Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “design pattern”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Moiré engineering in van der Waals heterostructures

Isolated atomic planes can be assembled into a multilayer van der Waals (vdW) heterostructure in a precisely chosen sequence. These heterostructures feature moiré patterns if the constituent 2D material layers are stacked in an incommensurable way, due to a lattice mismatch or twist. This design-by-stacking has opened up the promising area of moiré engineering, a term that can be understood in two different perspectives, namely, (i) structural—engineering a moiré pattern by introducing twist, relative strain, or defects that affect the commensurability of the layers and (ii) functional—exploiting a moiré pattern to find and tune resulting physical properties of a vdW heterostructure. The latter meaning, referring to the application of a moiré pattern, is seen in the literature in the specific context of the observation of correlated electronic states and unconventional superconductivity in twisted bilayer graphene. The former meaning, referring to the design of the moiré pattern itself, is present in the literature but less commonly discussed or less understood. The underlying link between these two perspectives lies in the deformation field of the moiré superlattice. In this Perspective, we describe a path from designing a moiré pattern to employing the moiré pattern to tune physical properties of a vdW heterostructure. We also discuss the concept of moiré engineering in the context of twistronics, strain engineering, and defect engineering in vdW heterostructures. Although twistronics is always associated with moiré superlattices, strain and defect engineering are often not. Here, in this work, we demonstrate how strain and defect engineering can be understood within the context of moiré engineering. Adopting this perspective, we note that moiré engineering creates a compelling opportunity to design and develop multiscale electronic devices.

2D materials↗
DOE OSTI2019

Design of semiconductor surface pits for fabrication of regular arrays of quantum dots and nanorings

We report a systematic computational study on the formation of complex nanostructures consisting of quantum dots and nanorings on surfaces of coherently strained thin films grown epitaxially on pit-patterned substrates. The analysis is based on self-consistent dynamical simulations according to a film surface evolution model that has been validated experimentally by comparison of its predictions with experimental observations on Ge films grown on Si pit-patterned substrates and is supported by linear stability theory that explains the film surface nanopattern formation as the outcome of a Stranski-Krastanow instability. Emphasis is placed on the design of conical pit patterns and the effects on the resulting film surface nanopattern of varying geometrical design parameters including film thickness, pit-pattern period, pit depth, pit opening diameter, and pit wall inclination. We demonstrate that varying the pit opening diameter and the pit wall slope leads to formation of complex nanostructures inside the pits of a regular pit pattern on the film surface, which include quantum dots, as well as single nanorings and multiple concentric nanorings that may or may not surround a central quantum dot inside each pit. Our simulation predictions demonstrate that the ordered nanostructure patterns forming on the film surface can be controlled precisely by tuning the geometrical parameters of the pits on the pit-patterned substrate. Our findings have important implications for designing optimal semiconductor surface patterns toward enabling future nanofabrication technologies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Channel capacity enhancement by adjustable graphene-based MIMO antenna in THz band

This paper offers the design of a graphene-based MIMO antenna with an adjustable radiation pattern for THz communications. To make the radiation pattern adjustable a superstrate layer of graphene based patch, is added to the designed MIMO antenna which increases Channel Capacity. In addition to adjustable radiation pattern, the gain of antenna in the main lobe is also increased. The losses of THz channel is investigated and the angle of the main lobe of the designed antenna is set to the angle with the lowest loss. The channel capacity is evaluated and compared with the antenna without the superstrate layer. It is shown that channel capacity is significantly enhanced.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2011

Frequency-Selective Near-Field Radiative Heat Transfer between Photonic Crystal Slabs: A Computational Approach for Arbitrary Geometries and Materials

Here, we demonstrate the possibility of achieving enhanced frequency-selective near-field radiative heat transfer between patterned (photonic-crystal) slabs at designable frequencies and separations, exploiting a general numerical approach for computing heat transfer in arbitrary geometries and materials based on the finite-difference time-domain method. Our simulations reveal a tradeoff between selectivity and near-field enhancement as the slab-slab separation decreases, with the patterned heat transfer eventually reducing to the unpatterned result multiplied by a fill factor (described by a standard proximity approximation). We also find that heat transfer can be further enhanced at selective frequencies when the slabs are brought into a glide-symmetric configuration, a consequence of the degeneracies associated with the nonsymmorphic symmetry group.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Power Grid Behavioral Patterns and Risks of Generalization in Applied Machine Learning

