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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Oxidation mechanism in a refractory multiple-principal-element alloy at high temperature

Refractory multiple-principal-element alloys (RMPEAs) are promising structural materials to enable increased power efficiency in high-temperature oxidation environments, but the oxidation behavior and microstructures of the oxides, especially at the beginning of the oxidation, have received limited attention. Here, the oxidation mechanism in an equimolar W-Mo-Ta-Nb-V was investigated at 1300 °C and compared with the equimolar W-Mo-Ta-Nb alloy without V. The oxide scale on WMoTaNbV after 1 min exposure is shown to be composed of a degradation layer at the interface of the alloy/oxide, an initial oxide transition layer, followed by the main phase aggregate oxide layer, and an outermost oxide layer. At the early stage of oxidation, the absorption of oxygen by the RMPEA substrate forms a solid solution. Vanadium accelerates the initial degradation process as it forms VO. The initial oxidation-induced degradation of RMPEA follows a sequence governed by the free energy change accompanied by local element segregation. Liquid V-Mo oxides aggregate in the intermediate oxide layer. The inward growth of the oxide scale is controlled by the local composition changes, the orientation of the substrate, the crystal structure, and physical properties such as melting points of the oxides.

36 MATERIALS SCIENCE↗
NASA NTRS1991

Measured and computed performance of a microstrip filter composed of semi-insulating GaAs on a fused quartz substrate

The performance of a microstrip hammerhead filter that has been fabricated on an electrically thin layer of semiinsulating GaAs backed by a fused quartz substrate was measured and compared to results of a three-dimensional finite-difference time-domain (FD-TD) program used to calculate the response of the filter both with and without the GaAs layer. The program, presented by Sheen et al. (1990), discretizes the entire structure and then simulates the propagation of a Gaussian pulse through the filter. The microstrip filter is intended for applications involving ultrathin lifted-off or etched-back GaAs containing both active devices and passive microstrip circuitry backed by a much thicker mechanically rigid low-loss, low-dielectric-constant substrate. The low-pass characteristics of the hammerhead filter with the intermediate GaAs layer are compared with those of the same filter on quartz alone. Both the measured and computed data show a significant shift in cutoff frequency (about 10 percent at the 3 dB points) for a GaAs layer that is 0.007 wavelengths thick at 4 GHz.

Siegel, Peter H.↗
DOE OSTI2024

Unraveling the Highly Plastic Behavior of ALD-Aluminum Oxide Encapsulations by Small-Scale Tensile Testing

We present a study directly measuring the electron-beam-induced plasticity of amorphous Al 2 O 3 coatings. Core–shell nanostructures are employed as small-scale model systems for two-dimensional coatings made by atomic layer deposition (ALD). Copper nanowires (NWs) are used as substrates for ALD deposition, representing a model system for interconnects commonly found in integrated circuits. Experiments are performed in situ in a transmission electron microscope (TEM) and further analyzed with electron energy loss spectroscopy (EELS). Our in situ TEM tensile experiments reveal the highly plastic behavior of the ALD shell, which withstands a maximum strain of 188%. Comparable samples under beam-off conditions show a brittle fracture, which underlines the effect of electron irradiation. The electron-beam-activated bond switching within the amorphous network enables compensation of the applied tensile strain, leading to viscous flow. By incorporating an intermediate nanocrystalline layer within the Al 2 O 3 shell, the plasticity is suppressed and brittle fracture occurs. This work directly demonstrates the tuning of mechanical properties in amorphous ALD structures through electron irradiation.

36 MATERIALS SCIENCE↗
NASA NTRS1972

Acoustic fatigue and sound transmission characteristics of a ram composite panel design

An experimental study to determine the acoustic fatigue characteristics of a flat multi-layered structural panel is described. The test panel represented a proposed design for the outer skin of a research application module to be housed within the space shuttle orbiter vehicle. The test specimen was mounted in one wall of the Wyle 100,000 cu ft reverberation room and exposed to a broadband acoustic environment having an overall level of 145 db. The test panel was exposed to nine separate applications of the acoustic environment, each application consisting of 250 seconds duration. Upon completion of the ninth test run, the specimen was exposed to a simulated micrometeoroid impact near the panel center. One additional test run of 250 seconds duration was then performed to complete the overall simulation of 50 flight missions. The experimental results show that no significant fatigue damage occurred until the test specimen was exposed to a simulated micrometeoroid impact. The intermediate foam layer forming the core of the test specimen suffered considerable damage due to this impact, causing a marked variation in the dynamic characteristics of the overall test panel. During the final application of the acoustic environment, the strain and acceleration response spectra showed considerable variation from those spectra obtained prior to impact of the panel. Fatigue damage from acoustic loading however, was limited to partial de-bonding around the edges of the composite panel.

