M. Nouh

Energy harvesting from a standing wave thermoacoustic-piezoelectric resonator

In this paper, a one-dimensional thermoacoustic-piezoelectric (TAP) resonator is developed to convert thermal energy, such as solar or waste heat energy, directly into electrical energy. The thermal energy is utilized to generate a steep temperature gradient along a porous stack which is optimally sized and placed near one end of the resonator. At a specific threshold of the temperature gradient, self-sustained acoustic waves are generated inside the resonator. The resulting pressure fluctuations excite a piezoelectric diaphragm, placed at the opposite end of the resonator, which converts the acoustic energy directly into electrical energy without the need for any moving components. The theoretical performance characteristics of this class of thermoacoustic-piezoelectric resonators are predicted using the Design Environment for Low-amplitude ThermoacousticEnergy Conversion Software. These characteristics are validated experimentally on a small prototype of the system. Particular emphasis is placed on monitoring the temperature field using infrared camera, the flow field using particle image velocimetry, the acoustic field using an array of microphones, and the energy conversion efficiency. Comparisons between the theoretical predictions and the experimental results are also presented. The developed theoretical and experimental techniques can be invaluable tools in the design of TAP resonators for harvesting thermal energy in areas far from the power grid such as nomadic communities and desert regions for light, agricultural, air conditioning, and communication applications.

Vibration Characteristics of Metamaterial Beams With Periodic Local Resonances

Vibration characteristics of metamaterial beams manufactured of assemblies of periodic cells with built-in local resonances are presented. Each cell consists of a base structure provided with cavities filled by a viscoelastic membrane that supports a small mass to form a source of local resonance. This class of metamaterial structures exhibits unique band gap behavior extending to very low-frequency ranges. A finite element model (FEM) is developed to predict the modal, frequency response, and band gap characteristics of different configurations of the metamaterial beams. The model is exercised to demonstrate the band gap and mechanical filtering capabilities of this class of metamaterial beams. The predictions of the FEM are validated experimentally when the beams are subjected to excitations ranging between 10 and 5000 Hz. It is observed that there is excellent agreement between the theoretical predictions and the experimental results for plain beams, beams with cavities, and beams with cavities provided with local resonant sources. The obtained results emphasize the potential of the metamaterial beams for providing significant vibration attenuation and exhibiting band gaps extending to low frequencies. Such characteristics indicate that metamaterial beams are more effective in attenuating and filtering low-frequency structural vibrations than plain periodic beams of similar size and weight.

Periodic metamaterial plates with smart tunable local resonators

Vibration band gaps and elastic wave propagation are examined in the metamaterial plates manufactured with periodic locally resonant membranes arranged in a square array. Periodic metamaterials exhibit unique dynamic characteristics stemming from their ability to act as mechanical filters for wave propagation. As a result, waves propagate along the periodic cells only within specific frequency bands called the pass bands, while being blocked within other frequency bands called the stop bands. The proposed metamaterial plates are equipped with sources of local resonances which act as local absorbers of mechanical vibrations. The macroscopic dynamical properties of the resulting periodic structures depend on the resonant properties of substructures which contribute to the rise of interesting effects such as broad stop band characteristics that extend to lower frequencies. Externally excited piezoelectric polyvinylidene difluoride membranes are used to support the local resonators. The stiffness of the piezo-membranes is tunable by means of an external voltage allowing us to control the location and bandwidth of the local resonance frequencies. The predicted band structures are validated by investigating the frequency response of the plate to external mechanical excitations using a comprehensive finite element model of the entire structure. By examining the proposed metamaterial plate, it is shown that it would be possible to actively control the wave propagation both in the spectral and spatial domains in an attempt to steer, stop, and/or confine the propagation of undesirable external disturbances.