Recent years have seen a rich literature of data-driven approaches designed for power grid applications. However, insufficient consideration of domain knowledge can impose a high risk to the practicality of the methods. Specifically, ignoring the grid-specific spatiotemporal patterns (in load, generation, and topology, etc.) can lead to outputting infeasible, unrealizable, or completely meaningless predictions on new inputs. To address this concern, this paper investigates real-world operational data to provide insights into power grid behavioral patterns, including the time-varying topology, load, and generation, as well as the spatial differences (in peak hours, diverse styles) between individual loads and generations. Then based on these observations, we evaluate the generalization risks in some existing ML works caused by ignoring these grid-specific patterns in model design and training.

Li, Shimiao↗
DOE OSTI2012

Thorium Fuel Options for Sustained Transuranic Burning in Pressurized Water Reactors - 12381

As described in companion papers, Westinghouse is proposing the adoption of a thorium-based fuel cycle to burn the transuranics (TRU) contained in the current Used Nuclear Fuel (UNF) and transition towards a less radio-toxic high level waste. A combination of both light water reactors (LWR) and fast reactors (FR) is envisaged for the task, with the emphasis initially posed on their TRU burning capability and eventually to their self-sufficiency. Given the many technical challenges and development times related to the deployment of TRU burners fast reactors, an interim solution making best use of the current resources to initiate burning the legacy TRU inventory while developing and testing some technologies of later use is desirable. In this perspective, a portion of the LWR fleet can be used to start burning the legacy TRUs using Th-based fuels compatible with the current plants and operational features. This analysis focuses on a typical 4-loop PWR, with 17x17 fuel assembly design and TRUs (or Pu) admixed with Th (similar to U-MOX fuel, but with Th instead of U). Global calculations of the core were represented with unit assembly simulations using the Linear Reactivity Model (LRM). Several assembly configurations have been developed to offer two options that can be attractive during the TRU transmutation campaign: maximization of the TRU transmutation rate and capability for TRU multi-recycling, to extend the option of TRU recycling in LWR until the FR is available. Homogeneous as well as heterogeneous assembly configurations have been developed with various recycling schemes (Pu recycle, TRU recycle, TRU and in-bred U recycle etc.). Oxide as well as nitride fuels have been examined. This enabled an assessment of the potential for burning and multi-recycling TRU in a Th-based fuel PWR to compare against other more typical alternatives (U-MOX and variations thereof). Results will be shown indicating that Th-based PWR fuel is a promising option to multi-recycle and burn TRU in a thermal spectrum, while satisfying top-level operational and safety constraints. Various assembly designs have been proposed to assess the TRU burning potential of Th-based fuel in PWRs. In addition to typical homogeneous loading patterns, heterogeneous configurations exploiting the breeding potential of thorium to enable multiple cycles of TRU irradiation and burning have been devised. The homogeneous assembly design, with all pins featuring TRU in Th, has the benefit of a simple loading pattern and the highest rate of TRU transmutation, but it can be used only for a few cycles due to the rapid rise in the TRU content of the recycled fuel, which challenges reactivity control, safety coefficients and fuel handling. Due to its simple loading pattern, such assembly design can be used as the first step of Th implementation, achieving up to 3 times larger TRU transmutation rate than conventional U-MOX, assuming same fraction of MOX assemblies in the core. As the next step in thorium implementation, heterogeneous assemblies featuring a mixed array of Th-U and Th-U-TRU pins, where the U is in-bred from Th, have been proposed. These designs have the potential to enable burning an external supply of TRU through multiple cycles of irradiation, recovery (via reprocessing) and recycling of the residual actinides at the end of each irradiation cycle. This is achieved thanks to a larger breeding of U from Th in the heterogeneous assemblies, which reduces the TRU supply and thus mitigates the increase in the TRU core inventory for the multi-recycled fuel. While on an individual cycle basis the amount of TRU burned in the heterogeneous assembly is reduced with respect to the homogeneous design, TRU burning rates higher than single-pass U-MOX fuel can still be achieved, with the additional benefits of a multi-cycle transmutation campaign recycling all TRU isotopes. Nitride fuel, due its higher density and U breeding potential, together with its better thermal properties, ideally suits the objectives and constraints of the heterogeneous assemblies. However, significant technological advancements must be made before nitride fuels can be employed in an LWR: its water resistance needs to be improved and a viable technology to enrich N in N-15 must be devised. Moreover, for the nitride heterogeneous configurations examined in this study, the enhancement in TRU burning performance is achieved not only by replacing oxide with nitride fuel, but also by increasing the fuel rod size. This latter modification, allowed by the high thermal conductivity of nitride fuel, leads however to a very tight lattice, which may challenge reactor coolant pumps and assembly hold-down mechanisms, the former through an increase in core pressure drop and the latter through an increase in assembly lift-off forces. To alleviate these issues, while still achieving the large fuel-to-moderator ratios resulting from using tight lattices, wire wraps could be used in place of grid spacers. For tight lattices, typical grid spacers are hard to manufacture and their replacement with wire wraps is known to allow for a pressure drop reduction by at least 2 times. The studies, while certainly very preliminary, provide a starting point to devise an optimum strategy for TRU transmutation in Th-based PWR fuel. The viability of the scheme proposed depends on the timely phasing in of the associated technologies, with proper lead time and to solve the many challenges. These challenges are certainly substantial, and make the current once-through U-based scheme pursued in the US by far a more practical (and cheaper) option. However, when compared to other transmutation schemes, the proposed one has arguably similar challenges and unknowns with potentially bigger rewards. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2014

