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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Thermodynamic assessment of the quaternary WTaCrV refractory high entropy alloy as a means to guide experimental approaches

The deployment of fusion energy poses challenges for materials in plasma facing components to withstand high temperatures and thermal gradients, particle implantation and neutron damage. The current material of choice is tungsten, although property degradation limits its consideration in future fusion reactors. Hence, materials with better resistance to harsh environments need to be developed for fusion energy to become a reality. High entropy alloys are being explored as potential candidates with some compositions showing good radiation resistance to defect cluster formation. One of these materials is the WTaCrV system, although only one composition has been tested under ion irradiation. In this work, we study the thermodynamic properties of the entire quaternary alloy composition range. Coupling first principles calculations, cluster expansion approaches, and Monte Carlo methods, we access the free energy functionals, short-range ordering as a function of temperature, and atomic configurations that can be compared to experimental observations. We use this data to inform experiments into compositions with higher propensity to form solid solutions, instead of phase separating. With this formalism we have developed thermodynamic database (TDB) files that can be used to plot quaternary phase diagrams.

Cluster Expansion↗
DOE OSTI2024

Multiphysics Degradation Modeling of Energy Storage Materials via RKPM with a Neural Network-Enhancement

In energy storage materials, strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking during charge/discharge cycling, resulting in reduced performance and service life. A coupled electro-chemo-mechanical reproducing kernel particle method (RKPM) formulation is developed, and a patch-test is formulated to certify optimal convergence of the proposed RKPM method for the coupled physics system. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based model construction by RKPM is then used to represent the complex material microstructures for modeling the coupled physics of these systems. Further, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1, 2] is introduced to effectively model damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. Reference: [1] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, pp 4422-4454, https://doi.org/10.1002/nme.7040, 2022. [2] Baek, J., Chen, J. S., "A Neural Network-Based Enrichment of Reproducing Kernel Approximation for Modeling Brittle Fracture", Computer Methods in Applied Mechanics and Engineering Vol. 410, 116590, 2024.

electro-chemo-mechanical coupling↗
DOE OSTI2021

Direct Subsurface Measurements through Precise Micro Drilling

Wellbore integrity is a significant problem in the U.S. and worldwide, which has serious adverse environmental and energy security consequences. Wells are constructed with a cement barrier designed to last about 50 years. Indirect measurements and models are commonly used to identify wellbore damage and leakage, often producing subjective and even erroneous results. The research presented herein focuses on new technologies to improve monitoring and detection of wellbore failures (leaks) by developing a multi-step machine learning approach to localize two types of thermal defects within a wellbore model, a prototype mechatronic system for automatically drilling small diameter holes of arbitrary depth to monitor the integrity of oil and gas wells in situ, and benchtop testing and analyses to support the development of an autonomous real-time diagnostic tool to enable sensor emplacement for monitoring wellbore integrity. Each technology was supported by experimental results. This research has provided tools to aid in the detection of wellbore leaks and significantly enhanced our understanding of the interaction between small-hole drilling and wellbore materials.

42 ENGINEERING↗
DOE OSTI2025

High-Resolution Modeling of the Gulf of Mexico using E3SM

Coastal ocean modeling is a high priority in the DOE‘s Energy Exascale Earth System Model (E3SM). The goal is to accurately predict the risk of damage to coastal resources and infrastructure due to a changing climate in the coming decades. North American coastal communities are areas of particular interest, as this fits under the topic of US national security and planning assessments in a changing climate. LANL Institutional Computing time for the Tier 1 allocation ”Coastal Ocean and Sea Ice Modeling” have been used for development and testing of numerical methods needed for E3SM coastal applications.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Structural Health Monitoring: Using an Autoencoder to Identify Damage in a Bolted Joint [Capstone Project]