Energy Harvesting of Thermoacoustic-Piezo Systems With a Dynamic Magnifier

This study presents a novel approach for enhancing the performance of one of the promising systems in the field of energy harvesting, namely the standing wave thermoacoustic engine. Currently, conventional thermoacoustic engines have been integrated with piezoelectric membranes to harness the acoustic energy associated with this class of engines. In these thermoacoustic-piezoelectric (TAP) harvesters, the acoustic to electric energy conversion efficiency vary typically from 10% to 15%. In this paper, an attempt is made to magnify the electric energy harnessed from the piezo membranes by providing the harvester with a dynamic magnifier. The proposed system will be referred to as a dynamically magnified thermoacoustic-piezo system (DMTAP). The main purpose of the dynamic magnifier, as implied by the name, is to magnify the strain experienced by the piezo-element. With proper selection of the design parameters of such a magnifier, the output power can be significantly increased. The theory as well as the equations governing the operation of the system before and after the addition of the dynamic magnification is presented. Numerical examples are provided to illustrate the performance characteristics and merits of the improved (DMTAP) system as compared with those of a conventional TAP.

On the spatial sampling and beat effects in discrete wave profiles of lumped acoustic metamaterials

Acoustic metamaterials are sub-wavelength locally resonant structures known for their band gap behavior and unique response. To capture their working mechanisms, the analysis typically discretizes the continuum model into lumped cells at the interface with the resonators with a cell size chosen appropriately to satisfy homogenization limits. This paper investigates steady-state wave profiles computed from the numerically obtained displacement field of the adjacent discrete cells. It is shown that predicted wave properties often deviate from those obtained via dispersion analysis of the unit cell. For a metamaterial comprised of a finite series of locally resonant cells, the resolution of the discretized waves on both sides of the band gap depends heavily on the shape of the dispersion branches, excitation frequencies, spacing, and properties of the cell constituents. A few examples are used to show the effect of these parameters on the spatial sampling of the propagating wave at both acoustic and optic modes, and the consequences of inadequate resolution on the harmonic response such as apparent modulation of longer wavelengths and beat-like effects in the resultant profiles. These effects are explained in light of defined parameters such as the number of cells per wavelength and the equivalent spatial Nyquist rate.

Pole distribution in finite phononic crystals: Understanding Bragg-effects through closed-form system dynamics

Bragg band gaps associated with infinite phononic crystals are predicted using wave dispersion models. This paper departs from the Bloch-wave solution and presents a comprehensive dynamic systems analysis of finite phononic systems. Closed form transfer functions are derived for two systems where phononic effects are achieved by periodic variation of material property and boundary conditions. Using band structures, differences in dispersion characteristics are highlighted and followed by an analytical derivation of the eigenvalues. The latter is used to derive the end-to-end transfer function of a finite phononic crystal as a function of any given parameters. The analysis reveals intriguing features that explain the evolution of Bragg band gaps in the frequency response. It quantifies how the split of eigenvalues into sub- and super-band-gap natural frequencies contribute to band gap formation. The unique distribution of poles allows the closely packed sub-band gap natural frequencies to achieve maximum attenuation in the Bode response. At that point, the impact of the super-band-gap frequencies on the opposing side becomes significant causing the attenuation to fade and the band gap to come to an end. Finally, the effect of splitting the poles further apart is presented in both phononic systems, with material and boundary condition periodicities.

Formation of local resonance band gaps in finite acoustic metamaterials: A closed-form transfer function model

Abstract The objective of this paper is to use transfer functions to comprehend the formation of band gaps in locally resonant acoustic metamaterials. Identifying a recursive approach for any number of serially arranged locally resonant mass in mass cells, a closed form expression for the transfer function is derived. Analysis of the end-to-end transfer function helps identify the fundamental mechanism for the band gap formation in a finite metamaterial. This mechanism includes (a) repeated complex conjugate zeros located at the natural frequency of the individual local resonators, (b) the presence of two poles which flank the band gap, and (c) the absence of poles in the band-gap. Analysis of the finite cell dynamics are compared to the Bloch-wave analysis of infinitely long metamaterials to confirm the theoretical limits of the band gap estimated by the transfer function modeling. The analysis also explains how the band gap evolves as the number of cells in the metamaterial chain increases and highlights how the response varies depending on the chosen sensing location along the length of the metamaterial. The proposed transfer function approach to compute and evaluate band gaps in locally resonant structures provides a framework for the exploitation of control techniques to modify and tune band gaps in finite metamaterial realizations.