Study of optical Laue diffraction

We present the study of the optical diffraction pattern of one and two-dimensional gratings with defects, designed using desktop pc and printed on OHP sheet using laser printer. Gratings so prepared, using novel low cost technique provides good visual aid in teaching. Diffraction pattern of the monochromatic light (632.8nm) from the grating so designed is similar to that of x-ray diffraction pattern of crystal lattice with point defects in one and two-dimensions. Here both optical and x-ray diffractions are Fraunhofer. The information about the crystalline lattice structure and the defect size can be known.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Demonstration of a directional sonic prism in two dimensions using an air-acoustic leaky wave antenna

Analysis and experimental demonstration of a two-dimensional acoustic leaky wave antenna is presented for use in air. The antenna is comprised of a two-dimensional waveguide patterned with radiating acoustic shunts. When excited using a single acoustic source within the waveguide, the antenna acts as a sonic prism that exhibits frequency steering. This design allows for control of acoustic steering angle using only a single source transducer and a patterned aperture. Aperture design was determined using transmission line analysis and finite element methods. The designed antenna was fabricated and the steering angle measured. The performance of the measured aperture was within 9% of predicted angle magnitudes over all examined frequencies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Hierarchical probing for estimating the trace of the matrix inverse on toroidal lattices

The standard approach for computing the trace of the inverse of a very large, sparse matrix $A$ is to view the trace as the mean value of matrix quadratures, and use the Monte Carlo algorithm to estimate it. This approach is heavily used in our motivating application of Lattice QCD. Often, the elements of $A^{-1}$ display certain decay properties away from the non zero structure of $A$, but random vectors cannot exploit this induced structure of $A^{-1}$. Probing is a technique that, given a sparsity pattern of $A$, discovers elements of $A$ through matrix-vector multiplications with specially designed vectors. In the case of $A^{-1}$, the pattern is obtained by distance-$k$ coloring of the graph of $A$. For sufficiently large $k$, the method produces accurate trace estimates but the cost of producing the colorings becomes prohibitively expensive. More importantly, it is difficult to search for an optimal $k$ value, since none of the work for prior choices of $k$ can be reused.

