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At least 109 records · Page 6

A method for estimating soil moisture availability

A method for estimating values of soil moisture based on measurements of infrared surface temperature is discussed. A central element in the method is a boundary layer model. Although it has been shown that soil moistures determined by this method using satellite measurements do correspond in a coarse fashion to the antecedent precipitation, the accuracy and exact physical interpretation (with respect to ground water amounts) are not well known. This area of ignorance, which currently impedes the practical application of the method to problems in hydrology, meteorology and agriculture, is largely due to the absence of corresponding surface measurements. Preliminary field measurements made over France have led to the development of a promising vegetation formulation (Taconet et al., 1985), which has been incorporated in the model. It is necessary, however, to test the vegetation component, and the entire method, over a wide variety of surface conditions and crop canopies.

Carlson, T. N.↗

MIT research in telerobotics

Ongoing MIT research in telerobotics (vehicles capable of some autonomous sensing and manipulating, having some remote supervisory control by people) and teleoperation (vehicles for sensing and manipulating which are fully controlled remotely by people) is discussed. The current efforts mix human and artificial intelligence/control. The idea of adjustable impedance at either end of pure master-slave teleoperation, and simultaneous coordinated control of teleoperator/telerobotic systems which have more than six degrees of freedom (e.g., a combined vehicle and arm, each with five or six DOF) are discussed. A new cable-controlled parallel link arm which offers many advantages over conventional arms for space is briefly described. Predictor displays to compensate for time delay in teleoperator loops, the use of state estimation to help human control decisions in space, and ongoing research in supervisory command language are covered. Finally, efforts to build a human flyable real-time dynamic computer-graphic telerobot simulator are described. These projects represent most, but not all, of the telerobotics research in our laboratory, supported by JPL, NASA Ames and NOAA.

Sheridan, T. B.↗

Response of joint dominated space structures

An efficient linearization method is presented for calculating the transient response of nonlinear systems due to initial disturbances. The method is an extension of the describing function approach in which the steady state response of the system is calculated by representing the nonlinear element, typically joints in the case of space structures, by impedances which are functions of the amplitude of response. Thus, the problem of solving the differential equation for the steady state response becomes one of solving a set of nonlinear algebraic equations involving the steady state amplitudes and phases of the system. It is shown that for the transient case the steady state impedances can be averaged over the range of responses in order to provide equivalent values of stiffness and damping that, for a given set of initial displacements, may be treated as being constant for purposes of calculating system response. Single degree of freedom system are used to demonstrate the method and to develop an approach for optimizing the joint's characteristics so as to minimize transient response times. The use of this method for response estimation and optimization in multiple degree of freedom systems is investigated.

Source record↗

Spacecraft Internal Acoustic Environment Modeling

Acoustic modeling can be used to identify key noise sources, determine/analyze sub-allocated requirements, keep track of the accumulation of minor noise sources, and to predict vehicle noise levels at various stages in vehicle development, first with estimates of noise sources, later with experimental data. In FY09, the physical mockup developed in FY08, with interior geometric shape similar to Orion CM (Crew Module) IML (Interior Mode Line), was used to validate SEA (Statistical Energy Analysis) acoustic model development with realistic ventilation fan sources. The sound power levels of these sources were unknown a priori, as opposed to previous studies that RSS (Reference Sound Source) with known sound power level was used. The modeling results were evaluated based on comparisons to measurements of sound pressure levels over a wide frequency range, including the frequency range where SEA gives good results. Sound intensity measurement was performed over a rectangular-shaped grid system enclosing the ventilation fan source. Sound intensities were measured at the top, front, back, right, and left surfaces of the and system. Sound intensity at the bottom surface was not measured, but sound blocking material was placed tinder the bottom surface to reflect most of the incident sound energy back to the remaining measured surfaces. Integrating measured sound intensities over measured surfaces renders estimated sound power of the source. The reverberation time T6o of the mockup interior had been modified to match reverberation levels of ISS US Lab interior for speech frequency bands, i.e., 0.5k, 1k, 2k, 4 kHz, by attaching appropriately sized Thinsulate sound absorption material to the interior wall of the mockup. Sound absorption of Thinsulate was modeled in three methods: Sabine equation with measured mockup interior reverberation time T60, layup model based on past impedance tube testing, and layup model plus air absorption correction. The evaluation/validation was carried out by acquiring octave band microphone data simultaneously at ten fixed locations throughout the mockup. SPLs (Sound Pressure Levels) predicted by our SEA model match well with measurements for our CM mockup, with a more complicated shape. Additionally in FY09, background NC noise (Noise Criterion) simulation and MRT (Modified Rhyme Test) were developed and performed in the mockup to determine the maximum noise level in CM habitable volume for fair crew voice communications. Numerous demonstrations of simulated noise environment in the mockup and associated SIL (Speech Interference Level) via MRT were performed for various communities, including members from NASA and Orion prime-/sub-contractors. Also, a new HSIR (Human-Systems Integration Requirement) for limiting pre- and post-landing SIL was proposed.

