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DOE OSTI2021

Structure and Interdigitation of Chain-Asymmetric Phosphatidylcholines and Milk Sphingomyelin in the Fluid Phase

We addressed the frequent occurrence of mixed-chain lipids in biological membranes and their impact on membrane structure by studying several chain-asymmetric phosphatidylcholines and the highly asymmetric milk sphingomyelin. Specifically, we report trans-membrane structures of the corresponding fluid lamellar phases using small-angle X-ray and neutron scattering, which were jointly analyzed in terms of a membrane composition-specific model, including a headgroup hydration shell. Focusing on terminal methyl groups at the bilayer center, we found a linear relation between hydrocarbon chain length mismatch and the methyl-overlap for phosphatidylcholines, and a non-negligible impact of the glycerol backbone-tilting, letting the sn1-chain penetrate deeper into the opposing leaflet by half a CH 2 group. That is, penetration-depth differences due to the ester-linked hydrocarbons at the glycerol backbone, previously reported for gel phase structures, also extend to the more relevant physiological fluid phase, but are significantly reduced. Moreover, milk sphingomyelin was found to follow the same linear relationship suggesting a similar tilt of the sphingosine backbone. Complementarily performed molecular dynamics simulations revealed that there is always a part of the lipid tails bending back, even if there is a high interdigitation with the opposing chains. The extent of this back-bending was similar to that in chain symmetric bilayers. For both cases of adaptation to chain length mismatch, chain-asymmetry has a large impact on hydrocarbon chain ordering, inducing disorder in the longer of the two hydrocarbons.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Fault Diagnosis of Double Pitch Time-Sharing Meshing Toothed Conveyor Chain Transmission System Based on Neural Network

With the rapid development of industry, the production and demand of automobiles have increased significantly. The generation of cars often requires tens of thousands of processes, consisting of hundreds of assembly lines to complete. Chain conveyors are widely used in the transportation of automobile assembly lines. The existing conveyor chains are roller chains. With the improvement of the requirements for conveyor reliability, synchronization, and environmental friendliness, the characteristics of roller conveyor chains restrict the further development of chain conveyors. It is urgent to study a new conveyor chain system to improve the synchronization, reliability, and environmental friendliness of chain conveyors on hundreds of assembly lines. In this paper, the mathematical modeling, meshing analysis, reliability, and environmental friendliness of the parameters of the components of the double pitch time-sharing meshing toothed conveyor chain system are studied. In addition, a novel fault diagnosis method of double pitch time-sharing meshing toothed conveyor chain transmission system based on neural network model is proposed in this paper.

Ding, Song↗

DOE OSTI2026

Cyote-attack Chain Estimator

Attack Chain Estimator (ACE) Application Overview The Attack Chain Estimator (ACE) Application is a sophisticated tool designed for the ingestion, classification, sequencing, and enrichment of cybersecurity threat reports. This application leverages advanced machine learning models and extensive historical data to provide comprehensive insights into cyber threats, specifically targeting Industrial Control Systems (ICS). Purpose The primary functions of the ACE Application include: Ingestion of Cybersecurity Threat Reporting: Capable of ingesting text-based threat reports in markdown or text file format. Supports ingestion of structured data from other sources in STIX/JSON format. Classification of Report’s Text-Based Events: Utilizes a DeBERTa classifier, specifically trained on cybersecurity data, to map the events to MITRE ATT&CK for ICS Tactics and Techniques. Classification is performed using multiple Jupyter notebooks and machine learning workflows hosted as FastAPI microservices: regex_data deberta_base_35_train_hft_classifier_mlflow.ipynb hft_regex_classifier_mlflow.ipynb param_train_hft_classifier_mlflow.ipynb regex_tactic_tech.ipynb Ordering of Tactics, Techniques, and Observable Events: Sequences the identified tactics, techniques, and events to form a coherent attack chain. Enrichment with Historical Attack Chain Details: Enhances the attack chain with details from historical attacks using a Markov model developed from CyOTE Precursor Analysis Report data. The Markov model is available as a FastAPI endpoint for seamless integration. Enrichment with Adversary Emulation Capabilities Data: Integrates adversary emulation capabilities data using MITRE Caldera for OT adversary abilities UUIDs. Export of Output Files: Provides options to export the enriched attack chain in JSON or CSV formats. Routing of Output to Other Applications: Facilitates routing of output to various platforms and applications, including: Threat Intelligence Platforms COREII Scout for Threat Intelligence Analysis COREII Modeling and Simulation for Adversary Emulation Technical Description The ACE Application is an advanced cybersecurity tool designed to provide detailed threat analysis and sequence generation. It is built on a robust architecture that integrates natural language processing, machine learning, and historical data modeling. Key Components: Data Ingestion Module: Handles the input of threat reports and data from various formats, ensuring flexibility in data sources. Classification Engine: Employs DeBERTa-based classifiers hosted as FastAPI microservices to analyze and classify threat report events in accordance with the MITRE ATT&CK framework for ICS. Sequence Generator: Orders the classified events into a logical attack chain, providing clear insight into the sequence of tactics and techniques used in the threat. Enrichment Engine: Integrates historical data and adversary emulation capabilities to enhance the attack chain with valuable context and additional details. The historical data enrichment is powered by a Markov model, which is available as a FastAPI endpoint. Export and Routing Module: Facilitates the export of the enriched attack chain in multiple formats and routes the output to designated applications for further analysis or emulation.