Cockburn, J. A.↗
DOE OSTI2021

Convergent Hydraulic Redistribution and Groundwater Access Supported Facilitative Dependency Between Trees and Grasses in a Semi‐Arid Environment

Abstract Hydraulic redistribution is the transport of water from wet to dry soil layers, upward or downward, through plant roots. Often in savanna and woodland ecosystems, deep‐rooted trees, and shallow‐rooted grasses coexist. The degree to which these different species compete for or share soil‐water derived from precipitation or groundwater, as well as how these interactions are altered by hydraulic redistribution, is unknown. We use a multilayer canopy model and field observations to examine how the presence of deep, but tree‐root accessible, groundwater impacts seasonal patterns of hydraulic redistribution, and interaction between coexisting vegetation species in a semiarid riparian woodland (US‐CMW). Based on the simulation, trees absorb moisture at the water table (∼10 m depth) and release it in the shallow soil depth (0–3 m) during the dry pre‐monsoon season. We observed the occurrence of a new convergent hydraulic redistribution pattern during the monsoon season, where moisture is transported from both the near‐surface (0–0.5 m) and the water table to intermediate soil layers (1–5 m) through tree roots. We found that hydraulic redistribution demonstrates a growth facilitation effect at this site, supporting 49% of growing season tree transpiration and 14% of the grass transpiration. Compared to a similarly structured upland savanna without accessible groundwater, the riparian site shows an increased amount of hydraulically redistributed water and more facilitative water use between coexisting grasses and trees. These results shed light on the linkage between accessible groundwater and the role of hydraulic redistribution on the interaction between deep‐rooted and shallow‐rooted vegetation.

Lee, E.↗
DOE OSTI2024

Making Uintah Performance Portable for Department of Energy Exascale Testbeds

To help ease ports to forthcoming Department of Energy (DOE) exascale systems, testbeds have been made available to select users. These testbeds are helpful for preparing codes to run on the same hardware and similar software as in their respective exascale systems. This paper describes how the Uintah Computational Framework, an open-source asynchronous many-task (AMT) runtime system, has been modified to be performance portable across the DOE Crusher, DOE Polaris, and DOE Sunspot testbeds in preparation for portable simulations across the exascale DOE Frontier and DOE Aurora systems. The Crusher, Polaris, and Sunspot testbeds feature the AMD MI250X, NVIDIA A100, and Intel PVC GPUs, respectively. This performance portability has been made possible by extending Uintah’s intermediate portability layer [18] to additionally support the Kokkos::HIP, Kokkos::OpenMPTarget, and Kokkos::SYCL back-ends. This paper also describes notable updates to Uintah’s support for Kokkos, which were required to make this extension possible. Results are shown for a challenging radiative heat transfer calculation, central to the University of Utah’s predictive boiler simulations. These results demonstrate single-source portability across AMD-, NVIDIA-, and Intel-based GPUs using various Kokkos back-ends.

Holmen, John↗
DOE OSTI2022

A performance comparison between GaInP-on-Si and GaAs-on-Si 3-terminal tandem solar cells

The pursuit of ever-higher solar cell efficiencies has focused heavily on multijunction technologies. In tandem cells, subcells are typically either contacted via two terminals (2T) or four terminals (4T). Simulations show that the less-common three-terminal (3T) design may be comparable to 4T tandem cells in its compatibility with a range of materials, operating conditions, and methods for subcell integration, yet the 3T design circumvents shading losses of the 4T intermediate conductive layers. This study analyzes the performance of two superstrate 3T III-V-on-Si (III-V//Si) tandem cells: One has slightly greater current contribution from the Si bottom cell (GaInP//Si) and the other has substantially greater current contribution from the GaAs top cell (GaAs//Si). Our results show that both tandem cells exhibit the same efficiency (21.3%), thereby demonstrating that the third terminal allows for flexibility in the selection of the top cell material, similar to the 4T design.