Stathopoulos, Andreas↗
DOE OSTI2024

Mitigation for Removal of Building 01-103 in the Area 1 Subdock, Nevada National Security Site, Nye County, Nevada

Building 01-103, the Drill Bit Repair Building was originally recorded as SHPO Resource No. B18848 in 2020 during an architectural survey of the Area 1 Subdock (Collins et al. 2022). It was recommended individually eligible for listing in the NRHP under Criteria A and C and contributing to the significance of the Area 1 Subdock Historic District. The SHPO concurred with these determinations in a letter dated April 29, 2022 (Reed 2022). The Drill Bit Repair Building retains all seven aspects of integrity. The location, materials, workmanship, feeling, and association have not changed since its original construction. The design was modified slightly in 1996 with the addition of a removable and non-destructive chain-link fence. Nearby buildings 01-101 and 01-102 were removed (Collins and Menocal 2020) but the other buildings and storage yards remain. Therefore, the integrity of setting has been changed, but not to the degree that the building no longer conveys its significance (see Figures 4 and 5 for comparison). Building 01-103 was constructed in 1985 to coincide with the relocation of the Area 3 Subdock to Area 1. The design for the new Subdock provided a centralized cluster of buildings surrounded by two large storage yards. The buildings included administrative and engineering office space, warehouses, a radiograph building, and Building 01-103 as the drill bit maintenance and repair building, among others. The Drill Bit Repair Building was critical to the success of underground nuclear testing and is eligible under Criterion A for its contribution to broad patterns of history by maintaining specially designed equipment for underground nuclear testing at the NNSS. It is also eligible under Criterion C as it is the only recorded example of a facility built specifically for the maintenance of big-hole drill bits on the NNSS. As it retains both significance and integrity, it remains individually eligible under Criteria A and C. In addition to its individual significance, the Drill Bit Repair Building also contributes to the significance of the Area 1 Subdock Historic District as a representative of a big-hole drilling support facility necessary for underground nuclear testing. The building and the equipment therein were designed specifically for testing at the NNSS, where much of the early technology and methods for big-hole drilling were developed. Its removal will result in not only the demolition of a contributing element but also a change in the physical features of the district’s setting that contribute to its historic significance. The change in setting will diminish the district’s integrity. However, the district still contains numerous examples of other buildings constructed for the purpose of supporting big-hole drilling and remains eligible under Criteria A and C.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Thin-film ‘Thermal Well’ Emitters and Absorbers for High-Efficiency Thermophotovoltaics

Here, a new approach is introduced to significantly improve the performance of thermophotovoltaic (TPV) systems using low-dimensional thermal emitters and photovoltaic (PV) cells. By reducing the thickness of both the emitter and the PV cell, strong spectral selectivity in thermal emission and absorption can be achieved by confining photons in trapped waveguide modes inside the thin-films that act as thermal analogs to quantum wells. Simultaneously, photo-excited carriers travel shorter distances across the thin-films reducing bulk recombination losses resulting in a lower saturation current in the PV cell. We predict a TPV efficiency enhancement with near-field coupling between the thermal emitter and the PV cell up to 38.7% using a thin-film germanium (Ge) emitter at 1000 K and an ultra-thin gallium antimonide (GaSb) cell supported by perfect back reflectors separated by 100 nm. Even in the far-field limit, the efficiency is predicted to reach 31.5%, which is over an order of magnitude higher than the Shockley Queisser limit of 1.6% for a bulk GaSb cell and a blackbody emitter at 1000 K. The proposed design approach does not require nanoscale patterning of the emitter and PV cell surfaces, but instead offers a simple low-cost solution to improve the performance of thermophotovoltaic systems.

14 SOLAR ENERGY↗
DOE OSTI2023

Optimal design of chemoepitaxial guideposts for the directed self-assembly of block copolymer systems using an inexact Newton algorithm

Directed self-assembly (DSA) of block copolymers (BCPs) is one of the most promising developments in the cost-effective production of nanoscale devices. The process makes use of the natural tendency for BCP melts to form nanoscale structures upon phase separation. The phase separation can be directed through the use of chemically patterned substrates to promote the formation of morphologies that are essential to the production of semiconductor devices. Moreover, the design of substrate pattern can be formulated as an optimization problem for which we seek optimal substrate designs that effectively produce given target morphologies. In this paper, we adopt a phase field model given by a nonlocal Cahn–Hilliard partial differential equation (PDE) based on the minimization of the Ohta–Kawasaki free energy, and present an efficient PDE-constrained optimization framework for the optimal design problem. The design variables are the locations of circular- or strip-shaped guiding posts that are used to model the substrate chemical pattern. To solve the ensuing optimization problem, we propose a variant of an inexact Newton conjugate gradient algorithm tailored to this problem. Additionally, we demonstrate the effectiveness of our computational strategy on numerical examples that span a range of target morphologies. Owing to our second-order optimizer and fast state solver, the numerical results demonstrate five orders of magnitude reduction in computational cost over previous work. The efficiency of our framework and the fast convergence of our optimization algorithm enable us to rapidly solve the optimal design problem in not only two, but also three spatial dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Mitigation for Removal of Building 01-202681 in the Main Storage Yard of the Area 1 Subdock, Nevada National Security Site, Nye County, Nevada