Paul, Tony [Idaho National Laboratory (INL), Idaho↗

DOE OSTI2022

Carbon Capture, Transport, & Storage: Supply Chain Deep Dive Assessment (Final Report)

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2022

Grid Energy Storage: Supply Chain Deep Dive Assessment

The report “America’s Strategy to Secure the Supply Chain for a Robust Clean Energy Transition” lays out the challenges and opportunities faced by the United States in the energy supply chain as well as the Federal Government plans to address these challenges and opportunities. It is accompanied by several issue-specific deep dive assessments, including this one, in response to Executive Order 14017 “America’s Supply Chains,” which directs the Secretary of Energy to submit a report on supply chains for the energy sector industrial base. The Executive Order is helping the Federal Government to build more secure and diverse U.S. supply chains, including energy supply chains. To combat the climate crisis and avoid the most severe impacts of climate change, the U.S. is committed to achieving a 50 to 52 percent reduction from 2005 levels in economy-wide net greenhouse gas pollution by 2030, creating a carbon pollution-free power sector by 2035, and achieving net zero emissions economy-wide by no later than 2050. The U.S. Department of Energy (DOE) recognizes that a secure, resilient supply chain will be critical in harnessing emissions outcomes and capturing the economic opportunity inherent in the energy sector transition. Potential vulnerabilities and risks to the energy sector industrial base must be addressed throughout every stage of this transition. The DOE energy supply chain strategy report summarizes the key elements of the energy supply chain as well as the strategies the U.S. Government is starting to employ to address them. Additionally, it describes recommendations for Congressional action. DOE has identified technologies and crosscutting topics for analysis in the one-year time frame set by the Executive Order. Along with the capstone policy report, DOE is releasing 11 deep dive assessment documents, including this one, covering the following technology sectors: carbon capture materials; electric grid including transformers and high voltage direct current (HVDC); energy storage; fuel cells and electrolyzers; hydropower including pumped storage hydropower (PSH); neodymium magnets; nuclear energy; platinum group metals and other catalysts; semiconductors; solar photovoltaics (PV); and wind. DOE is also releasing two deep dive assessments on the following crosscutting topics: Commercialization and competitiveness; and cybersecurity and digital components. More information can be found at www.energy.gov/policy/supplychains.

25 ENERGY STORAGE↗

DOE OSTI2022

Wind Energy: Supply Chain Deep Dive Assessment

17 WIND ENERGY↗

DOE OSTI2022

Cybersecurity and Digital Components: Supply Chain Deep Dive Assessment

The report “America’s Strategy to Secure the Supply Chain for a Robust Clean Energy Transition” lays out the challenges and opportunities faced by the United States in the energy supply chain as well as the federal government plans to address these challenges and opportunities. It is accompanied by several issue-specific deep dive assessments, including this one, in response to Executive Order 14017 “America’s Supply Chains,” which directs the Secretary of Energy to submit a report on supply chains for the energy sector industrial base. The Executive Order is helping the federal government to build more secure and diverse U.S. supply chains, including energy supply chains. As the energy sector has become more globalized and increasingly complex, digitized, and even virtualized, its supply chain risk for digital components – the software, virtual platforms and services, and data – in energy systems has evolved and expanded. All digital components in U.S. energy sector systems are vulnerable and may be subject to cyber supply cha in risks stemming from a variety of threats, vulnerabilities, and impacts. This includes digital components in all systems within the ESIB, namely those systems operated by asset owners across different energy subsectors (e.g., electricity, oil and natural gas, and renewables) and the systems operated by a worldwide industrial complex with capabilities to perform research and development and design, produce, operate, and maintain energy sector systems, subsystems, components, or parts to meet U.S. energy requirements. Supply chain risks for digital components including software, virtual platforms and services, and data have grown in recent years as increasingly sophisticated cyber adversaries have targeted exploiting vulnerabilities in these digital assets. Supply chain risks for digital components in energy sector systems will continue to evolve and likely increase as these systems are increasingly interconnected, digitized, and remotely operated.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