Chu, SShao-sheng R.↗

Effect of Inductance and Requirements for Surge Current Testing of Tantalum Capacitors

Surge current testing is considered one of the most important techniques to evaluate reliability and/or screen out potentially defective tantalum capacitors for low-impedance applications. Analysis of this test, as it is described in the MIL-PRF-55365 document, shows that it does not address several issues that are important to assure adequate and reproducible testing. This work investigates the effect of inductance of the test circuit on voltage and current transients and analyzes requirements for the elements of the circuit, in particular, resistance of the circuit, inductance of wires and resistors, type of switching devices, and characteristics of energy storage bank capacitors. Simple equations to estimate maximum inductance of the circuit to prevent voltage overshooting and minimum duration of charging/discharging cycles to avoid decreasing of the effective voltage and overheating of the parts during surge current testing are suggested.

Teverosky, Alexander↗

Controls of interaction dynamics of orbital assembly

Building structures and spacecraft in orbit will require technologies for positioning, docking/berthing, and joining orbital structures. A fundamental problem underlying the operation of docking and berthing is that of controlling the contact dynamics of mechanical structures actuated by active mechanisms such as robotic devices. Control systems must be designed to control these active mechanisms so that both the free space motions and contact motions are stable and satisfy specifications on position accuracy and bounds on contact forces. For the large orbital structures of the future, the problem of interactive dynamics and control is fundamentally different in several ways than it was for spacecraft docking in the past. First, future space structures must be treated as flexible structures - the operations of docking, berthing, and assembly will need to respect the vibrations of the structures. Second, the assembly of these structures will require multiple-point contact, rather than the essentially single-point positioning of conventional spacecraft docking. Third, some assembly operations require the subassemblies to be brought and held in contact so that successful joining can be accomplished. A preliminary study of contact stability and compliance control design has resulted in the development of an analytical method and a design method to analyze stability. The analytical method analyzes the problem of stability when an actively-controlled structure contacts a passive structure. This method makes it possible to accurately estimate the stiffness of the passive structures with which the contact motion will become unstable. The analytic results suggest that passivity is neither achievable in practice, nor necessary as a design concept. A contact control system need only be passive up to a certain frequency; beyond that frequency the system can be stabilized with sufficiently small gains. With this concept the Center developed a design methodology for achieving desired compliant contact motions. This design method is based on H-infinity norm optimization, which makes it possible to consider both driving point mechanical impedance and systems robustness to modeling uncertainty. A laboratory facility was set up to verify experimentally the analytical and design theory.

Su, Renjeng↗

On the Character of the Zeros of Polynomials Relevant to the Small Curvature Approximation in Asymptotic Diffraction Theory

In dealing with the problem of estimating the high frequency coupling between two antennas mounted on a non-metallic aircraft skin, one is faced with approximation of the spectral integrals representing the propagation of rays along the geodesics of the surface between the antennas. When the antennas are sufficiently separated, the integrals can be conveniently represented as a rapidly convergent residue series. On the other hand, when the antennas are in close proximity, the residue series fails to converge rapidly and a power series representation proves to be efficacious. [Paknys and Wang, IEEE Trans. AP-35(3), 1987, 293-298]. When the effective surface impedance is not small, an intermediate region of separation appears in which neither the residue series nor the power series is effective. Recently, an asymptotic formalism was presented [Pogorzelski, National Radio Science Meeting, Boulder, CO, January 1995] which extends the earlier work of Bremmer [IRE Trans. AP-6, 1958, 267-272] and Wait curvature approximation' to the case of general (non-azimuthal) ray directions on the surface of a cylinder (excluding only axial propagation). Based on the formulation of Pearson [Radio Sci. 21(4), 1986] this asymptotic formalism provided a means of approximating the spectral integrals in the intermediate region of separation.