Los Alamos National Laboratory (LANL) is an important fixture in the United States Department of Energy’s (DOE) National Nuclear Security Agency (NNSA) complex. LANL is one of the largest national laboratories in the country, and the laboratory’s primary mission is to support the nation’s nuclear stockpile. The lab functions as a design agencies for the NNSA and performs extensive testing on weapons as part of that mission. The shock and vibration test team at LANL utilizes electrodynamic shaker systems for important qualification testing in support of the laboratory’s mission. Modern engineering relies heavily on bolted joints to connect two objects. During these shaker tests, engineers depend on bolted joints to secure the test article to a fixture and the fixture to the table. The test article may be hazardous and contain high explosives which could create a safety issue if a bolted joint failed. A loss of preload in a bolt will affect the way energy is input to the system and may introduce nonlinearities as the joint opens and closes. The loss of preload can create challenges controlling the test and make acquired signals useless. Being able to monitor preload within bolted joints during testing can improve the quality of the data and keep workers safe.

42 ENGINEERING↗
DOE OSTI2020

Mathematical Model of ATM Activation and Chromatin Relaxation by Ionizing Radiation

We propose a comprehensive mathematical model to study the dynamics of ionizing radiation induced Ataxia-telangiectasia mutated (ATM) activation that consists of ATM activation through dual mechanisms: the initiative activation pathway triggered by the DNA damage-induced local chromatin relaxation and the primary activation pathway consisting of a self-activation loop by interplay with chromatin relaxation. The model is expressed as a series of biochemical reactions, governed by a system of differential equations and analyzed by dynamical systems techniques. Radiation induced double strand breaks (DSBs) cause rapid local chromatin relaxation, which is independent of ATM but initiates ATM activation at damage sites. Key to the model description is how chromatin relaxation follows when active ATM phosphorylates KAP-1, which subsequently spreads throughout the chromatin and induces global chromatin relaxation. Additionally, the model describes how oxidative stress activation of ATM triggers a self-activation loop in which PP2A and ATF2 are released so that ATM can undergo autophosphorylation and acetylation for full activation in relaxed chromatin. In contrast, oxidative stress alone can partially activate ATM because phosphorylated ATM remains as a dimer. The model leads to predictions on ATM mediated responses to DSBs, oxidative stress, or both that can be tested by experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Multiparameter laser performance characterization of liquid crystals for polarization control devices in the nanosecond regime

Abstract Interactions of liquid crystals (LC’s) with polarized light have been studied widely and have spawned numerous device applications, including the fabrication of optical elements for high-power and large-aperture laser systems. Currently, little is known about both the effect of incident polarization state on laser-induced–damage threshold (LIDT) and laser-induced functional threshold (LIFT) behavior at sub-LIDT fluences under multipulse irradiation conditions. This work reports on the first study of the nanosecond-pulsed LIDT’s dependence on incident polarization for several optical devices employing oriented nematic and chiral-nematic LC’s oriented by surface alignment layers. Accelerated lifetime testing was also performed to characterize the ability of these devices to maintain their functional performance under multipulse irradiation as a function of the laser fluence at both 1053 nm and 351 nm. Results show that the LIDT varies as a function of input polarization by 30–80% within the same device, while the multipulse LIFT (which can differ from the nominal LIDT) depends on irradiation conditions such as laser fluence and wavelength.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Performance characterization of freeform finished surfaces of potassium dihydrogen phosphate using fluid jet polishing with a nonaqueous slurry

Abstract Potassium dihydrogen phosphate (KDP) and its deuterated analog (DKDP) are unique nonlinear optical materials for high power laser systems. They are used widely for frequency conversion and polarization control by virtue of the ability to grow optical-quality crystals at apertures suitable for fusion-class laser systems. Existing methods for freeform figuring of KDP/DKDP optics do not produce surfaces with sufficient laser-induced–damage thresholds (LIDT’s) for operation in the ultraviolet portion of high-peak-power laser systems. In this work, we investigate fluid jet polishing (FJP) using a nonaqueous slurry as a sub-aperture finishing method for producing freeform KDP surfaces. This method was used to selectively polish surface areas to different depths on the same substrate with removals ranging from 0.16 μm to 5.13 μm. The finished surfaces demonstrated a slight increase in roughness as the removal depth increased along with a small number of fracture pits. Laser damage testing with 351 nm, 1 ns pulses demonstrated excellent surface damage thresholds, with the highest values in areas devoid of fracture pits. This work demonstrates, for the first time, a method that enables fabrication of a waveplate that provides tailored polarization randomization that can be scaled to meter-sized optics. Furthermore, this method is based on FJP technology that incorporates a nonaqueous slurry specially designed for use with KDP. This novel nonaqueous FJP process can be also used for figuring other types of materials that exhibit similar challenging inherent properties such as softness, brittleness, water-solubility, and temperature sensitivity.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A Software/Hardware Framework for Efficient and Safe Emergency Response in Post-Crash Scenarios of Battery Electric Vehicles