NASA NTRSDate not supplied

Space Launch System Liftoff and Separation Dynamics Analysis Tool Chain

A flexible, hierarchical tool chain that is being applied to NASA’s Space Launch System (SLS) for critical dynamics phenomena is described. This tool chain, called CLVTOPS, is used to investigate lateral liftoff movement of the vehicle as it departs and clears the mobile launch tower and separation of the two solid rocket boosters without collision with the core stage and payload. The toolset’s architecture was configured to take advantage of a modern software engineering approach for maximum flexibility and utilization of open-source simulations and associated tools. As opposed to a “monolithic” approach, scripting languages were used to “bind” together a tool chain to configure and organize input data, execute and produce analysis results, and post-process these results to facilitate a rapid, iterative analysis process to quickly address issues and pursue alternatives with emphasis on analysis automation. Key capabilities in the tool chain include processing and mining of very large data sets, a wide range of graphical depictions, and high-fidelity, physics-based simulations. The paper begins with a problem description and the motivation for liftoff and separation dynamics analysis followed by a historical survey of dynamics analyses for previous NASA human-rated launch vehicles. Details of the tool chain and its components are then introduced and divided, first, into description of the scripting language architecture used to “bind” the simulation tools, programs, and scripts together and, second, the physics models and simulations. Representative analyses and data products for liftoff and booster separation dynamics are shown in order to provide in-depth insight into the tool chain’s capabilities. Supporting activities such as simulation tool chain verification, version archiving and data management, and training are addressed. The paper concludes with case examples on how the tool chain can be tailored to related aerospace dynamics analyses, both large and small. The flexibility and versatility of this tool chain in supporting analyses of such a diverse range of aerospace applications demonstrates the feasibility of applying these patterns and techniques for tool construction to other aerospace simulations.

6DOF↗

DOE OSTI2021

Towards a New Supply Chain Cybersecurity Risk Analysis Technique

Supply chain cyber-attacks, such as the SolarWinds Orion attack, are occurring with greater frequency. These attacks compromise a digital device before it is sent to customers, bypassing traditional security controls to remain persistent and undetected in operational environments. While supply chain attacks are prevalent, methods for analyzing the risk of these attacks are currently unavailable. This paper proposes new supply chain cyber-attack difficulty and risk metrics to evaluate the relative risk of an attack throughout the supply chain lifecycle. Difficulty metrics for each stakeholder in a digital device’s supply chain (e.g., hardware manufacturing, firmware development, software development, storage, and distribution entities) are calculated using scores from cybersecurity maturity questionnaires in a Bayesian Network leaky Noisy-MAX model. These difficulty metrics are then used to calculate an overall supply chain cyber-attack risk. Vulnerability and recoverability metrics are also proposed to evaluate the relative stakeholder influence in the attack risk. These proposed relative risk metrics enable continuous supply chain monitoring, provide decision-makers with information necessary for improved supplier selection, and help drive improvements in the cybersecurity posture of the stakeholders in their supply chain.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

The Nuclear Digital I&C System Supply Chain Cyber-Attack Surface

The nuclear supply chain attack surface is a large, complex network of interconnected stakeholders and activities. The global economy has widened and deepened the supply chain, resulting in larger numbers of geographically dispersed locations and increased difficulty ensuring the authenticity and security of digital assets. Although the nuclear industry has made significant strides in securing facilities from cyber-attacks, the supply chain remains vulnerable. This paper outlines supply chain threats and vulnerabilities and provides a Digital I&C System Supply Chain Cyber-Attack Surface diagram to illustrate the complexity of securing hardware, firmware, software, and system information throughout the entire supply chain lifecycle. The knowledge presented in this paper provides a foundation to use in cybersecurity supply chain risk analysis and to guide future supply chain research and development efforts leading to enhancement of a nuclear facility’s overall security posture.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2022

