Typically, the rectangular-shaped cantilever bimorph piezoelectric energy harvester is widely used in piezoelectric energy harvesting. Using the finite element analysis toolbox, we have compared the power efficiency of the triangular and trapezoidal shape bimorph piezoelectric energy harvester. The resonance frequency of these tapered shape harvesters has been extracted using modal analysis, at which maximum power efficiency of the harvester can be achieved. Our study shows that triangular shape bimorph piezoelectric energy harvesters generate more power than trapezoidal harvesters. In addition, lower resistance is required for the triangular bimorph harvester to generate maximum power at resonance, ensuring greater efficiency with minimal loss in sensing applications than the trapezoidal bimorph harvester.

A Cantilever-Based Piezoelectric MEMS for Arbitrary XY Path Generation.

This work pertains to the design of a cantilever-based piezoelectric MEMS device that is capable of generating arbitrary paths of its tip. The conceived device consists of a pair of rigidly coupled piezoelectric bimorph cantilevers, and a theoretical model is developed for the analytical evaluation of the proper voltage distribution to be supplied to the inner and outer electrodes of each piezoelectric actuator, in order to drive the tip along any desired trajectory. Such a device could be appealing in some microsurgical operations, i.e., the unclogging of arteries, endoluminal treatment of obstructive lesions, but also as a 2D micropositioning stage, etc. Theoretical predictions of voltage versus time that allow several pathways such as circles, ellipses, spirals, etc., to be accomplished have been verified with multiphysics FEM simulations and the numerical outcomes seem to corroborate the proposed model.

Duffing-type digitally programmable nonlinear synthetic inductance for piezoelectric structures

Piezoelectric shunt damping techniques using linear circuits (e.g. resistive-inductive) and switching circuits (e.g. synchronized switch on inductor) have been extremely well studied for suppressing resonant vibrations in flexible structures. Both analog circuits and synthetic impedance circuits with digital control have been explored for linear concepts. In a parallel body of work, from the domain of mechanical methods of vibration attenuation, it is also known that leveraging nonlinearities (e.g. stiffness nonlinearity) can enhance the frequency bandwidth and offer amplitude-dependent suppression over a range of frequencies. However, the existing piezoelectric shunt damping techniques have been mostly limited to linear or switching nonlinear circuits, with the exception of a few nonlinear capacitance efforts. This work aims to introduce cubic inductance to emulate Duffing-type hardening nonlinearity in the shunt circuit with precise digital programming and tuning capability. Experiments are performed on a piezoelectric bimorph cantilever under base excitation for concept demonstration and model validation. First, linear frequency response functions of the cantilever are obtained for the short- and open-circuit conditions, and for linear resistive-inductive synthetic shunt damping, to confirm the standard linear behavior and electromechanical model parameters. Then, cubic inductance is introduced to the circuit and nonlinear experiments (up- and down-frequency sweep) are conducted. Cantilever tip to base motion transmissibility frequency response is measured along with piezoelectric voltage to base motion counterpart for a range of base excitation amplitudes. The distortion of the frequency response curves with increased base acceleration levels is observed. The nonlinear cubic coefficient is then varied to alter the manifestation of nonlinear frequency response at a given base excitation level, demonstrating the ease of tuning and triggering the nonlinear behavior on demand by means of the digitally-controlled synthetic impedance shunt. Nonlinear electromechanical model simulations are also validated against the experiments, yielding a very good agreement.

Piezoelectric bimorph MEMS speakers

One of the key requirements for MEMS speakers is to increase the sound pressure level (SPL) while keeping the size as small as possible. In this paper we present a MEMS speaker based on piezoelectric bimorph cantilevers that produces a higher SPL than conventional unimorph cantilever speakers. The active diaphragm size is 1.4 × 1.4 mm2. The bimorph cantilevers are connected in parallel to make full use of the actuation voltage. At 1 kHz, the measured SPL reached 73 dB and the peak SPL reached 102 dB at the resonance frequency of 10 kHz in a 711 ear simulator under a driving voltage of 10 Vrms. The total harmonic distortion of the MEMS speaker was less than 3% in the range from 100 Hz to 20 kHz. Although the absolute SPL was not the highest, this work provides a better SPL for all piezoelectric MEMS speakers.

Piezoelectric Energy Harvesting from Low-Frequency Vibrations Based on Magnetic Plucking and Indirect Impacts

This work proposes a mono-axial piezoelectric energy harvester based on the innovative combination of magnetic plucking and indirect impacts, e.g., impacts happening on the package of the harvester. The harvester exploits a permanent magnet placed on a non-magnetic mass, free to move within a predefined bounded region located in front of a piezoelectric bimorph cantilever equipped with a magnet as the tip mass. When the harvester is subjected to a low-frequency external acceleration, the moving mass induces an abrupt deflection and release of the cantilever by means of magnetic coupling, followed by impacts of the same mass against the harvester package. The combined effect of magnetic plucking and indirect impacts induces a frequency up-conversion. A prototype has been designed, fabricated, fastened to the wrist of a person by means of a wristband, and experimentally tested for different motion levels. By setting the magnets in a repulsive configuration, after 50 s of consecutive impacts induced by shaking, an energy of 253.41 μJ has been stored: this value is seven times higher compared to the case of harvester subjected to indirect impacts only, i.e., without magnetic coupling. This confirms that the combination of magnetic plucking and indirect impacts triggers the effective scavenging of electrical energy even from low-frequency non-periodical mechanical movements, such as human motion, while preserving the reliability of piezoelectric components.

Piezoelectric elements subjected to low frequency excitation. Empirical determination of stress and frequency influence on piezoelectric parameters

Designing optimum energy harvesting devices is the aim of several developments based on numerical or analytical studies of different piezoelectric configurations that usually consider constant piezoelectric properties. Experimental tests on bending piezoelectric patches showed that the electrical response depended on the frequency and amplitude of the mechanical excitation for displacement-imposed systems. Analytical and numerical calculations required adapting piezoelectric parameters to properly represent experimental results. A novel formulation to calculate piezoelectric parameters using the mechanical stress and the excitation frequency as inputs is proposed and discussed. A linear dependency on the mechanical stress of the piezoelectric ceramic and a logarithmic dependency on the excitation frequency have been combined to propose a unique calculation procedure. Later, this procedure was applied to compute different piezoelectric parameters to set numerical (2% error) and analytical (1% error) calculations that accurately represented experimental results. Finally, the practical implications of considering or not considering the frequency and stress dependency of the piezoelectric properties was evaluated for a theoretical bimorph cantilever configuration, whose excitation frequency decreased whereas the amplitude was kept constant. Results showed that only 1/3 of the energy production that was predicted with constant piezoelectric properties can be expected when considering frequency and stress influence.