The adoption rate of battery electric vehicles (EVs) is rapidly increasing. Electric vehicles differ significantly from conventional internal combustion engine vehicles and vary widely across different manufacturers. Emergency responders (ERs) and recovery personnel may have less experience with EVs and lack timely access to critical information such as the extent of the stranded energy present, high-voltage safety hazards, and post-crash handling procedures in a user-friendly manner. This paper presents a software/hardware interactive tool named Electric Vehicle Information for Incident Response Solutions (EVIRS) to aid in the quick access to emergency response and recovery information. The current prototype of EVIRS identifies EVs using the VIN or Make, Model, and Year, and offers several useful features for ERs and recovery personnel. These features include integration and easy access to emergency response procedures tailored to an identified EV, vehicle structural schematics, the quick identification of battery pack specifications, and more. For EVs that are not severely damaged, EVIRS can perform calculations to estimate stranded energy in the EV’s battery and discharge time for various power loads using either EV dashboard information or operational data accessed through the CAN interface. Knowledge of this information may be helpful in the post-crash handling, management, and storage of an EV. The functionality and accuracy of EVIRS were demonstrated through laboratory tests using a 2021 Ford Mach-E and associated data acquisition system. The results indicated that when the remaining driving range was used as an input, EVIRS was able to estimate the pack voltage with an error of less than 3 V. Conversely, when pack voltage was used as an input, the estimated state of charge (SOC) error was less than 5% within the range of 30–90% SOC. Additionally, other features, such as retrieving emergency response guides for identified EVs and accessing lessons learned from archived incidents, have been successfully demonstrated through EVIRS for quick access. EVIRS can be a valuable tool for emergency responders and recovery personnel, both in action and during offline training, by providing crucial information related to assessing EV/battery safety risks, appropriate handling, de-energizing, transport, and storage in an integrated and user-friendly manner.

25 ENERGY STORAGE↗
DOE OSTI2025

Thermal shock resistance of lightweight cements developed for geothermal conditions

Cements are a critical component in well construction, as they act to prevent well fluid and gas escape, prevent corrosion of the casing, and strengthen the wellbore to prevent deformation. Under the high temperature/pressure conditions common in geothermal systems, the injection of cold water for energy production is expected to induce cyclic damage to the borehole cement through the rapid temperature fluctuations. These “thermal shocks” are expected to cause casing shrinkage, annulus formation, and cement tensile stresses. To understand the effect of cold water injection on the wellbore environment, a set of rock-cement-steel samples were created to simulate the structure of a geothermal well. Lightweight thermally-insulating cement blends were tested under thermal shock conditions in this study. In each test, the samples were pressurized to an effective pressure of ~3.5 MPa and placed at high temperatures. Thermal shocks were performed by injecting cold water (~10-15 °C) through the samples at a constant rate while keeping the samples at high temperatures until the sample temperature stopped decreasing and deformation ceased. Eight thermal shock tests were conducted with each sample – two at 100 °C and six at 200 °C. Post-tests analysis was then conducted by cutting open each sample to examine the damage in each component of the simulated wellbore. Experimental results suggest that all samples experienced similar degrees of axial and lateral contraction during cold water injection, but for the most part this contraction is recoverable when injection halts. Post-test analysis revealed that fly ash cenosphere pre-treatment had the best effect on improving thermal shock resistance in the cement blends. Thermomechanical modeling of likely stress paths experienced by the cements during heating/cooling cycles shows that elasto-plastic cement constitutive behavior results in most plastic strain occurring during the initial heating steps, with mostly elastic strain occurring during the thermal shock cycles. In conclusion, this agrees with experimental evidence, suggesting that cement damage from shocking occurs via other mechanisms such as chemical alteration, corrosion, and fatigue.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Simulation of DIII-D disruption with argon pellet injection and runaway electron beam