Smectic C Self‐Assembly in Mesogen‐Free Liquid Crystalline Chiral Polyethers with Sulfonylated Methyl‐Branched Side Chains

Abstract To realize advanced electrical applications for ferroelectric liquid crystalline polymers, high spontaneous polarization ( P s ) is highly desired. However, current ferroelectric liquid crystalline polymers usually exhibit a low P s . In this work, mesogen‐free, chiral polyethers containing sulfonylated methyl‐branched alkyl side chains with a (CH 2 ) 3 O spacer between the sulfonyl and the branched alkyl groups are designed and synthesized. In contrast to the linear n ‐alkyl side chains, the methyl‐branched alkyl side chains induce chain tilting in the smectic layers. When double chirality exists in both the main chain and the side chains, a crystalline structure is observed after mechanical stretching. Intriguingly, when single chirality exists in either the backbone or the side chains, a liquid crystalline smectic C phase is obtained. The electric displacement–electric field study, however, does not show typical ferroelectric switching, although the dielectric constants are relatively high for these liquid crystalline polymers. This is likely because the dipole–dipole interactions among neighboring sulfonyl groups along the main chain are so strong that the ferroelectric switching is hindered in the samples. For the future work, it is desired to weaken the dipole–dipole interaction to achieve ferroelectricity in these mesogen‐free liquid crystalline polymers.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Distance‐based reconstruction of protein quaternary structures from inter‐chain contacts

Abstract Predicting the quaternary structure of protein complex is an important problem. Inter‐chain residue‐residue contact prediction can provide useful information to guide the ab initio reconstruction of quaternary structures. However, few methods have been developed to build quaternary structures from predicted inter‐chain contacts. Here, we develop the first method based on gradient descent optimization (GD) to build quaternary structures of protein dimers utilizing inter‐chain contacts as distance restraints. We evaluate GD on several datasets of homodimers and heterodimers using true/predicted contacts and monomer structures as input. GD consistently performs better than both simulated annealing and Markov Chain Monte Carlo simulation. Starting from an arbitrarily quaternary structure randomly initialized from the tertiary structures of protein chains and using true inter‐chain contacts as input, GD can reconstruct high‐quality structural models for homodimers and heterodimers with average TM‐score ranging from 0.92 to 0.99 and average interface root mean square distance from 0.72 Å to 1.64 Å. On a dataset of 115 homodimers, using predicted inter‐chain contacts as restraints, the average TM‐score of the structural models built by GD is 0.76. For 46% of the homodimers, high‐quality structural models with TM‐score ≥ 0.9 are reconstructed from predicted contacts. There is a strong correlation between the quality of the reconstructed models and the precision and recall of predicted contacts. Only a moderate precision or recall of inter‐chain contact prediction is needed to build good structural models for most homodimers. Moreover, GD improves the quality of quaternary structures predicted by AlphaFold2 on a Critical Assessment of Techniques for Protein Structure Prediction–Critical Assessments of Predictions of Interactions dataset.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Multi-level impacts of climate change and supply disruption events on a potato supply chain: An agent-based modeling approach

Context: The world is experiencing frequent extreme weather events like droughts, snowstorms, and shifting of seasons due to climate change. Increased frequency and severity of these extreme weather events threaten food security because agriculture depends on climate conditions. Impacts of climate change on the agricultural system not only occur at the grower’s level, but also cascade to other levels along the supply chain. Objective: In this study, we aim to quantify a wide range of economic impacts of different extreme climate events on different stages of a food supply chain. Methods: We chose the potato supply chain in Idaho as a case study. We developed a multi-echelon supply chain simulation model using an agent-based modeling (ABM) approach with five types of agents—farmers, shippers, processors, retailers, and logistics companies. In addition to the business-as-usual (BAU) scenario, we designed two climate-related disruption events—drought and snowstorm. We quantified the heterogeneous impacts at different stages of the supply chain for both fresh and processed potatoes using key performance indicators (KPIs) including revenues, prices, lead times, traded quantities, and food waste quantity. Results and Conclusion: The impacts of the disruption events are different on different agents in the supply chain for different product categories. The price hike of fresh potatoes is far higher than processed potatoes during disruption events. This price hike makes consumers switch to processed potatoes, which require more fresh potatoes as an input that further reinforces the price hike. However, because processed potatoes have an elastic demand, once their prices go up due to higher input cost, their demand drops. Non-contracted farmers gain additional revenues from the disruption events, whereas contracted farmers incur a loss due to lock-in price and lower than usual harvest. Significance: The methodology developed in this study could be applied to other food and agricultural supply chains for understanding the vulnerabilities at agent levels due to climate change disruption events. Furthermore, the findings would help develop mitigation strategies or policies to improve the well-being of the overall supply chain.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Quantum phase transitions in long-range interacting hyperuniform spin chains in a transverse field