Optimum design of thermoacoustic-piezoelectric systems with dynamic magnifiers

This study presents optimum design strategies for selecting the parameters of a class of energy harvesters, namely thermoacoustic-piezoelectric (TAP) systems, in order to improve various metrics that govern its performance. Augmenting a conventional TAP harvester with a properly designed elastic structure in order to amplify the strain experienced by the piezo-element is shown to significantly increase both its output power and efficiency. The proposed system is referred to as a dynamically magnified thermoacoustic-piezoelectric (DMTAP) harvester. The optimum design parameters of the DMTAP harvester are selected based on optimizing multi-objective criteria including power, efficiency and temperature difference. The resulting optimal performance metrics are computed and compared with those obtained by conventional means. Several configurations of the DMTAP harvesters are optimized and the obtained results indicate that these harvesters are capable of achieving around 1.6 times the maximum efficiency and requiring only about three-quarters of the temperature difference necessary to produce self-sustained oscillations in the harvester, compared with conventional TAP devices of the same size.

Metamaterial structures with periodic local resonances

Vibration characteristics of metamaterial structures manufactured of assemblies of periodic cells with built-in local resonances are presented. Each cell consists of a base structure provided with cavities filled by a viscoelastic membrane that supports a small mass to form a source of local resonance. This class of metamaterial structures exhibits unique band gap behavior extending to very low frequency ranges. This work presents a physical realization of this class of metamaterials in the form of beams and plates with periodic local resonances. A finite element model (FEM) is developed to predict the modal, frequency response, and band gap characteristics of different configurations of the developed metamaterial structures. The model is exercised to demonstrate the structures’ band gap and mechanical filtering capabilities. The predictions of the FEM are validated experimentally when the structures are subjected to excitations ranging between 10-5000Hz. It is observed that there is excellent agreement between the theoretical predictions and the experimental results for plain structures, structures with cavities, and structures with cavities provided with local resonant sources. The obtained results emphasize the potential of the metamaterial beams and plates with periodic local resonances for providing significant vibration attenuation and exhibiting band gaps extending to low frequencies. Such characteristics indicate that metamaterial structures are more effective in attenuating and filtering low frequency structural vibrations than plain periodic structures of similar size and weight.

Analysis and optimization of thermoacoustic-piezoelectric energy harvesters: an electrical circuit analogy approach

The performance of standing and traveling wave thermoacoustic-piezoelectric energy harvesters are developed using an electrical circuit analogy approach. The harvesters convert thermal energy, such as solar or waste heat energy, directly into electrical energy without the need for any moving components. The input thermal energy generates a steep temperature gradient along a porous medium. At a critical threshold of the temperature gradient, self-sustained acoustic waves are developed inside an acoustic resonator. The associated pressure fluctuations impinge on a piezoelectric diaphragm, placed at the end of the resonator. The resulting interaction is accompanied by a direct conversion of the acoustic energy into electrical energy. The behavior of these two classes of harvesters is modeled using an electrical circuit analogy approach. The developed models are multi-field models which combine the descriptions of the acoustic resonator and the stack with the characteristics of the piezoelectric diaphragm. The onset of self-sustained oscillations of the harvesters are predicted using the root locus method and SPICE software (Simulation Program with Integrated Circuit Emphasis). The predictions are validated against published results. The developed electrical analogs and the associated analysis approach present invaluable tools for the design and the optimization of efficient thermoacoustic-piezoelectric energy harvesters.