Abstract The next generation of large tokamaks, including ITER, will be equipped with a disruption mitigation system (DMS) that can be activated if a disruption is deemed to be imminent. Introducing impurities by pellet (large or shattered) or massive gas injection has been shown to be an effective mitigation mechanism on many tokamaks. The goal of the mitigation is to lessen the thermal and electromagnetic loads from the disruption without generating enough high-energy (runaway) electrons to damage the device. Variations of this mitigation process with impurity injection are presently being tested on many experiments. We have modeled one such impurity injection experiment on DIII-D using the M3D-C1 nonlinear 3D extended MHD code (Jardin et al 2012 Comput. Sci. Discovery 6 014002), The model includes an argon large pellet injection and ablation model, impurity ionization, recombination, and radiation, and runaway electron formation and subsequent evolution, including both Dreicer and avalanche sources. We obtain reasonable agreement with the experimental results for the timescale of the thermal and current quench and for the magnitude of the runaway electron plateau formed during the mitigation. This is the first 3D full MHD simulation with pellets and REs to simulate the disruption process and it also provides a partial validation of the M3D-C1 DMS model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Elucidating regulatory processes of intense physical activity by multi-omics analysis

Abstract Background Physiological and biochemical processes across tissues of the body are regulated in response to the high demands of intense physical activity in several occupations, such as firefighting, law enforcement, military, and sports. A better understanding of such processes can ultimately help improve human performance and prevent illnesses in the work environment. Methods To study regulatory processes in intense physical activity simulating real-life conditions, we performed a multi-omics analysis of three biofluids (blood plasma, urine, and saliva) collected from 11 wildland firefighters before and after a 45 min, intense exercise regimen. Omics profiles post- versus pre-exercise were compared by Student’s t -test followed by pathway analysis and comparison between the different omics modalities. Results Our multi-omics analysis identified and quantified 3835 proteins, 730 lipids and 182 metabolites combining the 3 different types of samples. The blood plasma analysis revealed signatures of tissue damage and acute repair response accompanied by enhanced carbon metabolism to meet energy demands. The urine analysis showed a strong, concomitant regulation of 6 out of 8 identified proteins from the renin-angiotensin system supporting increased excretion of catabolites, reabsorption of nutrients and maintenance of fluid balance. In saliva, we observed a decrease in 3 pro-inflammatory cytokines and an increase in 8 antimicrobial peptides. A systematic literature review identified 6 papers that support an altered susceptibility to respiratory infection. Conclusion This study shows simultaneous regulatory signatures in biofluids indicative of homeostatic maintenance during intense physical activity with possible effects on increased infection susceptibility, suggesting that caution against respiratory diseases could benefit workers on highly physical demanding jobs.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Early-Time (E1) High-Altitude Electromagnetic Pulse Effects on Trip Coils

A High-Altitude Electromagnetic Pulse (HEMP) is a potential threat to the power grid. HEMP can couple to transmission lines and cables, causing significant overvoltages which can be harmful to line connected equipment. The effects of overvoltages on various types of power systems components need to be understood. HEMP effects on trip coils were tested and presented in this report. A high voltage pulser was built to replicate the induced voltage waveform from a HEMP. The pulser was used to test breaker trip coils with increasing pulse magnitudes ranging from 20 kV to 80 kV. The State-of-Health of each trip coils was measured via mechanical operation and impedance measurements before and after each insult to identify any damage or degradation to the trip coils. Dielectric breakdown was observed at the conductor leads during testing, causing the HEMP insult to be diverted to the grounded casing. However, the dielectric breakdown did not cause interference with regular device operation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Fracture toughness evaluation for Zr-4 clad tubing structure with pellet inserts

