Stephen Leadenham

Nonlinear M-shaped broadband piezoelectric energy harvester for very low base accelerations: primary and secondary resonances

It has been well demonstrated over the past few years that vibration energy harvesters with intentionally designed nonlinear stiffness components can be used for frequency bandwidth enhancement under harmonic excitation for sufficiently high vibration amplitudes. In order to overcome the need for high excitation intensities that are required to exploit nonlinear dynamic phenomena, we have developed an M-shaped piezoelectric energy harvester configuration that can exhibit a nonlinear frequency response under very low vibration levels. This configuration is made from a continuous bent spring steel with piezoelectric laminates and a proof mass but no magnetic components. Careful design of this nonlinear architecture that minimizes piezoelectric softening further enables the possibility of achieving the jump phenomenon in hardening at few milli-g base acceleration levels. In the present work, such a design is explored for both primary and secondary resonance excitations at different vibration levels and load resistance values. Following the primary resonance excitation case that offers a 660% increase in the half-power bandwidth as compared to the linear system at a root-mean-square excitation level as low as 0.04g, secondary resonance behavior is investigated with a focus on 1:2 and 1:3 superharmonic resonance neighborhoods. A multi-term harmonic balance formulation is employed for a computationally effective yet high-fidelity analysis of this high-quality-factor system with quadratic and cubic nonlinearities. In addition to primary resonance and secondary (superharmonic) resonance cases, multi-harmonic excitation is modeled and experimentally validated.

On the mechanism of bandgap formation in locally resonant finite elastic metamaterials

Elastic/acoustic metamaterials made from locally resonant arrays can exhibit bandgaps at wavelengths much longer than the lattice size for various applications spanning from low-frequency vibration/sound attenuation to wave guiding and filtering in mechanical and electromechanical devices. For an effective use of such locally resonant metamaterial concepts in finite structures, it is required to bridge the gap between the lattice dispersion characteristics and modal behavior of the host structure with its resonators. To this end, we develop a novel argument for bandgap formation in finite-length elastic metamaterial beams, relying on the modal analysis and the assumption of infinitely many resonators. We show that the dual problem to wave propagation through an infinite periodic beam is the modal analysis of a finite beam with an infinite number of resonators. A simple formula that depends only on the resonator natural frequency and total mass ratio is derived for placing the bandgap in a desired frequency range, yielding an analytical insight and a rule of thumb for design purposes. A method for understanding the importance of a resonator location and mass is discussed in the context of a Riemann sum approximation of an integral, and a method for determining the optimal number of resonators for a given set of boundary conditions and target frequency is introduced. The simulations of the theoretical framework are validated by experiments for bending vibrations of a locally resonant cantilever beam.

Fourier transform-based design of a patterned piezoelectric energy harvester integrated with an elastoacoustic mirror

We explore efficient transformation of structure-borne propagating waves into low-power electricity using patterned polymer piezoelectrics integrated with an elastoacoustic mirror configuration. Fourier transform-based spatial optimization of a piezoelectric energy harvester domain weakly coupled to a thin plate housing a continuous elliptical elastoacoustic mirror is presented. Computational modeling and experimental testing are employed to quantify performance enhancement in power generation using the presented approach. Excellent agreement is observed between numerical simulations and experimental measurements. Specifically, dramatic enhancement of the harvested power output is reported by patterning the electrodes of a rectangular polyvinylidene fluoride piezoelectric energy harvester in the elliptical mirror domain.

A general theory for bandgap estimation in locally resonant metastructures

Abstract Locally resonant metamaterials are characterized by bandgaps at wavelengths that are much larger than the lattice size, enabling low-frequency vibration attenuation. Typically, bandgap analyses and predictions rely on the assumption of traveling waves in an infinite medium, and do not take advantage of modal representations typically used for the analysis of the dynamic behavior of finite structures. Recently, we developed a method for understanding the locally resonant bandgap in uniform finite metamaterial beams using modal analysis. Here we extend that framework to general locally resonant 1D and 2D metastructures (i.e. locally resonant metamaterial-based finite structures) with specified boundary conditions using a general operator formulation. Using this approach, along with the assumption of an infinite number of resonators tuned to the same frequency, the frequency range of the locally resonant bandgap is easily derived in closed form. Furthermore, the bandgap expression is shown to be the same regardless of the type of vibration problem under consideration, depending only on the added mass ratio and target frequency. For practical designs with a finite number of resonators, it is shown that the number of resonators required for the bandgap to appear increases with increased target frequency, i.e. more resonators are required for higher vibration modes. Additionally, it is observed that there is an optimal, finite number of resonators which gives a bandgap that is wider than the infinite-resonator bandgap, and that the optimal number of resonators increases with target frequency and added mass ratio. As the number of resonators becomes sufficiently large, the bandgap converges to the derived infinite-resonator bandgap. Furthermore, the derived bandgap edge frequencies are shown to agree with results from dispersion analysis using the plane wave expansion method. The model is validated experimentally for a locally resonant cantilever beam under base excitation. Numerical and experimental investigations are performed regarding the effects of mass ratio, non-uniform spacing of resonators, and parameter variations among the resonators.

Harmonic Balance Analysis and Experimental Validation of a Nonlinear Broadband Piezoelectric Energy Harvester for Low Ambient Vibrations

It has been shown by several research groups over the past few years that vibration energy harvesters with intentionally designed nonlinear stiffness components can be used for frequency bandwidth enhancement under harmonic excitation for sufficiently strong vibration amplitudes. In order to overcome the need for high excitation intensities that are required to exploit nonlinear dynamic phenomena, we have developed an M-shaped piezoelectric energy harvester configuration that can exhibit a nonlinear frequency response under low vibration levels. This configuration is made from a continuous bent spring steel with piezoelectric laminates and a proof mass, and no magnetic components. Careful design of this nonlinear architecture that minimizes piezoelectric softening further enables the possibility of achieving the jump phenomenon in hardening at base acceleration levels on the order of a few milli-g. In the present work, such a design is explored for both primary and secondary resonance excitations at different vibration levels and for different electrical loads. Following the primary resonance excitation case that offers more than 600 % increase in the half-power bandwidth as compared to the linear system at a root-mean-square excitation level as low as 0.04g, secondary resonance behavior is investigated with a focus on 1:2 and 1:3 superharmonic resonance neighborhoods. A multi-term harmonic balance formulation is employed for a computationally effective yet high-fidelity analysis of this high-quality-factor system with quadratic and cubic nonlinearities. In addition to primary resonance and secondary (superharmonic) resonance cases, multi-harmonic excitation is modeled and experimentally validated.Copyright

Power conditioning for low-voltage piezoelectric stack energy harvesters

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.

Ultrasound acoustic wave energy transfer and harvesting

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.

Nonlinear modeling, strength-based design, and testing of flexible piezoelectric energy harvesters under large dynamic loads for rotorcraft applications

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.

Optimal piezoelectric energy harvesting using elastoacoustic mirrors by frequency-wavenumber domain investigation

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.

Metamaterial piezoelectric beam with synthetic impedance shunts

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.