Zeros Polynomials↗

Space Induced Discharge Model to Be Used on Interface Circuit Vulnerability Assessment

Charging can occur in space due to plasma and high energy particles. Charging is especially severe in certain earth orbits such as geostationary orbit, medium earth orbit and highly inclined orbit. A spacecraft that travels to other planets such as Jupiter also encounters high level of charging due to Jupiter’s radiation belt. The major concern for spacecraft operation due to charging is the survival of sensitive electrical circuits. Dielectrics and floating metal can charge up and discharge onto interface circuits. The electrical circuits need to be evaluated for survival from the electrostatic-discharge (ESD) threat. Both ESD induced upset and damage need to be assessed. The interface circuits are often located inside a shielded unit in the spacecraft structure or a shielded vault with sufficient radiation shielding to avoid surface and internal charging. The materials external to the highly shielded area can charge up and discharge onto wires that can directly dissipate the ESD onto the interface circuits. Figure 1 shows a possible discharge mechanism onto the interfacing circuits. If the wire has an external shield or a coaxial line, some or most of the discharge can flow on the shield to chassis ground. There is always coupling from external discharge. If the wire has no shield, the discharge flows onto the interface circuit. Fig. 1 Possible discharge paths onto the interface circuits. The purpose of this article is to address how to model the ESD threat to be used as the discharge source onto the interface circuit based on the electron beam test data. Different models are needed for different impedances associated with the interface circuits. Once those models are derived, one needs to analyze the interface circuit with the corresponding model using an electrical simulation tool. Then, the circuit’s front-end components can be assessed for damage and upset. Upset is highly dependent on the circuit operation and system requirements, and thus it is not addressed any further. Damage of electrical parts is often rated under Human-Body-Model (HBM) ESD. One can utilize this industry-wide available information to assess the damage vulnerability due to space discharges. However, the HBM waveform does not always match the discharge waveform. To estimate the damage vulnerability of the circuit and set margin, one needs to compare the equivalent energy delivered to the victim between a HBM discharge and the results from an ESD source model based on actual discharges. This paper presents such a comparison for a few select cases.

Xie, Julie↗

NASA Tech Briefs, September 2009

opics covered include: Filtering Water by Use of Ultrasonically Vibrated Nanotubes; Computer Code for Nanostructure Simulation; Functionalizing CNTs for Making Epoxy/CNT Composites; Improvements in Production of Single-Walled Carbon Nanotubes; Progress Toward Sequestering Carbon Nanotubes in PmPV; Two-Stage Variable Sample-Rate Conversion System; Estimating Transmitted-Signal Phase Variations for Uplink Array Antennas; Board Saver for Use with Developmental FPGAs; Circuit for Driving Piezoelectric Transducers; Digital Synchronizer without Metastability; Compact, Low-Overhead, MIL-STD-1553B Controller; Parallel-Processing CMOS Circuitry for M-QAM and 8PSK TCM; Differential InP HEMT MMIC Amplifiers Embedded in Waveguides; Improved Aerogel Vacuum Thermal Insulation; Fluoroester Co-Solvents for Low-Temperature Li+ Cells; Using Volcanic Ash to Remove Dissolved Uranium and Lead; High-Efficiency Artificial Photosynthesis Using a Novel Alkaline Membrane Cell; Silicon Wafer-Scale Substrate for Microshutters and Detector Arrays; Micro-Horn Arrays for Ultrasonic Impedance Matching; Improved Controller for a Three-Axis Piezoelectric Stage; Nano-Pervaporation Membrane with Heat Exchanger Generates Medical-Grade Water; Micro-Organ Devices; Nonlinear Thermal Compensators for WGM Resonators; Dynamic Self-Locking of an OEO Containing a VCSEL; Internal Water Vapor Photoacoustic Calibration; Mid-Infrared Reflectance Imaging of Thermal-Barrier Coatings; Improving the Visible and Infrared Contrast Ratio of Microshutter Arrays; Improved Scanners for Microscopic Hyperspectral Imaging; Rate-Compatible LDPC Codes with Linear Minimum Distance; PrimeSupplier Cross-Program Impact Analysis and Supplier Stability Indicator Simulation Model; Integrated Planning for Telepresence With Time Delays; Minimizing Input-to-Output Latency in Virtual Environment; Battery Cell Voltage Sensing and Balancing Using Addressable Transformers; Gaussian and Lognormal Models of Hurricane Gust Factors; Simulation of Attitude and Trajectory Dynamics and Control of Multiple Spacecraft; Integrated Modeling of Spacecraft Touch-and-Go Sampling; Spacecraft Station-Keeping Trajectory and Mission Design Tools; Efficient Model-Based Diagnosis Engine; and DSN Simulator.