14 SOLAR ENERGY↗
DOE OSTI2024

Enhanced Stability and Sensitivity for CA-125 Detection Under Microfluidic Shear Flow Using Polyethylene Glycol-Coated Biosensor

The microfluidic-based point-of-care (POC) diagnostic tool has garnered significant interest in recent years, offering rapid and cost-effective disease detection. There is a growing trend toward integrating microfluidic platforms with biosensors, aligning lab-on-a-chip technologies with POC diagnostic devices. Despite numerous efforts to incorporate biosensors into microfluidic systems, researchers have performed very limited investigations on the stability of biomarker detection when biosensors operate under microfluidic shear flow conditions. Gold nanoparticles (AuNPs) are a widely employed material in capacitive biosensors for antibody immobilization and sensitivity enhancement. However, AuNPs have limitations in providing stable detection of biomarkers within microfluidic shear flow due to their agglomeration nature. This study addresses these limitations by employing 2 kDa polyethylene glycol (PEG) as an intermediate biofunctional layer to immobilize CA-125 antibodies on gold-interdigitated electrodes for the stable and accurate detection of CA-125 antigens. The stabilities and sensitivities of AuNPs and PEG-coated biosensors are evaluated under both static drop and microfluidic shear flow conditions for CA-125 antigen detection. The experimental results demonstrate a capacitive signal response (5660 pF at 10 kHz) 2.2 times higher using the PEG-coated biosensor than the signal (2551 pF at 10 kHz) measured by the AuNP-coated biosensor in the detection of CA-125 antigen–antibody conjugation under static drop conditions, indicating the higher sensitivity of the PEG-coated biosensor. Additionally, the PEG-coated biosensor exhibits better consistency for the CA-125 antigen detection between static drop and microfluidic shear flow conditions (Cp decrease in percentage (ΔCp%↓) = 2.9% at 10 kHz) compared to the electrical signals measured using the AuNP-coated biosensor (ΔCp%↓ = 32.4% at 10 kHz), which suggests that the PEG-coated biosensor demonstrates higher stability for CA-125 antigen detection under microfluidic shear flow conditions. With these significant improvements brought by the PEG-coated biosensor, especially under microfluidic conditions, a substantial hurdle in developing electrical biosensors for POC diagnostic applications has been overcome, expediting further advancements in the field.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Type-I CdS/ZnS Core/Shell Quantum Dot-Gold Heterostructural Nanocrystals for Enhanced Photocatalytic Hydrogen Generation

Developing Type-I core/shell quantum dots is of great importance toward fabricating stable and sustainable photocatalysts. However, the application of Type-I systems has been limited due to the strongly confined photogenerated charges by the energy barrier originating from the wide-bandgap shell material. In this project, we found that through the decoration of Au satellite-type domains on the surface of Type-I CdS/ZnS core/shell quantum dots, such an energy barrier can be effectively overcome and an over 400-fold enhancement of photocatalytic H(2) evolution rate was achieved compared to bare CdS/ZnS quantum dots. Transient absorption spectroscopic studies indicated that the charges can be effectively extracted and subsequently transferred to surrounding molecular substrates in a subpicosecond time scale in such hybrid nanocrystals. Based on density functional theory calculations, the ultrafast charge separation rates were ascribed to the formation of intermediate Au2S layer at the semiconductor-metal interface, which can successfully offset the energy confinement introduced by the ZnS shell. In conclusion, our findings not only provide insightful understandings on charge carrier dynamics in semiconductor-metal heterostructural materials but also pave the way for the future design of quantum dot-based hybrid photocatalytic systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Baroclinic Residual Circulation and Mass Transport Due to Internal Tides

