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At least 289 records · Page 16

Dynamic Microgrids in Resilient Distribution Systems With Reconfigurable Cyber-Physical Networks

Modern distribution systems energized by inverter-interfaced distributed generators (DGs) operate as coupled cyber-physical networks (C/P-networks), where the controllable components in the physical network (P-network) are coordinated through the cyber network (C-network). The concept of dynamic microgrids (MGs) operation has been adopted to enable distribution system autonomous operation with varying electric boundaries. To further enhance system operation resiliency and flexibility, dynamic MGs operation with reconfigurable C/P-networks is discussed in this work. An evaluation framework is proposed to assess the operational feasibility of distribution feeders with multiple inverter-based dynamic MGs and come out with possible restoration solutions in the context of cross-layer C/P-network reconfiguration. Furthermore, distributed controllers are developed for components with different operating characteristics to realize seamless system topology variations and provide coordinated secondary regulation in various operation modes. Furthermore, the proposed evaluation framework along with the developed distributed controller has been validated using a Hardware-in-the-Loop (HIL) real-time CPS testbed.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Integrating Cybersecurity with System Operations and Restoration

This presentation covers the interaction of the discipline of system operations with the discipline of cybersecurity. First is discussion of a number of fundamental concepts for system operators - organizational division of responsibilities, human and machine cooperation, goals, and priorities. The next section covers the importance of cybersecurity for a system operator organization and explains different risk management approaches based on the consequence and frequency of events. Finally the role of system operators in the security of the grid categorized by the NIST Cybersecurity Framework is discussed to present recommendations and ideas for future work.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Design and simulation of EVA tools for first servicing mission of HST

The Hubble Space Telescope (HST) was launched into near-earth orbit by the Space Shuttle Discovery on April 24, 1990. The payload of two cameras, two spectrographs, and a high-speed photometer is supplemented by three fine-guidance sensors that can be used for astronomy as well as for star tracking. A widely reported spherical aberration in the primary mirror causes HST to produce images of much lower quality than intended. A Space Shuttle repair mission in January 1994 installed small corrective mirrors that restored the full intended optical capability of the HST. The First Servicing Mission (FSM) involved considerable Extra Vehicular Activity (EVA). Special EVA tools for the FSM were designed and developed for this specific purpose. In an earlier report, the details of the Data Acquisition System developed to test the performance of the various EVA tools in ambient as well as simulated space environment were presented. The general schematic of the test setup is reproduced in this report for continuity. Although the data acquisition system was used extensively to test a number of fasteners, only the results of one test each carried on various fasteners and the Power Ratchet Tool are included in this report.

Naik, Dipak↗

Solar concentrator technology development for space based applications, volume 1

Thermoelectric conversion using a radio-isotope heat source has been used where outer planetary space craft are too far away for absorbing significant solar energy. Solar dynamic power (SDP) conversion is one technology that offers advantages for applications within the inner planet region. Since SDP conversion efficiency can be 2 to 3 times higher than photovoltaic, the collecting surfaces are much reduced in area and therefore lighter. This becomes an advantage in allocating more weight to launched payloads. A second advantage results for low earth orbit applications. The reduced area results in lower drag forces on the spacecraft and requires less reboost propellant to maintain orbit. A third advantage occurs because of the sun-to-shade cycling while in earth orbit. Photovoltaic systems require batteries to store energy for use when in the shade, and battery life for periods of 10 to 15 years is not presently achievable. For these reasons the Solar Dynamics and Thermal Systems Branch at NASA LeRC has funded work in developing SDP systems. The generic SDP system uses a large parabolic solar concentrator to focus solar energy onto a power conversion device. The concentrators are large areas and must therefore be efficient and have low specific weights. Yet these surfaces must be precise and capable of being stowed in a launch vehicle and then deployed and sometimes unfurled in space. There are significant technical challenges in engineering such structures, and considerable investigation has been made to date. This is the first of two volumes reporting on the research done by the Advanced Manufacturing Center at Cleveland State University to assist NASA LeRC in evaluating this technology. The objective of the grant was to restore the solar concentrator development technology of the 1960s while improving it with advances that have occurred since then. This report summarizes the work done from January 1989 through December 1991.