The Main Storage Yard was originally recorded as SHPO Resource No. S2772 in 2020 during an architectural survey of the Area 1 Subdock (Collins et al. 2022). It was recommended individually eligible for listing in the NRHP under Criteria A and C and as contributing to the significance of the potential Area 1 Subdock Historic District. The SHPO concurred with these determinations in a letter dated April 29, 2022 (Reed). The Main Storage Yard retains all seven aspects of integrity. The location, design, materials, workmanship, feeling, and association have not changed since the original construction. Since the purpose of the yard is to maintain storage equipment that is actively being used, the design and feeling will change each time equipment is moved. Such actions reinforce the integrity of design and feeling. Buildings 01-101 and 01-102 were removed (Collins and Menocal 2020), but the other buildings and storage yard remain. Therefore, the setting has been changed, but not to the degree that the Main Storage Yard no longer conveys its significance (see Figures 4 and 5 for comparison). The Main Storage Yard was designed to facilitate the relocation of the Area 3 Subdock to Area 1 in 1985. The design for the overall Subdock provided a centralized cluster of buildings surrounded by two large storage yards. While the North Storage Yard largely serves as overflow storage, the Main Storage Yard holds the majority of drill rigs and drilling equipment needed to support big hole drilling. The Main Storage Yard and its contents were essential elements of the nuclear testing drilling program on the NNSS thus making it eligible for the NRHP under Criterion A for its contribution to broad patterns of history by storing specially designed equipment for underground nuclear testing at the NNSS. It is also eligible under Criterion C as it is an engineered landscape that now serves as an open-air repository of drilling technology and nuclear testing. In addition to its individual significance, the Main Storage Yard also contributes to the significance of the Area 1 Subdock Historic District as it showcases a variety of big-hole drilling equipment, support facilities, and warehouses that were specially designed for nuclear testing at the NNSS. Despite the demolition of two contributing elements to date, the district still contains numerous examples of other facilities with the purpose of supporting big-hole drilling; therefore, the district still remains eligible under Criteria A and C.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A helical actuator driven by biased SMA: design, model, and experiment

A helical actuator driven by biased shape memory alloy (SMA) patterns embedded into a soft composite ribbon base is presented in this work. Instead of common U-shape SMA wires, a single SMA wire is woven into planar patterns, which enable helical deformation of the composite ribbon from an initially flat geometry. An analytical static model is established for accurate and rapid prediction of the helical reconfiguration arising from the shape memory effect of woven SMA patterns, followed by validation of the static model using the finite element method (FEM). The finite element results are compared with the analytical solutions given by this static model, which show a high agreement. Parametric study of the influences of eight independent design variables on the dependent helical parameters, such as combined curvatures, pitches, and helical angles, is completed. It is found that the helically deformed geometry is mainly dominated by diameters, biased positions, inclined angles, and numbers of skewed segments of the SMA wire. Fabrication and in-situ experimental test of a prototype of such helical actuators qualitatively demonstrate its dramatic three-dimensional (3D) spiral reconfiguration from a two-dimensional (2D) flat ribbon. In conclusion, such SMA patterns will allow more diverse designs of soft actuators for a wider range of robotic applications.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Chemical Design of Spin Frustration to Realize Topological Spin Glasses