Baroclinic (BC) tidal residual circulation due to internal tides is investigated around islands over a shallow ridge using a numerical ocean model. Internal tides enhance vertical mixing over shallow slopes, leading to horizontal density gradients that drive BC residual circulation along the main thermocline. For a strongly stratified summer case, the vertical diffusivity estimated by the Mellor and Yamada turbulence closure model exceeds 1 × 10 -2 m 2 s -1 , and the velocity of BC residual circulations reaches 0.2 m s -1 . The magnitude of BC residual circulation is larger than that of barotropic residual tidal circulation, implying that BC residual circulation due to internal tides plays an important role in coastal ocean circulation. Furthermore, BC residual flow accounts for an equal percentage (5%) of the total tidal kinetic energy as the barotropic residual flow under summer stratification conditions. Results from a coupled sediment resuspension and transport model show the growth of intermediate nepheloid layers formed by strong bottom shear stress and BC residual flow. The residual component contributes largely (23% of the total in summer) to the total suspended sediment flux. Seasonal variability is explored, with weaker winter stratification leading to reduced mixing, and thus weaker BC residual circulation and sediment flux. Lastly, the magnitude of the BC residual circulation is also shown to be proportional to the square of the tidal amplitude.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Model fusion with physics-guided machine learning: Projection-based reduced-order modeling

The unprecedented amount of data generated from experiments, field observations, and large-scale numerical simulations at a wide range of spatiotemporal scales has enabled the rapid advancement of data-driven and especially deep learning models in the field of fluid mechanics. Although these methods are proven successful for many applications, there is a grand challenge of improving their generalizability. This is particularly essential when data-driven models are employed within outer-loop applications like optimization. In this work, we put forth a physics-guided machine learning (PGML) framework that leverages the interpretable physics-based model with a deep learning model. Leveraging a concatenated neural network design from multi-modal data sources, the PGML framework is capable of enhancing the generalizability of data-driven models and effectively protects against or inform about the inaccurate predictions resulting from extrapolation. We apply the PGML framework as a novel model fusion approach combining the physics-based Galerkin projection model and long- to short-term memory (LSTM) network for parametric model order reduction of fluid flows. We demonstrate the improved generalizability of the PGML framework against a purely data-driven approach through the injection of physics features into intermediate LSTM layers. Our quantitative analysis shows that the overall model uncertainty can be reduced through the PGML approach, especially for test data coming from a distribution different than the training data. Moreover, we demonstrate that our approach can be used as an inverse diagnostic tool providing a confidence score associated with models and observations. The proposed framework also allows for multi-fidelity computing by making use of low-fidelity models in the online deployment of quantified data-driven models.

42 ENGINEERING↗
DOE OSTI2022

Temporal and spatial laser intensification within nodular defects overcoated with multilayer dielectric mirrors over a wide range of defect geometries

The nodular defect shape and the laser incidence angle have a dramatic impact on the spatial distribution of light intensification within the nodule as well as how the laser light is drained from the defect. Nodular defect geometries unique to ion beam sputtering, ion-assisted deposition, and electron-beam (e-beam) deposition, respectively, are modeled in this parametric study over a wide range of nodular inclusion diameters and layer count for optical interference mirror coatings constructed with quarter-wave thicknesses and capped with a half wave of the low index material. It was found for hafnia ($n$=1.9) and silica ($n$=1.45) multilayer mirrors that the light intensification in nodular defects with a $C$ factor of 8, typical of e-beam deposited coatings deposited with a wide range of deposition angles, was maximized for a 24-layer design. For intermediate size inclusion diameters, increasing the layer count for normal incidence multilayer mirrors reduced the light intensification within the nodular defect. A second parametric study explored the impact of the nodule shape on the light intensification for a fixed number of layers. In this case, there is a strong temporal trend for the different nodule shapes. Narrow nodules tend to drain more laser energy through the bottom of the nodule into the substrate while wide nodules tend to drain more laser energy through the top of the nodule when irradiated at normal incidence. Further, at a 45° incidence angle, waveguiding is an additional method to drain laser energy from the nodular defect. Finally, laser light resonates within nodular defects longer than within the adjacent nondefective multilayer structure.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Grid-Connected Modular Soft-Switching Solid State Transformers (M-S4T)

