We present a metamaterial beam based on a piezoelectric bimorph with segmented electrodes. Previously, we found the theoretical response of the beam using the assumed-modes method, and derived the effect of the shunt circuit impedance applied to each pair of electrodes. The structural response is governed by a frequency- dependent stiffness term, which depends on a material/geometry-based electromechanical coupling parameter and the impedance of the shunt circuits. A simple way to interpret the response of the system with frequency- dependent stiffness is the root locus method, which immediately yields the poles of each mode of the system using simple geometric rules. Case studies are shown for creating locally resonant bandgap with or without negative capacitance. To justify the use of these admittances that often require power input to the system, the concept of synthetic impedance is extended to symmetric voltages, as are encountered in series-connected piezoelectric bimorphs. Synthetic impedance or admittance is a method for obtaining an arbitrary impedance across a load by measuring the voltage and applying the corresponding current using digital signal processing and an analog circuit. Time domain simulations using these synthetic impedance circuits are compared to the ideal frequency domain results with good agreement. Surprisingly, the necessary digital sampling rate for stability is significantly higher than the Nyquist frequency.
Low-power vibration and acoustic energy harvesting scenarios typically require a storage component to be charged to enable wireless sensor networks, which necessitates power conditioning of the AC output. Piezoelectric beam-type bending mode energy harvesters or other devices that operate using a piezoelectric element at resonance produce high voltage levels, for which AC-DC converters and step-down DC-DC converters have been previously investigated. However, for piezoelectric stack energy harvesters operating off-resonance and producing low voltage outputs, a step-up circuit is required for power conditioning, such as seen in electromagnetic vibration energy scavengers, RF communications, and MEMS harvesters. This paper theoretically and experimentally investigates power conditioning of a low-voltage piezoelectric stack energy harvester.
The harvesting of mechanical strain and kinetic energy has received great attention over the past two decades in order to power wireless electronic components such as those used in passive and active monitoring applications. Piezoelectric ceramics, such as PZT (lead zirconate titanate), constitute the most commonly used electromechanical interface in vibration energy harvesters. However, there are applications in which piezoelectric ceramics cannot be used due to their low allowable curvature and brittle nature. Soft polymer PVDF (polyvinylidene fluoride) is arguably the most popular non-ceramic soft piezoelectric energy harvester material for such scenarios. Another type of polymer that has received less attention is PP (polypropylene) for electret-based energy harvesting using the thickness mode (33- mode). This work presents figure of merit comparison of PP versus PVDF for off-resonant energy harvesting in thickness mode operation, revealing substantial advantage of PP over PVDF. For thickness mode energy harvesting scenarios (e.g. dynamic compression) at reasonable ambient vibration frequencies, the figure of merit for the maximum power output is proportional to the square of the effective piezoelectric strain constant divided by the effective permittivity constant. Under optimal conditions and for the same volume, it is shown that PP can generate more than two orders of magnitude larger electrical power as compared to PVDF due to the larger effective piezoelectric strain constant and lower permittivity of the former.
This work aims to demonstrate the detrimental effect of fluid damping on the bandwidth of a flexible nonlinear energy harvester and thereby further enhance the performance by minimizing nonlinear damping. A vacuum setup has been introduced to conduct nonlinear base excitation experiments at different air pressure levels in an effort to control the quadratic (velocity-squared) damping coefficient. It is shown that reduced air pressure substantially enhances the frequency bandwidth for primary resonance excitation. The empirical electromechanical model is modified to express the fluid damping in terms of fluid pressure and validated experimentally for different excitation levels.
Intentionally designed nonlinearities have been employed by several research groups to enhance the frequency bandwidth of vibration energy harvesters. Another type of nonlinear resonance behavior emerges from the piezoelectric constitutive behavior for high excitation levels and is manifested in the form of softening stiffness. This material nonlinearity does not result in the jump phenomenon in soft piezoelectric ceramics, e.g. PZT-5A and PZT-5H, due to their large internal dissipation. This paper explores the potential for wideband energy harvesting using a hard (relatively high quality factor) PZT-8 bimorph by exploiting its material softening. A wide range of base excitation experiments conducted for a set of resistive electrical loads confirms the frequency bandwidth enhancement.
KEYWORDS: Data modeling, Electrodes, Ferroelectric materials, Energy harvesting, Resistance, Systems modeling, Dynamical systems, Vibration control, Electroluminescent displays, Data acquisition
Electroelastic and dissipative nonlinearities of commonly used soft piezoelectrics (PZT-5A and PZT-5H) are pronounced in various engineering applications such as actuation, sensing, vibration control, and most recently, in energy harvesting from dynamical systems. The present work investigates the nonlinear nonconservative dynamic behavior of bimorph piezoelectric cantilevers under low-to-high excitation levels with a focus on most popular soft piezoceramics: PZT-5A and PZT-5H. A unified mathematical framework we recently developed is analyzed by using the method of harmonic balance to identify and validate nonlinear system parameters based on a set of rigorous experiments for different samples.
In this work we explore efficient transformation of broadband wave energy into low-power electricity using patterned polymer piezoelectrics integrated with an Elliptical Acoustic Mirror (EAM) configuration. The mirror under consideration features a semi-elliptical continuous mirror with a rectangular arrangement of harvesting material overlapping the geometrical focus of the mirror. Spatial and temporal transformation of the wave propagation field into the frequency-wavenumber domain is performed in order to identify the wavenumber content inside the mirror region. A frequency-domain Root-Mean-Square (RMS) evaluation is then applied in order to guarantee broadband harvesting characteristics to the resulting Distributed Harvester (DH). Computational modeling and experimental testing are employed to quantify performance enhancement of the presented approach in the 20-120 kHz range, where broadband focusing characteristics of the continuous EAM are confirmed experimentally. Additionally the patterned configuration with proper wiring results in substantial power enhancement over 20-60 kHz, i.e. the neighborhood of the center frequency used in its Fourier transform-based design.