Patterning spins to generate collective behavior is at the core of condensed matter physics. Physicists develop techniques, including the fabrication of magnetic nanostructures and precision layering of materials specifically to engender frustrated lattices. As chemists, we can access such exotic materials through targeted chemical synthesis and create new lattice types by chemical design. Here, in this study, we introduce a new approach to induce magnetic frustration on a modified honeycomb lattice through a competition of alternating antiferromagnetic (AFM) and ferromagnetic (FM) nearest-neighbor interactions. By subtly modulating these two types of interactions through facile synthetic modifications, we created two systems: (1) a topological spin glass and (2) a frustrated spin-canted magnet with low-temperature exchange bias. To design this unconventional magnetic lattice, we used a metal–organic framework (MOF) platform, Ni 3 (pymca) 3 X 3 (NipymcaX where pymca = pyrimidine-2-carboxylato and X = Cl, Br). We isolated two MOFs, NipymcaCl and NipymcaBr, featuring canted Ni 2+ -based moments. Despite this similarity, differences in the single-ion anisotropies of the Ni 2+ spins result in distinct magnetic properties for each material. NipymcaCl is a topological spin glass, while NipymcaBr is a rare frustrated magnet with low-temperature exchange bias. Density functional theory calculations and Monte Carlo simulations on the NipymcaX lattice support the presence of magnetic frustration as a result of alternating AFM and FM interactions. Our calculations enabled us to determine the ground-state spin configuration and the distribution of spin–spin correlations relative to paradigmatic kagomé and triangular lattices. This modified honeycomb lattice is similar to the electronic Kekulé-O phase in graphene and provides a highly tunable platform to realize unconventional spin physics.

Exchange bias↗
DOE OSTI2013

Energy Saving Melting and Revert Reduction Technology (Energy-SMARRT): Clean Steel Casting Production

Inclusions in steel castings can cause rework, scrap, poor machining, and reduced casting performance, which can obviously result in excess energy consumption. Significant progress in understanding inclusion source, formation and control has been made. Inclusions can be defined as non-metallic materials such as refractory, sand, slag, or coatings, embedded in a metallic matrix. This research project has focused on the mold filling aspects to examine the effects of pouring methods and gating designs on the steel casting cleanliness through water modeling, computer modeling, and melting/casting experiments. Early in the research project, comprehensive studies of bottom-pouring water modeling and low-alloy steel casting experiments were completed. The extent of air entrainment in bottom-poured large castings was demonstrated by water modeling. Current gating systems are designed to prevent air aspiration. However, air entrainment is equally harmful and no prevention measures are in current practice. In this study, new basin designs included a basin dam, submerged nozzle, and nozzle extension. The entrained air and inclusions from the gating system were significantly reduced using the new basin method. Near the end of the project, there has been close collaboration with Wescast Industries Inc., a company manufacturing automotive exhaust components. Both computer modeling using Magma software and melting/casting experiments on thin wall turbo-housing stainless steel castings were completed in this short period of time. Six gating designs were created, including the current gating on the pattern, non-pressurized, partially pressurized, naturally pressurized, naturally pressurized without filter, and radial choke gating without filter, for Magma modeling. The melt filling velocity and temperature were determined from the modeling. Based on the simulation results, three gating designs were chosen for further melting and casting experiments on the same casting pattern using the lip pouring method. It was observed again that gating designs greatly influenced the melt filling velocity and the number of inclusion defects. The radial choked gating showed improvements in casting cleanliness and yield over the other gatings, even though no mold filters were used in the gating system.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

A multiscale design method using interpretable machine learning for phononic materials with closely interacting scales

Manipulating the dispersive characteristics of vibrational waves is beneficial for many applications, e.g., high-precision instruments. architected hierarchical phononic materials have sparked promise tunability of elastodynamic waves and vibrations over multiple frequency ranges. In this article, hierarchical unit-cells are obtained, where features at each length scale result in a band gap within a targeted frequency range. Our novel approach, the ‘‘hierarchical unit-cell template method,’’ is an interpretable machine-learning approach that uncovers global unit-cell shape/topology patterns corresponding to predefined band-gap objectives. A scale-separation effect is observed where the coarse-scale band-gap objective is mostly unaffected by the fine-scale features despite the closeness of their length scales, thus enabling an efficient hierarchical algorithm. Moreover, the hierarchical patterns revealed are not predefined or self-similar hierarchies as common in current hierarchical phononic materials. Furthermore, our approach offers a flexible and efficient method for the exploration of new regions in the hierarchical design space, extracting minimal effective patterns for inverse design in applications targeting multiple frequency ranges.

Architected materials↗