Applying fracture mechanics approach to spent nuclear fuel (SNF) system reliability investigation is warranted due to the inherent flaws and hydride structures existed in a SNF system after nuclear reactor operation. However, none of the existing fracture toughness data deal with fuel cladding specific geometry or spent fuel material conditions, such as cladding structure with the pellet-inserts and the associated pellet clad mechanical interactions induced mixed-mode damage mechanisms. Thus, the development of an intrinsic fracture mechanics approach that is suitable for SNF materials is needed. Due to thin wall and small dimension of clad tubing structure, the spiral notch torsion test (SNTT) method of small specimen approach was used to estimate the clad tubing structure fracture toughness. The estimated fracture toughness for Zr-4 cladding with alumina-pellet inserts are presented in this report. For SNTT samples with a short or medium crack length, between 5.4-mm and 8-mm, the estimate JIQ upon fracture initiation for the baseline Zr-4 cladding is at 50 kJ/m2 with 2-sigma uncertainty of 3.26 kJ/m2, and the associated KIQ is at 67.46 MPa√m. For SNTT samples with a long crack length, around 13-mm, the crack initialization is deviated from that of the Mode-I tensile fracture and appears to be a mixed-mode fracture of Mode I – tensile stress and Mode III – out of plane shear stress; the estimated JMQ is at 18.9 kJ/m2, the associated KMQ is at 41.4 MPa√m.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Assessment of the High Flux Isotope Reactor Cybersecurity Initiative

Recent cyber-attacks on industrial control systems, and inadvertent exposure of nuclear plant systems to cyber-exploits underscore the need for plant operators to adopt and deploy cyber-security defense solutions made for industrial control systems. Of increasing concern is the fact that international cyber hackers are beginning to target critical infrastructure, and because these more modern controls systems depend on advanced use of digital systems, they are more vulnerable than ever before to cyber-attacks. Traditional cyber defense strategies and products that have been available for decades are tailored for use on IT or corporate networks but can cause interruptions and catastrophic damage when deployed on industrial control system networks. The Department of Energy (DOE) Office of Nuclear Energy established the Gateway for Accelerated Innovation in Nuclear (GAIN) program to provide private companies pursuing innovative nuclear energy technologies with access to the technical support necessary to move toward commercialization. One of these GAIN small business vouchers was awarded to Dragos, Inc. to enable collaboration with Oak Ridge National Laboratory (ORNL) to evaluate the Dragos Platform on a production nuclear reactor test bed, hence laying the path for future commercial adoption. The vision was to provide a guide for industrial operators on implementing an industrial monitoring solution and to show how these solutions can be deployed without causing safety and reliability issues. This report documents the results of the collaboration between ORNL and Dragos, Inc.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

The effect of current and lambda on white-etch-crack failures

White etching cracks (WECs) have been associated with premature failure of wind turbine roller bearings. Various drivers for the generation of WECs have been identified such as loading conditions, slip, steel quality, lubrication, hydrogen embrittlement, corrosion fatigue cracking, and stray electrical currents passing through the surface. Here, in this work, a benchtop test rig utilizing a three-ring-on-roller test configuration was used to investigate the effect of electrical current and operation in different lubricating regimes, defined by lambda (λ), on high-quality bearing steel samples tested in a commercially available power transmission EP gear lubricant. It was observed that there is an inverse correlation between the magnitude of electric current applied to the ring/ roller system and time-to-failure. Higher current magnitudes lead to shorter time-to-failure than lower current magnitudes, with macropitting as the main failure mode. Sub-surface investigation revealed the presence of WECs in all cases. For the same current magnitude, tests conducted in boundary and mixed lubrication regimes showed that time-to-failure increased as lambda increased, and the tests resulted in WEC related macropits, whereas tests conducted in near-hydrodynamic regime resulted in surface damage with no macropit. It was also noted that a shift toward near-hydrodynamic lubrication resulted in a distinct surface distress on the roller surface. Furthermore, there seems to be a transition in the mixed regime during which the surface distress occurred. The damage on the surface of the test samples resembled non-spatially, periodic, groove-like corrugations and, in some cases, crater-like depressions. Sub-surface imaging, performed by sequential sectioning, revealed the presence of WECs in all cases, and broad, branching cracks that were more prevalent under the more severe boundary conditions.