The objective of this project is to develop and verify the concept of a flexible and modular soft-switching solid-state transformer (M-S4T) for direct grid-connected applications. The ability to directly connect power electronics converters to the medium voltage grid (4 kV – 13 kV), and to potentially replace the passive and bulky, but ubiquitous 60 hertz service transformer in the 25 kVA to 100 kVA range, with a more flexible and controllable device, has been regarded as the ‘holy grail’ in grid control. However, this has proven to be extremely difficult. This project has developed the solutions to several key challenges of the direct grid-connected power electronics and realized a 7.2 kV M-S4T prototype. First, a protection method to protect the M-S4T from the high voltages (110 kV for the 13 kV system) that occur on the grid due to transients and lightning strikes have been developed and experimentally verified. Second, the realization and the operation of the M-S4T based on high-voltage SiC devices (>3.3 kV) and a medium-frequency medium-voltage low-leakage transformer in a single-stage solid-state transformer with zero-voltage switching, low dv/dt, and low electromagnetic interference has been successfully demonstrated up to 7.5 kV peak. Third, an oil-cooling system and stable communication and distributed control system for converter module voltage sharing have been developed and experimentally verified. The developed M-S4T has realized a modular universal high-performance power conversion system. This conversion system is scalable to different voltage and power levels and adaptable to four-quadrant bidirectional operation. Moreover, the use of passive cooling techniques meets the equipment life requirements, and the lightning protection scheme fulfills the basic insulation level specifications for direct grid connection. Such power conversion system opens up near-term opportunities, including energy storage, solar PV, or electric vehicle charging with significant cost and footprint savings. In the longer term, the possibility of replacing the utility distribution transformer with an M-S4T will be transformative for future distribution grids with a compact footprint and full controllability to enable high renewable energy and storage penetration. In addition to the main project, this report expands on the Plus-Up projected including as part of the main award. This project developed and demonstrated the technology for autonomous collaborative inverters that can be connected in an ad hoc manner to the grid. The aim of the project was to: (1) evaluate the existing techniques for grid-connected inverters and find their limitations; (2) develop detailed requirements for grid-connected inverters in the modern grid with millions of active nodes; (3) design a unified control strategy that brings more autonomy and intelligence to grid-connected inverters, and addresses parts of the issues with the existing techniques. The proposed technique, called UniCon, enables inverters to 1) connect/disconnect to/from the grid in an ad hoc manner; (2) work based on local sensing. Slow communication could be used for a more optimized behavior; (3) work automatically in both grid-forming/grid-following mode; (4) handle large disturbances, e.g., big load step and fault, in an oscillation-free manner; (5) work collaboratively with other inverters in steady-state and during transients. UniCon can be implemented in the middle-level control; hence it is agnostic to the vendor and to the implementation of the inner voltage/current and protection loops. Furthermore, a new synchronization scheme, based on deep learning, was developed that can extract the grid voltage phase and amplitude in a stable manner. The method is cheap to implement can improve the dynamic performance of the grid-connected inverters during fast transients, e.g., fault. The proposed control scheme was validated by (1) MATLAB/Simulink; (2) hardware-in-the-loop results, and; (3) experimental results using three inverters that form a microgrid in a down-scaled feeder. Lastly, both the M-S4T and UniCon have achieved promising tangible paths to markets. In the case of the M-S4T, the underlying technology — the Soft Switching Solid State Transformer (S4T) developed at the Georgia Tech Center for Distributed Energy (GT-CDE) has been licensed by GridBlock from the Georgia Tech Research Corporation, and GridBlock has been working with manufacturing partner Jabil (one of the largest US-based contract manufacturers) and system integrator Power Secure (largest deployer of microgrids in the US with 4.7 GW under management), to meet the strong initial demand. Similarly, GridBlock has an exclusive license to the UniCon technology, developed under this award by GT-CDE. The UniCon provides an intermediate control layer that enables the implementation of the higher-level ‘transactive’ control commands for the system. The architecture of the system - slow communications with the cloud for system optimization and setpoints, and the use of locally measured quantities for real-time control, provide a very robust and secure way of implementing a real-time must-run grid that is also secure and stable. This is a brand-new functionality that is critical for the future grid and key to GridBlock’s business model.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1976

Shear strength of metal-sapphire contacts

The shear strength of polycrystalline Ag, Cu, Ni, and Fe contacts on clean (0001) sapphire has been studied in ultrahigh vacuum. Both clean metal surfaces and surfaces exposed to O2, Cl2, and C2H4 were used. The results indicate that there are two sources of strength of Al2O3-metal contacts: an intrinsic one that depends on the particular clean metal in contact with Al2O3 and an additional one due to intermediate films. The shear strength of the clean metal contacts correlated directly with the free energy of oxide formation for the lowest metal oxide, in accord with the hypothesis that a chemical bond is formed between metal cations and oxygen anions in the sapphire surface. Contacts formed by metals exposed to chlorine exhibited uniformly low shear strength indicative of van der Waals bonding between chlorinated metal surfaces and sapphire. Contacts formed by metals exposed to oxygen exhibited enhanced shear strength, in accord with the hypothesis that an intermediate oxide layer increases interfacial strength.