Hyperuniform states of matter are characterized by anomalous suppression of long-wavelength density fluctuations. While most of the interesting cases of disordered hyperuniformity are provided by complex many-body systems such as liquids or amorphous solids, classical spin chains with certain long-range interactions have been shown to demonstrate the same phenomenon. Such spin-chain systems are ideal models for exploring the effects of quantum mechanics on hyperuniformity. It is well-known that the transverse field Ising model shows a quantum phase transition (QPT) at zero temperature. Under the quantum effects of a transverse magnetic field, classical hyperuniform spin chains are expected to lose their hyperuniformity. High-precision simulations of these cases are complicated because of the presence of highly nontrivial long-range interactions. We perform an extensive analysis of these systems using density matrix renormalization group simulations to study the possibilities of phase transitions and the mechanism by which they lose hyperuniformity. Even for a spin chain of length 30, we see discontinuous changes in properties like the “τ order metric” of the ground state, the measure of hyperuniformity, and the second cumulant of the total magnetization along the x-direction, all suggestive of first-order QPTs. An interesting feature of the phase transitions in these disordered hyperuniform spin chains is that, depending on the parameter values, the presence of a transverse magnetic field may lead remarkably to an increase in the order of the ground state as measured by the “τ order metric,” even if hyperuniformity is lost. Therefore, it would be possible to design materials to target specific novel quantum behaviors in the presence of a transverse magnetic field. Our numerical investigations suggest that these spin chains can show no more than two QPTs. We further analyze the long-range interacting spin chains via the Jordan-Wigner mapping onto a system of spinless fermions, showing that under the pairwise-interaction approximation and a mean-field treatment, there can be at most two quantum phase transitions. Here, based on these numerical and theoretical explorations, we conjecture that for spin chains with long-range pair interactions that have convergent cosine transforms, there can be a maximum of two quantum phase transitions at zero temperature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

The Demand for a Domestic Offshore Wind Energy Supply Chain

In March of 2021, the Biden-Harris Administration established a National Offshore Wind Target to install 30 GW by 2030. This ambitious goal was not only intended to help reduce dependencies on fossil fuels, but also represents an opportunity to establish a new and sustainable industry in the United States. The announcement referenced the potential benefits of establishing a domestic supply chain, including the opportunity for existing suppliers to produce thousands of components while creating tens of thousands of jobs over the course of the decade. This vision by the Biden-Harris Administration aligns with the perspective of the offshore wind industry. At a Leadership 100 event hosted by the Business Network for Offshore wind in 2019, offshore wind developers and manufacturers identified the need for a roadmap outlining a pathway to a domestic supply chain as the top priority facing the industry. Building up domestic manufacturing capabilities will not only energize local industries but can potentially de-risk individual project by reducing reliance on importing resources from European or Asian markets. Although establishing a domestic supply chain will require significant investment, it has the potential to create substantial benefits throughout the industry and, by extension, on the decarbonization goals of the United States. This study characterizes the challenges and opportunities facing the growth of a domestic supply chain industry and evaluates the potential benefits that could be achieved through the creation of the supply chain. This report is the first of a two-part series which will describe the full supply chain roadmap and the associated benefits; the current report focuses on the high-level deployment, workforce, and component requirements that need to be met to achieve the National Offshore Wind Target. We will present: 1. A deployment pipeline that demonstrates the pathway to 30 GW, the associated demand for major fixed-bottom and floating offshore wind components (turbines, foundations, cables, substations), and the vessel and port requirements to support these installation activities. 2. A series of sensitivity analyses showing how the demand for components, ports, and vessels changes for different technology pathways and availability of the global supply chain. 3. An estimate of the total number of jobs that would be required to support these deployment scenarios under varying levels of assumed domestic content. 4. A comprehensive list of the Tier 1, 2, and 3 components (finished components, subassemblies, and subcomponents) required to construct fixed-bottom and floating offshore wind projects. 5. A discussion of critical path components that represent a significant challenge, bottleneck, or risk for a future domestic supply chain.