17 WIND ENERGY↗
DOE OSTI2023

SAM Code Development for Source Term Modeling in Fluoride-salt-cooled High-temperature Reactors

The SAM code is under development and supported by DOE-NE’s Nuclear Energy Advanced Modeling and Simulation program as a modern system-level modeling and simulation tool for advanced non-light water reactor safety analyses. These advanced reactor concepts incorporate novel and improved approaches to achieve safety and economic feasibility. Many concepts leverage higher operating temperatures for improved efficiency with a variety of coolants and structural materials to support those needs. Such design choices may also pose unique radiological source term risks. There are continuous efforts to incorporate new physics and phenomena relevant to advanced reactor concepts, including capabilities to enable system-level source term modeling. The Pebble-Bed Fluoride-salt-cooled High-temperature Reactor (PB-FHR) is a promising candidate among advanced nuclear reactor concepts with its improved passive safety characteristics and high thermal efficiency. In addition to past efforts to support the development and utilization of SAM for PB-FHR safety analysis, the species transport modeling capabilities in SAM have been extended to simulate source term phenomena in concepts like the PB-FHR. The PB-FHR concept utilizes pebble-form TRISO fuel and FLiBe salt coolant to provide robust barriers to the release of almost all fission products and radiological source terms. However, tritium poses a unique radiological risk due to its significant production from neutron interactions with 6 Li and 9 Be in the FLiBe as well as its high mobility at elevated temperatures where it can permeate through structural metals. Secondly, the use of graphite at elevated temperatures poses the risk of oxidation damage to any structural components or fuel pebbles that are exposed to accidental air ingress. This report summarizes progress made in modeling these phenomena in SAM, which leverages the system-level multi-physics thermal hydraulic simulation to support an effective engineering-scale source term modeling capability. A tritium transport model is developed to simulate the various transport pathways in FHR and MSR concepts and is presented through verification and validation examples as well as demonstrations simulating experimental test loops and reference plant FHR models. A graphite oxidation model is also introduced to calculate local oxidation rates and is presented with initial validation results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Earthquake-induced impact of base-isolated buildings: theory, numerical modeling, and design solutions

Earthquake shaking more intense than that used to size the horizontal clearance between a base–isolated building and near–rigid perimeter moat wall will result in hard impact, producing high–frequency, high–amplitude acceleration response in the structure and supported equipment. Herein this paper provides a design solution for the damaging effects of hard impact by installing a compliant engineered element in the load path between the base–isolated building and the moat wall, resulting in soft impact and a much smaller acceleration response. The engineered element assumed herein is a commercial–off–the–shelf marine fender with mechanical properties determined by physical testing. The attachment of a flexible engineered element, with well–defined stiffness and damping, to a near–rigid moat wall, simplifies the numerical modeling of the building–moat wall system and eliminates the need to bound the lateral stiffness of the wall for impact calculations. The simple model of the engineered element can be implemented in commercial finite element codes. Theory is developed for two–sided impact of a single–degree–of–freedom oscillator. Analytical solutions are derived for the shifted first–mode frequency of the impacted oscillator and for its free–vibration response. The shifted first–mode frequency is a function of the composite lateral stiffness of the isolator–engineered element assembly and its earthquake–induced displacement. Local peaks in the spectral response of the impacted oscillator form at odd integer multiples of the shifted first–mode frequency. The analytical solutions can be used to verify, in part, the numerical model used for impact analysis.

42 ENGINEERING↗