This paper investigates low-power electricity generation from ultrasound acoustic wave energy transfer combined with piezoelectric energy harvesting for wireless applications ranging from medical implants to naval sensor systems. The focus is placed on an underwater system that consists of a pulsating source for spherical wave generation and a harvester connected to an external resistive load for quantifying the electrical power output. An analytical electro-acoustic model is developed to relate the source strength to the electrical power output of the harvester located at a specific distance from the source. The model couples the energy harvester dynamics (piezoelectric device and electrical load) with the source strength through the acoustic-structure interaction at the harvester-fluid interface. Case studies are given for a detailed understanding of the coupled system dynamics under various conditions. Specifically the relationship between the electrical power output and system parameters, such as the distance of the harvester from the source, dimensions of the harvester, level of source strength, and electrical load resistance are explored. Sensitivity of the electrical power output to the excitation frequency in the neighborhood of the harvester’s underwater resonance frequency is also reported.
There has been growing interest in enabling wireless health and usage monitoring for rotorcraft applications, such as helicopter rotor systems. Large dynamic loads and acceleration fluctuations available in these environments make the implementation of vibration-based piezoelectric energy harvesters a very promising choice. However, such extreme loads transmitted to the harvester can also be detrimental to piezoelectric laminates and overall system reliability. Particularly flexible resonant cantilever configurations tuned to match the dominant excitation frequency can be subject to very large deformations and failure of brittle piezoelectric laminates due to excessive bending stresses at the root of the harvester. Design of resonant piezoelectric energy harvesters for use in these environments require nonlinear electroelastic dynamic modeling and strength-based analysis to maximize the power output while ensuring that the harvester is still functional. This paper presents a mathematical framework to design and analyze the dynamics of nonlinear flexible piezoelectric energy harvesters under large base acceleration levels. A strength-based limit is imposed to design the piezoelectric energy harvester with a proof mass while accounting for material, geometric, and dissipative nonlinearities, with a focus on two demonstrative case studies having the same linear fundamental resonance frequency but different overhang length and proof mass values. Experiments are conducted at different excitation levels for validation of the nonlinear design approach proposed in this work. The case studies in this work reveal that harvesters exhibiting similar behavior and power generation performance at low excitation levels (e.g. less than 0.1g) can have totally different strength-imposed performance limitations under high excitations (e.g. above 1g). Nonlinear modeling and strength-based design is necessary for such excitation levels especially when using resonant cantilevers with no geometric constraint.
Inherent nonlinearities of piezoelectric materials are inevitably pronounced in various engineering applications
such as sensing, actuation, their combined applications for vibration control, and most recently, energy harvesting
from dynamical systems. The existing literature focusing on the dynamics of electroelastic structures
made of piezoelectric materials have explored such nonlinearities in a disconnected way for the separate problems
of mechanical and electrical excitation such that nonlinear resonance trends have been assumed to be due to
different additional terms in constitutive equations by different researchers. Similar manifestations of softening
nonlinearities have been attributed to purely elastic nonlinear terms, coupling nonlinearities, hysteresis, or a
combination of these effects, by various authors. However, a reliable nonlinear constitutive equation for a given
piezoelectric material is expected to be rather unique and valid regardless of the application, e.g. energy harvesting,
sensing, or actuation. A systematic approach focusing on the two-way coupling can result in a sound
mathematical framework. To this end, the present work investigates the nonlinear dynamic behavior of a bimorph
piezoelectric cantilever under low-to-high mechanical and electrical excitation levels in energy harvesting,
sensing, and actuation. A physical model is proposed including both ferroelastic hysteresis, stiffness, and electromechanical
coupling nonlinearities. A lumped parameter electroelastic model is developed by accounting for
these nonlinearities to analyze the primary resonance of a cantilever using the method of harmonic balance.
Strong agreement between the model and experimental investigation is found, providing solid evidence that the
the dominant source of observed softening nonlinear effects in geometrically linear piezolectric cantilever beams
is well represented by a quadratic term resulting from ferroelastic hysteresis. Electromechanical coupling and
cubic softening nonlinearities are observed to become effective only near the physical limits of the brittle and stiff
bimorph cantilever used in the experiments, revealing that the quadratic nonlinearity associated with hysteresis
has the primary role in nonlinear nonconservative dynamic behavior.
Recent work has demonstrated efficient transformation of structure-borne propagating waves into low-power electricity using metamaterial-inspired mirror configurations. Elastoacoustic waves (i) originating from a point source and (ii) arriving as plane waves have been successfully focused on a piezoelectric energy harvester using elliptical and parabolic mirror concepts, respectively. Our present work investigates the spatial optimization of a piezoelectric energy harvester domain weakly coupled to a thin plate housing an elastoacoustic mirror (or lens). Mirrors considered include elliptical arrangements of periodic stubs, and an elliptical arrangement of continuous material. Spatial and temporal transformation of the wave propagation field into the frequency- wavenumber domain is performed in order to identify the wavenumber content inside the mirror. A frequency- domain root-mean-square (RMS) evaluation is then applied to the transformed field in order to extract the preferred propagation directions. Computational modeling and experimental testing are employed to quantify performance enhancement of the presented approach. Specifically, dramatic enhancement of the harvested power output is reported by patterned electroding of a rectangular PVDF harvester in the elliptical mirror domain.
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