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A Critical Look at Coulomb Counting Approach for State of Charge Estimation in Batteries

In this paper, we consider the problem of state-of-charge estimation for rechargeable batteries. Coulomb counting is a well-known method for estimating the state of charge, and it is regarded as accurate as long as the battery capacity and the beginning state of charge are known. The Coulomb counting approach, on the other hand, is prone to inaccuracies from a variety of sources, and the magnitude of these errors has not been explored in the literature. We formally construct and quantify the state-of-charge estimate error during Coulomb counting due to four types of error sources: (1) current measurement error; (2) current integration approximation error; (3) battery capacity uncertainty; and (4) timing oscillator error/drift. It is demonstrated that the state-of-charge error produced can be either time-cumulative or state-of-charge-proportional. Time-cumulative errors accumulate over time and have the potential to render the state-of-charge estimation utterly invalid in the long term. The proportional errors of the state of charge rise with the accumulated state of charge and reach their worst value within one charge/discharge cycle. The study presents methods for reducing time-cumulative and state-of-charge-proportional mistakes through simulation analysis.

Battery management system↗

Characterization of AlMn TES Impedance, Noise, and Optical Efficiency in the First 150 mm Multichroic Array for Advanced ACTPol

The Advanced ACTPol (AdvACT) upgrade to the Atacama Cosmology Telescope features large arrays of multichroic pixels consisting of two orthogonal-polarization pairs of superconducting bolometers at two observing frequency bands. We present measurements of the detector properties and noise data in a subset of a fielded multichroic array of AlMn transition-edge sensor (TES) detectors. In this array, the distribution of critical temperature T(sub c) across detectors appears uniform at the percent level. The measured noise-equivalent power (NEP) distributions over approximately 1200 detectors are consistent with expectations. We find median NEPs of 4.0×10(exp −17) W/ √ Hz for low-band detectors and 6.2×10(exp −17) W/ √ Hz for high-band detectors under covered-window telescope test conditions with optical loading comparable to observing with precipitable water vapor approximately 0.5 mm. Lastly, we show the estimated detector optical efficiency, and demonstrate the ability to perform optical characterization over hundreds of detectors at once using a cryogenic blackbody source.

Crowley, Kevin T.↗

Exploration of the Theoretical Physical Capacity of the John F. Kennedy International Airport Runway System

A design study was completed to explore the theoretical physical capacity (TPC) of the John F. Kennedy International Airport (KJFK) runway system for a northflow configuration assuming impedance-free (to throughput) air traffic control functionality. Individual runways were modeled using an agent-based, airspace simulation tool, the Airspace Concept Evaluation System (ACES), with all runways conducting both departures and arrivals on a first-come first-served (FCFS) scheduling basis. A realistic future flight schedule was expanded to 3.5 times the traffic level of a selected baseline day, September 26, 2006, to provide a steady overdemand state for KJFK runways. Rules constraining departure and arrival operations were defined to reflect physical limits beyond which safe operations could no longer be assumed. Safety buffers to account for all sources of operational variability were not included in the TPC estimate. Visual approaches were assumed for all arrivals to minimize inter-arrival spacing. Parallel runway operations were assumed to be independent based on lateral spacing distances. Resulting time intervals between successive airport operations were primarily constrained by same-runway and then by intersecting-runway spacing requirements. The resulting physical runway capacity approximates a theoretical limit that cannot be exceeded without modifying runway interaction assumptions. Comparison with current KJFK operational limits for a north-flow runway configuration indicates a substantial throughput gap of approximately 48%. This gap may be further analyzed to determine which part may be feasibly bridged through the deployment of advanced systems and procedures, and which part cannot, because it is either impossible or not cost-effective to control. Advanced systems for bridging the throughput gap may be conceptualized and simulated using this same experimental setup to estimate the level of gap closure achieved.