Pintz, A.↗

History and Flight Devleopment of the Electrodynamic Dust Shield

The surfaces of the moon, Mars, and that of some asteroids are covered with a layer of dust that may hinder robotic and human exploration missions. During the Apollo missions, for example, lunar dust caused a number of issues including vision obscuration, false instrument readings, contamination, and elevated temperatures. In fact, some equipment neared failure after only 75 hours on the lunar surface due to effects of lunar dust. NASA's Kennedy Space Center has developed an active technology to remove dust from surfaces during exploration missions. The Electrodynamic Dust Shield (EDS), which consists of a series of embedded electrodes in a high dielectric strength substrate, uses a low power, low frequency signal that produces an electric field wave that travels across the surface. This non-uniform electric field generates dielectrophoretic and electrostatic forces capable of moving dust out of these surfaces. Implementations of the EDS have been developed for solar radiators, optical systems, camera lenses, visors, windows, thermal radiators, and fabrics The EDS implementation for transparent applications (solar panels, optical systems, windows, etc.) uses transparent indium tin oxide electrodes on glass or transparent lm. Extensive testing was performed in a roughly simulated lunar environment (one-sixth gravity at 1 mPa atmospheric pressure) with lunar simulant dust. EDS panels over solar radiators showed dust removal that restored solar panel output reaching values very close to their initial output. EDS implementations for thermal radiator protection (metallic spacecraft surfaces with white thermal paint and reflective films) were also extensively tested at similar high vacuum conditions. Reflectance spectra for these types of implementations showed dust removal efficiencies in the 96% to 99% range. These tests indicate that the EDS technology is now at a Technology Readiness Level of 4 to 5. As part of EDS development, a flight version is being prepared for several flight opportunities. The flight version of the EDS will incorporate significantly smaller electronics, with an expected mass and volume of 500 g and 350 cm(exp. 3) respectively. One of the opportunities is an International Space Station (ISS) experiment: Materials for International Space Station Experiment 10 (MISSE-10). This experiment aims to verify the EDS can withstand the harsh environment of space and will look to closely replicate the solar environment experienced on the moon. A second flight opportunity exists to provide an EDS to several companies as part of NASA's Lunar CATALYST program. The current mission concept would fly the EDS on the footpad of one of the Lunar CATALYST vehicles. Dust will likely deposit on the footpad through normal surface rover activities, but also upon landing where lunar dust is expected to be uplifted. To analyze the e effectiveness of the EDS system, photographs of the footpad with one of the spacecrafts onboard cameras are anticipated. If successful in these test flights, the EDS technology will be ready to be used in the protection of actual mission equipment for future NASA and commercial missions to the moon, asteroids, and Mars.

Lunar↗

Applying a Space-Based Security Recovery Scheme for Critical Homeland Security Cyberinfrastructure Utilizing the NASA Tracking and Data Relay (TDRS) Based Space Network

Protection of the national infrastructure is a high priority for cybersecurity of the homeland. Critical infrastructure such as the national power grid, commercial financial networks, and communications networks have been successfully invaded and re-invaded from foreign and domestic attackers. The ability to re-establish authentication and confidentiality of the network participants via secure channels that have not been compromised would be an important countermeasure to compromise of our critical network infrastructure. This paper describes a concept of operations by which the NASA Tracking and Data Relay (TDRS) constellation of spacecraft in conjunction with the White Sands Complex (WSC) Ground Station host a security recovery system for re-establishing secure network communications in the event of a national or regional cyberattack. Users would perform security and network restoral functions via a Broadcast Satellite Service (BSS) from the TDRS constellation. The BSS enrollment only requires that each network location have a receive antenna and satellite receiver. This would be no more complex than setting up a DIRECTTV-like receiver at each network location with separate network connectivity. A GEO BSS would allow a mass re-enrollment of network nodes (up to nationwide) simultaneously depending upon downlink characteristics. This paper details the spectrum requirements, link budget, notional assets and communications requirements for the scheme. It describes the architecture of such a system and the manner in which it leverages off of the existing secure infrastructure which is already in place and managed by the NASAGSFC Space Network Project.