17 WIND ENERGY↗

DOE OSTI2022

Manipulating Conjugated Polymer Backbone Dynamics through Controlled Thermal Cleavage of Alkyl Side Chains

The morphological stability of an organic photovoltaic (OPV) device is greatly affected by the dynamics of donors and acceptors occurring near the device's operational temperature. These dynamics can be quantified by the glass transition temperature (T g ) of conjugated polymers (CPs). Because flexible side chains possess much faster dynamics, the cleavage of the alkyl side chains will reduce chain dynamics, leading to a higher T g . In this work, the T g s for CPs are systematically studied with controlled side chain cleavage. Isothermal annealing of polythiophenes featuring thermally cleavable side chains at 140 °C, is found to remove more than 95% of alkyl side chains in 24 h, and raise the backbone T g from 23 to 75 °C. Coarse grain molecular dynamics simulations are used to understand the T g dependence on side chain cleavage. X-ray scattering indicates that the relative degree of crystallization remains constantduring isothermal annealing process. The effective conjugation length is not influenced by thermal cleavage; however, the density of chromophore is doubled after the complete removal of alkyl side chains. Here, the combined effect of enhancing T g and conserving crystalline structures during the thermal cleavage process can provide a pathway to improving the stability of optoelectronic properties in future OPV devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Intertwined charge, spin, and orbital degrees of freedom under electronic correlations in the one-dimensional Fe 3+ chalcogenide chain

Motivated by recent developments in the study of quasi-one-dimensional iron systems with Fe 2+ , we comprehensively study an Fe 3+ chalcogenide chain system. Based on first-principles calculations, the Fe 3+ chain has a similar electronic structure to that discussed before for the Fe 2+ chain, because of the similar Fe⁢𝑋 4 (𝑋 = S or Se) tetrahedron-chain geometry. Furthermore, a three-orbital electronic Hubbard model for this chain was constructed using the density matrix renormalization group method. A robust antiferromagnetic coupling was unveiled in the chain direction. In addition, in the intermediate electronic correlation 𝑈/𝑊 region, we found an interesting orbital-selective Mott phase with the coexistence of localized and itinerant electrons (𝑈 is the on-site Hubbard repulsion, while 𝑊 is the electronic bandwidth) based on the orbital-selective behavior observed in the charge fluctuations. Furthermore, we do not observe any obvious pairing tendency in the Fe 3+ chain in the electronic-correlation 𝑈/𝑊 region, where superconducting pairing tendencies were reported before in iron ladders. This suggests that superconductivity is unlikely to emerge in the Fe 3+ systems. Finally, our results clearly establish the similarities and differences between Fe 2+ and Fe 3+ iron chains, as well as iron ladders.

density matrix renormalization group↗

DOE OSTI2022

Closed-form existence conditions for bandgap resonances in a finite periodic chain under general boundary conditions

Bragg scattering in periodic media generates bandgaps, frequency bands where waves attenuate rather than propagate. Yet, a finite periodic structure may exhibit resonance frequencies within these bandgaps. This is caused by boundary effects introduced by the truncation of the nominal infinite medium. Previous studies of discrete systems determined existence conditions for bandgap resonances, although the focus has been limited to mainly periodic chains with free–free boundaries. In this paper, we present closed-form existence conditions for bandgap resonances in discrete diatomic chains with general boundary conditions (free–free, free–fixed, fixed–free, or fixed–fixed), odd or even chain parity (contrasting or identical masses at the ends), and the possibility of attaching a unique component (mass and/or spring) at one or both ends. The derived conditions are consistent with those theoretically presented or experimentally observed in prior studies of structures that can be modeled as linear discrete diatomic chains with free–free boundary conditions. An intriguing case is a free–free chain with even parity and an arbitrary additional mass at one end of the chain. Introducing such an arbitrary mass underscores a transition among a set of distinct existence conditions, depending on the type of chain boundaries and parity. The proposed analysis is applicable to linear periodic chains in the form of lumped-parameter models, examined across the frequency spectrum, as well as continuous granular media models, or similar configurations, examined in the low-frequency regime.

Bastawrous, Mary V.↗