Neitzke, Kurt W.↗

Thundercloud current determination from measurements at the earth's surface

For the analysis of the actual dominant mechanism or mechanisms of electrification in a given storm cell, it is of great importance to make observations which can be used to determine the configuration and the magnitudes of the currents and impedances of the generator systems in active thunderclouds. Krider and Musser (1982) have measured Maxwell currents below Florida thunderclouds and shown that their patterns are consistent with simple generator geometries. It is, therefore, of great interest to study the extent to which a set of Maxwell current measurements can be inverted to obtain the generator currents and locations. Nisbet (1983) has developed an electrical model for active thunderclouds which solves equations for current densities and electric fields. The present investigation is concerned with the extent to which such a model can be used to derive data about the cloud generator magnitudes and locations, taking into account also the conductivity profile from ground-based measurements or estimates of the Maxwell current density.

Nisbet, J. S.↗

Angular and Polarization Response of Multimode Sensors with Resistive-Grid Absorbers

High sensitivity receiver systems with near ideal polarization sensitivity are highly desirable for development of millimeter and sub-millimeter radio astronomy. Multimoded bolometers provide a unique solution to achieve such sensitivity, for which hundreds of single-mode sensors would otherwise be required. The primary concern in employing such multimoded sensors for polarimetery is the control of the polarization systematics. In this paper, we examine the angular- and polarization- dependent absorption pattern of a thin resistive grid or membrane, which models an absorber used for a multimoded bolometer. The result shows that a freestanding thin resistive absorber with a surface resistivity of eta/2, where eta is the impedance of free space, attains a beam pattern with equal E- and H-plane responses, leading to zero cross polarization. For a resistive-grid absorber, the condition is met when a pair of grids is positioned orthogonal to each other and both have a resistivity of eta/2. When a reflective backshort termination is employed to improve absorption efficiency, the cross-polar level can be suppressed below −30 dB if acceptance angle of the sensor is limited to < or approx. 60deg. The small cross-polar systematics have even-parity patterns and do not contaminate the measurements of odd-parity polarization patterns, for which many of recent instruments for cosmic microwave background are designed. Underlying symmetry that suppresses these cross-polar systematics is discussed in detail. The estimates and formalism provided in this paper offer key tools in the design consideration of the instruments using the multimoded polarimeters.

High sensitivity receiver systems↗

Experimental Validation of Numerical Simulations for an Acoustic Liner in Grazing Flow

A coordinated experimental and numerical simulation effort is carried out to improve our understanding of the physics of acoustic liners in a grazing flow as well our computational aeroacoustics (CAA) method prediction capability. A numerical simulation code based on advanced CAA methods is developed. In a parallel effort, experiments are performed using the Grazing Flow Impedance Tube at the NASA Langley Research Center. In the experiment, a liner is installed in the upper wall of a rectangular flow duct with a 2 inch by 2.5 inch cross section. Spatial distribution of sound pressure levels and relative phases are measured on the wall opposite the liner in the presence of a Mach 0.3 grazing flow. The computer code is validated by comparing computed results with experimental measurements. Good agreements are found. The numerical simulation code is then used to investigate the physical properties of the acoustic liner. It is shown that an acoustic liner can produce self-noise in the presence of a grazing flow and that a feedback acoustic resonance mechanism is responsible for the generation of this liner self-noise. In addition, the same mechanism also creates additional liner drag. An estimate, based on numerical simulation data, indicates that for a resonant liner with a 10% open area ratio, the drag increase would be about 4% of the turbulent boundary layer drag over a flat wall.