Cybersecurity↗

Machine Vision-based Robot Manipulators for Nuclear Applications - 20370

Decommissioning and dismantling of nuclear facilities are major challenges facing the nuclear industry. Robot manipulators with capabilities of restoring nuclear structures and significantly prolonging nuclear power generation in addition to their applications in decommissioning and dismantling (D and D) would immensely ease the above-mentioned challenge. Ability to remotely sense/monitor and analyze dangerous and hazardous environments such as nuclear reactors as well as performing reparatory tasks in such environments using robot manipulators require additional information from vision sensors. Structural sample collection and inspection as well as restoration require object and position information. Computer vision is used to obtain precise 3D position information. The current work uses the Sawyer robot with the integrated Cognex camera. The research presents an approach to facilitate and improve operations in a nuclear reactor using robotic vision control. The vision control system is modeled with Augmented Image Space-based visual servoing approach. Results showing accurate robot control. Object recognition is used to recognize the image and calculate it poses. To transform coordinates of the object's pose from the camera frame to the robotic frame transformation matrices are employed. Future work will employ a 3D camera (with depth information) using Denso robot. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Control of the forebody vortex orientation by asymmetric air injection. Part A: Application to enhance departure/spin recovery of fighter aircraft and Part B: Details of the flow structure

A concept developed to provide powerful directional control effectiveness for a fighter aircraft at high angles of attack is described. The concept utilizes the energy concentrated in the strong forebody vortices (which form on slender bodies of high relative incidence) by controlling the lateral orientation of the vortices with respect to the body. The objective was to utilize the side force associated with asymmetric vortices, in a controlled manner, to enhance the ability of the fighter to recover from a departure from controlled flight. The results from water tunnel and wind tunnel experiments show that a small amount of tangential blowing along the forebody near the apex can effectively alter the forebody vortex system and generate large restoring yawing moments. Six degree of freedom digital simulation results show that this concept can substantially enhance recovery characteristics of fighter aircraft with long, slender forebodies. Also, the results of experiments which were conducted on a cone model are discussed where the principal test objective was to develop an understanding of the fluid mechanics involved in the process of vortex control. Knowledge gained in these more generic tests should allow the concept to be applied to a wider range of configurations.

Skow, A. M.↗

Integrating Cybersecurity with System Operations and Restoration

This presentation covers the interaction of the discipline of system operations with the discipline of cybersecurity. First, a common mental model for risk - both cybersecurity and all-hazards - is presented, followed by a discussion of high-level management strategies for different kinds of cyber harm facing system operators, based on the consequences and frequencies of the harm. The next section covers the importance of cybersecurity for a system operator organization and explains some general concepts to understand the relationships. Finally the role of system operators in the security of the grid as a larger system of systems is discussed over the framework of a resilience event.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Light microscopic image analysis system to quantify immunoreactive terminal area apposed to nerve cells

The present report describes a desktop computer-based method for the quantitative assessment of the area occupied by immunoreactive terminals in close apposition to nerve cells in relation to the perimeter of the cell soma. This method is based on Fast Fourier Transform (FFT) routines incorporated in NIH-Image public domain software. Pyramidal cells of layer V of the somatosensory cortex outlined by GABA immunolabeled terminals were chosen for our analysis. A Leitz Diaplan light microscope was employed for the visualization of the sections. A Sierra Scientific Model 4030 CCD camera was used to capture the images into a Macintosh Centris 650 computer. After preprocessing, filtering was performed on the power spectrum in the frequency domain produced by the FFT operation. An inverse FFT with filter procedure was employed to restore the images to the spatial domain. Pasting of the original image to the transformed one using a Boolean logic operation called 'AND'ing produced an image with the terminals enhanced. This procedure allowed the creation of a binary image using a well-defined threshold of 128. Thus, the terminal area appears in black against a white background. This methodology provides an objective means of measurement of area by counting the total number of pixels occupied by immunoreactive terminals in light microscopic sections in which the difficulties of labeling intensity, size, shape and numerical density of terminals are avoided.