Pepper, S. V.↗
NASA NTRS1985

GaAs Schottky barrier photo-responsive device and method of fabrication

A gallium arsenide photo-responsive device is provided with an intermediate, transparent layer of a refractory metal or alkaline earth metal forming a tenacious bond between a non-hydroscopic oxide layer and a noble metal Schottky barrier layer. The device has a gallium arsenide substrate with a predetermined type conductivity and a gallium arsenide epitaxial layer with the same type conductivity but a lower charge carrier concentration grown on the substrate. The oxide layer is formed to cover the epitaxial layer, and the transparent metal layer followed by the noble metal layer are deposited upon the oxide layer. An interdigitated ohmic contact is then formed upon the noble metal layer.

Alcorn, G. E.↗
NASA NTRS1991

Composite Struts Would Damp Vibrations

New design of composite-material (fiber/matrix laminate) struts increases damping of longitudinal vibrations without decreasing longitudinal stiffness or increasing weight significantly. Plies with opposing chevron patterns of fibers convert longitudinal vibrational stresses into shear stresses in intermediate viscoelastic layer, which dissipate vibrational energy. Composite strut stronger than aluminum strut of same weight and stiffness.

Dolgin, Benjamin P.↗
NASA NTRS1989

Alkali metal-refractory metal biphase electrode for AMTEC

An electrode having increased output with slower degradation is formed of a film applied to a beta-alumina solid electrolyte (BASE). The film comprises a refractory first metal M.sup.1 such as a platinum group metal, suitably platinum or rhodium, capable of forming a liquid or a strong surface adsorption phase with sodium at the operating temperature of an alkali metal thermoelectric converter (AMTEC) and a second refractory metal insoluble in sodium or the NaM.sup.1 liquid phase such as a Group IVB, VB or VIB metal, suitably tungsten, molybdenum, tantalum or niobium. The liquid phase or surface film provides fast transport through the electrode while the insoluble refractory metal provides a structural matrix for the electrode during operation. A trilayer structure that is stable and not subject to deadhesion comprises a first, thin layer of tungsten, an intermediate co-deposited layer of tungsten-platinum and a thin surface layer of platinum.

Williams, Roger M.↗
NASA NTRS2008

Using Piezoelectric Devices to Transmit Power through Walls

A method denoted wireless acoustic-electric feed-through (WAEF) has been conceived for transmitting power and/or data signals through walls or other solid objects made of a variety of elastic materials that could be electrically conductive or nonconductive. WAEF would make it unnecessary to use wires, optical fibers, tubes, or other discrete wall-penetrating signal-transmitting components, thereby eliminating the potential for structural weakening or leakage at such penetrations. Avoidance of such penetrations could be essential in some applications in which maintenance of pressure, vacuum, or chemical or biological isolation is required. In a basic WAEF setup, a transmitting piezoelectric transducer on one side of a wall would be driven at resonance to excite ultrasonic vibrations in the wall. A receiving piezoelectric transducer on the opposite side of the wall would convert the vibrations back to an ultrasonic AC electric signal, which would then be detected and otherwise processed in a manner that would depend on the modulation (if any) applied to the signal and whether the signal was used to transmit power, data, or both. An electromechanical-network model has been derived as a computationally efficient means of analyzing and designing a WAEF system. This model is a variant of a prior model, known in the piezoelectric-transducer art as Mason's equivalent-circuit model, in which the electrical and mechanical dynamics, including electromechanical couplings, are expressed as electrical circuit elements that can include inductors, capacitors, and lumped-parameter complex impedances. The real parts of the complex impedances are used to account for dielectric, mechanical, and coupling losses in all components (including all piezoelectric-transducer, wall, and intermediate material layers). In an application to a three-layer piezoelectric structure, this model was shown to yield the same results as do solutions of the wave equations of piezoelectricity and acoustic propagation in their full complexity.

Sherrit, Stewart↗