Tam, Christopher K. W.↗

NASA Tech Briefs, October 2013

Topics include: A Short-Range Distance Sensor with Exceptional Linearity; Miniature Trace Gas Detector Based on Microfabricated Optical Resonators; Commercial Non-Dispersive Infrared Spectroscopy Sensors for Sub-Ambient Carbon Dioxide Detection; Fast, Large-Area, Wide-Bandgap UV Photodetector for Cherenkov Light Detection; Mission Data System Java Edition Version 7; Adaptive Distributed Environment for Procedure Training (ADEPT); LEGEND, a LEO-to-GEO Environment Debris Model; Electronics/Computers; Millimeter-Wave Localizers for Aircraft-to-Aircraft Approach Navigation; Impedance Discontinuity Reduction Between High-Speed Differential Connectors and PCB Interfaces; SpaceCube Version 1.5; High-Pressure Lightweight Thrusters; Non-Magnetic, Tough, Corrosion- and Wear-Resistant Knives From Bulk Metallic Glasses and Composites; Ambient Dried Aerogels; Applications for Gradient Metal Alloys Fabricated Using Additive Manufacturing; Passivation of Flexible YBCO Superconducting Current Lead With Amorphous SiO2 Layer; Propellant-Flow-Actuated Rocket Engine Igniter; Lightweight Liquid Helium Dewar for High-Altitude Balloon Payloads; Method to Increase Performance of Foil Bearings Through Passive Thermal Management; Unibody Composite Pressurized Structure; JWST Integrated Science Instrument Module Alignment Optimization Tool; Radar Range Sidelobe Reduction Using Adaptive Pulse Compression Technique; Digitally Calibrated TR Modules Enabling Real-Time Beamforming SweepSAR Architectures; Electro-Optic Time-to-Space Converter for Optical Detector Jitter Mitigation; Partially Transparent Petaled Mask/Occulter for Visible-Range Spectrum; Educational NASA Computational and Scientific Studies (enCOMPASS); Coarse-Grain Bandwidth Estimation Scheme for Large-Scale Network; Detection of Moving Targets Using Soliton Resonance Effect; High-Efficiency Nested Hall Thrusters for Robotic Solar System Exploration; High-Voltage Clock Driver for Photon-Counting CCD Characterization; Development of the Code RITRACKS; and Enabling Microliquid Chromatography by Microbead Packing of Microchannels.

Source record↗

How to Leverage the Power of SAR Observations for Forest Monitoring Systems

Earth observations from Synthetic Aperture Radar (SAR) can provide unique observations related to forest structure and condition. Furthermore, SAR has many potential applications in forest monitoring systems, particularly where clouds have impeded optical observations. Currently, there is a reliable, freely-available, provision of SAR datasets, such as Sentinel-1, and there are plans to have more observations in the near- future (NISAR, BIOMASS). Given SAR’s enhanced earth observation characteristics, there is broad interest in using SAR datasets for decision support systems, such as deforestation early warning systems. However, applications of SAR are still underutilized. What is preventing users from using SAR data in their decision support systems? This study documents the experiences and lessons learned from the SERVIR network on the main limitations of incorporating SAR datasets into existing forest monitoring systems. This research also focuses on the major technical and scientific barriers we experience and best practices to address them. The results of this study are part of the SERVIR- SilvaCarbon collaboration. The primary goal of this collaboration is to build capacity in the applied use of SAR for forest monitoring and biomass estimation. The products of this effort aim to start closing the gap between SAR-science and forest applications. We will also present results to generate applied-ready knowledge for SAR.

SAR↗

Mechanical response tissue analyzer for estimating bone strength

One of the major concerns for extended space flight is weakness of the long bones of the legs, composed primarily of cortical bone, that functions to provide mechanical support. The strength of cortical bone is due to its complex structure, described simplistically as cylinders of parallel osteons composed of layers of mineralized collagen. The reduced mechanical stresses during space flight or immobilization of bone on Earth reduces the mineral content, and changes the components of its matrix and structure so that its strength is reduced. Currently, the established clinical measures of bone strength are indirect. The measures are based on determinations of mineral density by means of radiography, photon absorptiometry, and quantitative computer tomography. While the mineral content of bone is essential to its strength, there is growing awareness of the limitations of the measurement as the sole predictor of fracture risk in metabolic bone diseases, especially limitations of the measurement as the sole predictor of fracture risk in metabolic bone diseases, especially osteoporosis. Other experimental methods in clinical trials that more directly evaluate the physical properties of bone, and do not require exposure to radiation, include ultrasound, acoustic emission, and low-frequency mechanical vibration. The last method can be considered a direct measure of the functional capacity of a long bone since it quantifies the mechanical response to a stimulus delivered directly to the bone. A low frequency vibration induces a response (impedance) curve with a minimum at the resonant frequency, that a few investigators use for the evaluation of the bone. An alternative approach, the method under consideration, is to use the response curve as the basis for determination of the bone bending stiffness EI (E is the intrinsic material property and I is the cross-sectional moment of inertia) and mass, fundamental mechanical properties of bone.

Arnaud, Sara B.↗