Non-NASA Center↗

Solar concentrator technology development for space based applications, volume 2

Thermoelectric conversion using a radio-isotope heat source has been used where outer planetary space craft are too far away for absorbing significant solar energy. Solar dynamic power (SDP) conversion is one technology that offers advantages for applications within the inner planet region. Since SDP conversion efficiency can be 2 to 3 times higher than photovoltaic, the collecting surfaces are much reduced in area and therefore lighter. This becomes an advantage in allocating more weight to launched payloads. A second advantage results for low earth orbit applications. The reduced area results in lower drag forces on the spacecraft and requires less reboost propellant to maintain orbit. A third advantage occurs because of the sun-to-shade cycling while in earth orbit. Photovoltaic systems require batteries to store energy for use when in the shade, and battery life for periods of 10 to 15 years is not presently achievable. For these reasons the Solar Dynamics and Thermal Systems Branch at NASA LeRC has funded work in developing SDP systems. The generic SDP system uses a large parabolic solar concentrator to focus solar energy onto a power conversion device. The concentrators are large areas and must therefore be efficient and have low specific weights. Yet these surfaces must be precise and capable of being stowed in a launch vehicle and then deployed and sometimes unfurled in space. There are significant technical challenges in engineering such structures, and considerable investigation has been made to date. This is the second of two volumes reporting on the research done by the Advanced Manufacturing Center at Cleveland State University to assist NASA LeRC in evaluating this technology. This volume includes the appendices of selected data sets, drawings, and procedures. The objective of the grant was to restore the solar concentrator development technology of the 1960s while improving it with advances that have occurred since then. This report summarizes the work done from January 1989 through December 1991.

Pintz, A.↗

Hue-saturation-intensity split-spectrum processing of Seasat radar imagery

Characteristics of terrain features in orbital radar imagery are investigated on the basis of radar physics and the human visual system. Signal scattering, the dominant factor in radar imagery, is caused by look angle and relief displacement. Power spectra characteristics are explored, noting that surface scattering dominates the low frequencies and slope significantly affects the high frequency tone variations. The maximum human visual response has been identified for achromatic scenes as 7 cycles per degree, whereas in radar imagery the low frequency half-power point occurs near 2.5 cycles/deg. Image feature size at a scale of 1:500,000 has been calculated for the maximum human response at 1.25 km. A hue-saturation-intensity transformation is presented for displaying two or three data sets on the same image and is demonstrated for Seasat SAR imagery. The transformation is shown to restore low spatial frequencies to the SAR imagery in order to identify terrain features which would otherwise not be visually discernible.

Daily, M.↗

NASA Tech Briefs, March 2010

Topics covered include: Software Tool Integrating Data Flow Diagrams and Petri Nets; Adaptive Nulling for Interferometric Detection of Planets; Reducing the Volume of NASA Earth-Science Data; Reception of Multiple Telemetry Signals via One Dish Antenna; Space-Qualified Traveling-Wave Tube; Smart Power Supply for Battery-Powered Systems; Parallel Processing of Broad-Band PPM Signals; Inexpensive Implementation of Many Strain Gauges; Constant-Differential-Pressure Two-Fluid Accumulator; Inflatable Tubular Structures Rigidized with Foams; Power Generator with Thermo-Differential Modules; Mechanical Extraction of Power From Ocean Currents and Tides; Nitrous Oxide/Paraffin Hybrid Rocket Engines; Optimized Li-Ion Electrolytes Containing Fluorinated Ester Co-Solvents; Probabilistic Multi-Factor Interaction Model for Complex Material Behavior; Foldable Instrumented Bits for Ultrasonic/Sonic Penetrators; Compact Rare Earth Emitter Hollow Cathode; High-Precision Shape Control of In-Space Deployable Large Membrane/Thin-Shell Reflectors; Rapid Active Sampling Package; Miniature Lightweight Ion Pump; Cryogenic Transport of High-Pressure-System Recharge Gas; Water-Vapor Raman Lidar System Reaches Higher Altitude; Compact Ku-Band T/R Module for High-Resolution Radar Imaging of Cold Land Processes; Wide-Field-of-View, High-Resolution, Stereoscopic Imager; Electrical Capacitance Volume Tomography with High-Contrast Dielectrics; Wavefront Control and Image Restoration with Less Computing; Polarization Imaging Apparatus; Stereoscopic Machine-Vision System Using Projected Circles; Metal Vapor Arcing Risk Assessment Tool; Performance Bounds on Two Concatenated, Interleaved Codes; Parameterizing Coefficients of a POD-Based Dynamical System; Confidence-Based Feature Acquisition; Algorithm for Lossless Compression of Calibrated Hyperspectral Imagery; Universal Decoder for PPM of any Order; Algorithm for Stabilizing a POD-Based Dynamical System; Mission Reliability Estimation for Repairable Robot Teams; Processing AIRS Scientific Data Through Level 3; Web-Based Requesting and Scheduling Use of Facilities; AutoGen Version 5.0; Time-Tag Generation Script; PPM Receiver Implemented in Software; Tropospheric Emission Spectrometer Product File Readers; Reporting Differences Between Spacecraft Sequence Files; Coordinating "Execute" Data for ISS and Space Shuttle; Database for Safety-Oriented Tracking of Chemicals; Apparatus for Cold, Pressurized Biogeochemical Experiments; Growing B Lymphocytes in a Three-Dimensional Culture System; Tissue-like 3D Assemblies of Human Broncho-Epithelial Cells; Isolation of Resistance-Bearing Microorganisms; Oscillating Cell Culture Bioreactor; and Liquid Cooling/Warming Garment.

