Jason A. Kulpe

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.

Bloch-wave expansion technique for predicting wave reflection and transmission in two-dimensional phononic crystals

In this paper acoustic wave reflection and transmission are studied at the interface between a phononic crystal (PC) and a homogeneous medium using a Bloch wave expansion technique. A finite element analysis of the PC yields the requisite dispersion relationships and a complete set of Bloch waves, which in turn are employed to expand the transmitted pressure field. A solution for the reflected and transmitted wave fields is then obtained using continuity conditions at the half-space interface. The method introduces a group velocity criterion for Bloch wave selection, which when not enforced, is shown to yield non-physical results. Following development, the approach is applied to example PCs and results are compared to detailed numerical solutions, yielding very good agreement. The approach is also employed to uncover bands of incidence angles whereby perfect acoustic reflection from the PC occurs, even for frequencies outside of stop bands.

A three-dimensional Bloch wave expansion to determine external scattering from finite phononic crystals

External scattering from a finite phononic crystal (PC) is studied using the Helmholtz-Kirchhoff integral theorem integrated with a Bloch wave expansion (BWE). The BWE technique is used to describe the internal pressure field of a semi-infinite or layered PC subject to an incident monochromatic plane wave. Following the BWE solution, the Helmholtz-Kirchhoff integral is used to determine the external scattered field. For cubic PCs, the scattered results are compared to numerical treatments in both the frequency and time domain. The presented approach is expected to be valid when the PC size is larger than the acoustic wavelength. However, very good agreement in the spatial beam pattern is also documented for both large and small (with respect to the wavelength) PCs. The result of this work is a fully-analytical, efficient, and verified approach for accurately predicting external scattering from finite, three-dimensional PCs.

Computation of acoustic absorption in media composed of packed microtubes exhibiting surface irregularity.

A multi-scale homogenization technique and a finite element-based solution procedure are employed to compute acoustic absorption in smooth and rough packed microtubes. The absorption considered arises from thermo-viscous interactions between the fluid media and the microtube walls. The homogenization technique requires geometric periodicity, which for smooth tubes is invoked using the periodicity of the finite element mesh; for rough microtubes, the periodicity invoked is that associated with the roughness. Analysis of the packed configurations, for the specific microtube radii considered, demonstrates that surface roughness does not appreciably increase the overall absorption, but instead shifts the peaks and values of the absorption curve. Additionally, the effect of the fluid media temperature on acoustic absorption is also explored. The results of the investigation are used to make conclusions about tailored design of acoustically absorbing microtube-based materials.

Acoustic scattering from phononic crystals with complex geometry.

This work introduces a formalism for computing external acoustic scattering from phononic crystals (PCs) with arbitrary exterior shape using a Bloch wave expansion technique coupled with the Helmholtz-Kirchhoff integral (HKI). Similar to a Kirchhoff approximation, a geometrically complex PCs surface is broken into a set of facets in which the scattering from each facet is calculated as if it was a semi-infinite plane interface in the short wavelength limit. When excited by incident radiation, these facets introduce wave modes into the interior of the PC. Incorporation of these modes in the HKI, summed over all facets, then determines the externally scattered acoustic field. In particular, for frequencies in a complete bandgap (the usual operating frequency regime of many PC-based devices and the requisite operating regime of the presented theory), no need exists to solve for internal reflections from oppositely facing edges and, thus, the total scattered field can be computed without the need to consider internal multiple scattering. Several numerical examples are provided to verify the presented approach. Both harmonic and transient results are considered for spherical and bean-shaped PCs, each containing over 100 000 inclusions. This facet formalism is validated by comparison to an existing self-consistent scattering technique.

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.

Determination of Acoustic Scattering From a Two-Dimensional Finite Phononic Crystal Using Bloch Wave Expansion

In this study the acoustic scattering is determined from a finite phononic crystal through an implementation of the Helmholtz-Kirchhoff integral theorem. The approach employs the Bloch theorem applied to a semi-infinite phononic crystal (PC) half-space. The internal pressure field of the half-space, subject to an incident acoustic monochromatic plane wave, is formulated as an expansion of the Bloch wave modes. Modal coefficients of reflected (diffracted) plane waves are arrived at via boundary condition considerations on the PC interface. Next, the PC inter-facial pressure, as determined by the Bloch wave expansion (BWE), is employed along with the Helmholtz-Kirchhoff integral equation to compute the scattered pressure from a large finite PC. Under a short wavelength limit approximation (wavelength much smaller than finite PC dimensions), the integral approach is employed to calculate the scattered pressure field for a large PC subject to an incident wave with two distinct incident angles. In two dimensions we demonstrate good agreement of scattered pressure results of large finite PC when compared against detailed finite element calculations. The work here demonstrates an efficient and accurate uniform computational framework for modeling the scattered and internal pressure fields of a large finite phononic crystal.Copyright

Broadband performance of a patterned piezoelectric energy harvester integrated with a continuous elastoacoustic mirror

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.