Non-reciprocal wave propagation in elastic structures has received considerable attention lately. A common mechanism to break elastic wave reciprocity is the use of phononic materials with traveling-wave-like properties. Among the popular methods to study wave dispersion in periodic media are the plane wave expansion and transfer matrix method (TMM). However, owing to the time-variant nature of such non-reciprocal systems, the implementation of both methods requires the truncation of harmonic terms. In this work, we adopt the TMM to extract the dispersion patterns of a moving phononic material with a prescribed velocity. In the presence of a temporal modulation of material properties in one direction accompanied by physical motion in an opposing direction, both effects cancel out and the problem becomes effectively time-invariant. This facilitates the analysis and yields interesting results. Subsequently, we exploit the well-established relationship between the momentumenergy spaces of moving and stationary elastic media to reconstruct exact dispersion diagrams of a stationary space-time-periodic system. The proposed approach provides a platform to incorporate the TMM in the analysis of non-reciprocal time-variant materials. Finally, given the lack of harmonic truncation, the accuracy of the new method does not diminish as the modulating speed increases.
Thermoacoustic systems generate high amplitude sound pressure waves from a thermal input, which can then be harvested via piezoelectric transducers. While a promising concept, current thermoacoustic energy harvesters suffer inherent design limitations which result in: (1) low acoustic power output and simple construction or (2) a reasonable output in a significantly large apparatus (i.e. low power density). The challenge is centered around the working gas oscillations being predominantly standing waves which exhibit a pressure-velocity time phasing that is detrimental to the energy output of such harvesters. The goal of this work is to induce temporal phase adjustments in the excited acoustic waves inside a sealed cavity, thus boosting the amount of useful acoustic power which can be effectively scavenged. By employing open and closed-loop feedback control in a thermoacoustic tube with dual sensing and actuating piezoelectric transducers located at two opposing ends, it is shown that the traveling wave portion of the resultant wave dynamics can be significantly increased with a relatively low level of power pumped into the system. As a result, the controlled device outperforms a conventional one of the same size and configuration and approaches the maximum theoretical potential of thermoacoustic energy harvesting.
Considerable research attention has been recently devoted to the study of periodic structures given their unique wave dispersion. Phononic crystals and acoustic metamaterials have emerged as two main categories of such periodic structures that can exhibit radically different band gap characteristics. Here, we present a novel configuration that combines hybrid wave attenuation attributes culminating in enhanced metadamping and energy dissipation properties. The results are compared with a benchmark example from literature to show the potential of the new design.
This work presents an effort to understand the evolution of Bragg scattering band gaps in the context of the transfer functions of finite Phononic Crystals (PCs). Following the dispersion analysis of an infinite PC based on a single unit cell, an analytical derivation of the natural frequencies of a finite PC with a given number of cells is presented. Next, the transfer function between the tip displacement of a finite PC and a force exerted at the other end is derived in closed-form, and used to establish an understanding of the band gap formation in the finite setting. The analysis reveals that the phenomenon can be attributed to the split of poles around the center of the band gap and the absence of any poles within it. The formation mechanism is then discussed in light of several numerical examples with different combinations of system parameters and number of cells.
Internal resonators in lumped spring-mass elastic metamaterials reveal unique wave dispersion characteristics. Using the Bloch-wave analysis and the Transfer Matrix Method (TMM), the band structure of a unit cell of a locally resonant metamaterial shows a band gap (region of near-perfect wave attenuation) despite the lack of any damping elements. This paper presents an analytical closed-form model of a finite metamaterial structure comprising a chain of unit cells to try to understand the band gap behavior. The poles and zeros of the derived transfer functions explain the formation mechanism of the band gap and ties the band structure predictions of the single cell to the structural dynamics of the resultant metamaterial.
Elastic metamaterials are sub-wavelength structures with locally resonant components that contribute to the rise of tunable stop bands, i.e. frequency ranges within which waves do not propagate. A new approach is presented here to quantify this stop band behavior by evaluating structural vibrational power in the different constituents of locally resonant metamaterials undergoing axial excitations. It is shown that the power flow patterns match wave propagation information extracted from the dispersion analysis of the metamaterial unit cell, and can thus be used to develop an algorithm that numerically predicts stop band frequencies for finite realizations with given dimensions and a known number of cells.
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.
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.
Thermoacoustic refrigeration is an emerging refrigeration technology which does not rely for in its operation
on the use of any moving parts or harmful refrigerants. This technology uses acoustic waves to pump heat across a
temperature gradient. The vast majority of thermoacoustic refrigerators to date have used electromagnetic
loudspeakers to generate the acoustic input. In this paper, the design, construction, operation, and modeling of a
piezoelectric-driven thermoacoustic refrigerator are detailed. This refrigerator demonstrates the effectiveness of
piezoelectric actuation in moving 0.3 W of heat across an 18 degree C temperature difference with an input power of
The performance characteristics of this class of thermoacoustic-piezoelectric refrigerator are modeled using
DeltaEC software and the predictions are validated experimentally. The obtained results confirm the validity of the
developed model. Furthermore, the potential of piezoelectric actuation as effective means for driving thermoacoustic
refrigerators is demonstrated as compared to the conventional electromagnetic loudspeakers which are heavy and
require high actuation energy.
The developed theoretical and experimental tools can serve as invaluable means for the design and testing of
other piezoelectric driven thermoacoustic refrigerator configurations.