Source record↗

Introducing the 9500 Node Distribution Test System to Support Advanced Power Applications: An Operations-Focused Approach

The 9500 Node Test System is a representative section of distribution power system model developed as a part of the GridAPPS-D™ project, an effort funded by DOE as a part of the Grid Modernization Lab Consortium (GMLC) program. The test system was developed to fulfill a growing need to represent the rapidly evolving state of electric distribution systems by combining elements of legacy infrastructure systems, modern feeder topologies, and an anticipated future with smart grid technologies. It also provides a network model capable of supporting the simulation of operational scenarios such as the ones in a utility distribution control center. This test system allows the evaluation of the performance of advanced power applications in real-time, such as one that simulates the operations of an Advanced Distribution Management Systems (ADMS), Distributed Energy Resource Management Systems (DERMS), etc. in a Distribution control center. This model is an extension of the widely used IEEE 8500 Node Test Feeder and is currently being validated to become an IEEE test case to help increase adoption and widespread usage among both academia and industry. It is a full-size model representative of a section of a utility’s distribution system with multiple feeders fed from different substations. The model includes multiple distribution circuits, a sub-transmission system, multiple substations, behind the meter customer rooftop photovoltaics (PV), and multiple utility-scale distributed energy resources. To enable accurate simulations of operational scenarios, the 9500 Node Test System is designed to support procedure-based operations, with the ability to realistically demonstrate switching operations, feeder reconfiguration, adjustment of volt-var control equipment, dispatch of distributed generation, and response to planned and unplanned outages. The 9500 Node Test System includes three radial distribution feeders with 12.3 MVA of average load, consisting of both medium voltage and low voltage equipment each supplied by a different distribution substation. The three distribution feeders are connected to each other through Normally-Open switches which can be closed when needed to simulate restoration scenarios due to a fault. One feeder represents today’s grid with low penetration of customer-side renewables. The second represents a potential future grid with microgrids and 100% renewable penetration. The third has no customer generation resources, a district steam plant, and a utility-scale solar farm. The three diverse circuits were created to allow the simulation of both today’s situation as well as potential future scenarios. All three feeders have customers connected by low-voltage secondary triplex lines. This test system meets all requirements outlined in the report for creating a simulation environment that would enable discussion between key technical stakeholders as well as having the potential to accelerate operational application development and their subsequent testing and integration. The new model is a possible representation of what we believe the distribution grid may look like in the future: a high penetration of renewables, reconfigurable radial and mesh topology, numerous DERs, islanded microgrids, and significantly increased data and measurement density. The system supports both the solution of existing and newer algorithms but also enables the evaluation of applications in a realistic operational environment defined by task oriented procedural steps that represent the interaction between the control center operator and field personnel.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Net-zero Microgrid Program Report: Microrred de la Montaña Feasibility Study (Executive Summary Extended)

This feasibility study provides the technical and economic rationale for the Microrred de la Montaña as a viable solution for supplying reliable and resilient electricity to an underserved region in Puerto Rico – a region that is the first to be disconnected from the grid and the last to be restored, enduring months long outages. It begins the process of the development of the microgrid through conceptual design, engineering, detailed electrical design, implementation, and operation. The Microrred de la Montaña is organized under the governance of the Cooperativa Hidroeléctrica de la Montaña (Cooperativa) which has legal status as a cooperative and power provider under the laws of Puerto Rico. The members are the municipalities of Adjuntas, Jayuya, Lares and Utuado with a combined population of 90,000. These municipalities are in central Puerto Rico – a mountainous region that is extremely vulnerable to weather events and excessive, long-duration power outages and are among the poorest and most disadvantaged regions in Puerto Rico. Funding from external sources is necessary to acquire the resources for a resilient power delivery system. Regulatory support is necessary to establish operational relationships with the incumbent power providers. The Microrred de la Montaña is envisioned as a resilient microgrid that manages distributed energy resources – local solar, storage, and hydroelectricity over an upgraded distribution network within the boundaries of four municipalities. This feasibility study provides the results of an extensive techno-economic analysis to form a sound basis for decision-making by community leaders, their constituents, funding and investment agencies, and regulators to realize the benefits that are achievable by fully implementing the design and planning recommended for the Microrred de la Montaña.

13 HYDRO ENERGY↗

Guest Editorial: Special Section on Sustainable Energy for Enhancing Grid Resiliency

Extreme weather threatens lives, disables communities, and devastates energy generation, transmission, and distribution systems. These extreme events are likely to become more frequent or more intense due to climate change. Energy networks have shown significant vulnerability during record hurricanes, deadly heat waves, destructive wildfires, and winter storms in the past few years. Because of the energy transition process, modern power grids will feature a high penetration level of the use of renewable resources. The adoption of renewable energy and the rise of omnidirectional power delivery mean that our energy network is more decentralized than ever. In this new environment, grid operation becomes more complex, and achieving resiliency is more difficult than in the past. Many utilities are seeking the latest technologies to improve energy security and responsiveness to severe events. On the one hand, sustainable energy resources can provide emergency power and assist grid restoration in disastrous events. On the other hand, their volatility, susceptibility, interdependency, and other unique features must be carefully considered when being used for grid resilience enhancement. This special section brings together 22 papers that range from innovative research advances tackling fundamental challenges of achieving more resilient grids to real-world demonstrations of leveraging sustainable energy resources to enhance grid resiliency. These papers can be categorized into three groups.

climate change↗

Guidance on EPAct section 707 Emergency Repair and Restoration Vehicle Exclusions: EPAct State and Alternative Fuel Provider Fleet Program Guidance Document

Section 707 of the Energy Policy Act of 2005 (EPAct 2005) amended section 301(9)(E) of EPAct 1992 by adding to the list of vehicles excluded from the definition of "fleet" a new subcategory of emergency motor vehicles, i.e., "vehicles directly used in the emergency repair of transmission lines and in the restoration of electricity service following power outages, as determined by the Secretary." Like other excluded vehicles, these light-duty vehicles (LDVs) do not count (1) when determining whether a fleet is covered under the U.S. Department of Energy's (DOE) State and Alternative Fuel Provider Fleet Program (Program), and (2) for fleets that are covered under the Program, when calculating annual alternative fuel vehicle (AFV)-acquisition requirements. If AFV models of excluded vehicles are acquired, however, a fleet may count them toward their acquisition requirement by including them in the calculation of the number of AFVs acquired. Exclusion Process.

ADVANCED PROPULSION SYSTEMS,ENERGY PLANNING, POLIC↗

On the accuracy of modelling the dynamics of large space structures

Proposed space missions will require large scale, light weight, space based structural systems. Large space structure technology (LSST) systems will have to accommodate (among others): ocean data systems; electronic mail systems; large multibeam antenna systems; and, space based solar power systems. The structures are to be delivered into orbit by the space shuttle. Because of their inherent size, modelling techniques and scaling algorithms must be developed so that system performance can be predicted accurately prior to launch and assembly. When the size and weight-to-area ratio of proposed LSST systems dictate that the entire system be considered flexible, there are two basic modeling methods which can be used. The first is a continuum approach, a mathematical formulation for predicting the motion of a general orbiting flexible body, in which elastic deformations are considered small compared with characteristic body dimensions. This approach is based on an a priori knowledge of the frequencies and shape functions of all modes included within the system model. Alternatively, finite element techniques can be used to model the entire structure as a system of lumped masses connected by a series of (restoring) springs and possibly dampers. In addition, a computational algorithm was developed to evaluate the coefficients of the various coupling terms in the equations of motion as applied to the finite element model of the Hoop/Column.

Diarra, C. M.↗