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A hybrid finite element/modal analysis/spectral analysis method is presented for the extraction of frequency dependent strain energy release rates and stress intensity factors. The approach is based on the crack closure technique and is formulated directly in the frequency domain. It is demonstrated for a center cracked panel subject to static in-plane and acoustic loading.
A spectral analysis method is presented for the extraction of frequency dependent strain energy release rates and stress intensity factors. The approach is based on the crack closure technique and is formulated directly in the frequency domain. Because of this, it is computationally more efficient than an alternative time domain approach for systems exhibiting peak behavior. The method is demonstrated for a center cracked panel subject to static in-plane and random acoustic loading.
We report results from searches for anisotropic stochastic gravitational-wave backgrounds using data from the first three observing runs of the Advanced LIGO and Advanced Virgo detectors. For the first time, we include Virgo data in our analysis and run our search with a new efficient pipeline called PyStochon data folded over one sidereal day. We use gravitational-wave radiometry(broadband and narrow band) to produce sky maps of stochastic gravitational-wave backgrounds and to search for gravitational waves from point sources. A spherical harmonic decomposition method is employed to look for gravitational-wave emission from spatially-extended sources. Neither technique found evidence of gravitational-wave signals. Hence we derive 95% confidence-level upper limit sky maps on the gravitational-wave energy flux from broadband point sources, ranging from F(α,Θ) < (0.013−7.6)×10^(−8)erg/sq. cm s Hz,and on the (normalized) gravitational-wave energy density spectrum from extended sources, ranging from Ω(α,Θ) < (0.57−9.3)×10^(−9) per sr, depending on direction (Θ) and spectral index (α). These limits improve upon previous limits by factors of 2.9−3.5. We also set 95% confidence level upper limits on the frequency-dependent strain amplitudes of quasimonochromatic gravitational waves coming from three interesting targets, Scorpius X-1, SN1987A and the Galactic Center, with best upper limits range fromh(0) < (1.7−2.1)×10^(−25), a factor of ≥ 2.0 improvement compared to previous stochastic radiometer searches.
Mass Mitigation in Structural Designs Via Dynamic Properties The reported efforts are focused on mitigating unnecessary mass in aerospace hardware via leveraging dynamic strength of materials and the frequency dependency of strain. Analytically predicted dynamic responses of structures are often applied as static loads in stress analyses that ultimately dictate the weight of a structural design. Assuming a dynamic response is a static load and then comparing resulting stress predictions to a static strength property is a long-standing engineering practice. Doing so is known to be, or is assumed to be, conservative. However, little indication of the order of magnitude of embedded conservatism has been identified. NASA/MSFC efforts in 2011, 2019, 2020, and now in 2021 have begun to qualitatively show the order of magnitude of that conservatism. A quick turnaround engineering method is pursued to leverage the subject facets of physics for the purpose of decreasing the weight of flight hardware. Tests performed using simple beams and significant observations are described.
The efforts reported here are focused on mitigating unnecessary mass in aerospace hardware. The approach to remove this undesired mass from the design is to leverage both the dynamic strength of materials and the frequency dependency of strain. Analytically predicted dynamic responses of structures are often applied as static loads in stress analyses that ultimately dictate the weight of a structural design. Assuming a dynamic response is a static load and then comparing resulting stress predictions to a static strength property is a long-standing engineering practice. Doing so is known to be, or is assumed to be, conservative. However, little indication of the order of magnitude of embedded conservatism has been identified. NASA/MSFC efforts in 2011, 2019, 2020, and now in 2021 have begun to qualitatively show the order of magnitude of that conservatism. A quick turnaround engineering method is pursued to leverage the subject facets of physics for the purpose of decreasing the weight of flight hardware. Tests performed using simple beams and significant observations are described.
This study is intended to investigate the frequency dependency of significant strain due to vibratory loads in aerospace vehicle components. The notion that "higher frequency" dynamic loads applied as static loads is inherently conservative is perceived as widely accepted. This effort is focused on demonstrating that principle and attempting to evolve methods to capitalize on it to mitigate undue conservatism. It has been suggested that observations of higher frequency modes that resulted in very low corresponding strain did so due to those modes not being significant. Two avionics boxes, one with its first significant mode at 341 Hz and the other at 857 Hz, were attached to a flat panel installed on a curved orthogrid panel which was driven acoustically in tests performed at NASA/MSFC. Strain and acceleration were measured at select locations on each of the boxes. When possible, strain gage rosettes and accelerometers were installed on either side of a given structural member so that measured strain and acceleration data would directly correspond to one another. Ultimately, a frequency above which vibratory loads can be disregarded for purposes of static structural analyses and sizing of typical robust aerospace components is sought.
The National Research Council's report entitled: A Strategy for Space Biology and Medical Science, highlighted several areas of fundamental scientific investigation which must be addressed to make long-term space exploration not only feasible, but safe. This "Goldberg Strategy," as well as several subsequent reports published by the NRC's Space Studies Board (e.g., Assessment of Programs in Space Biology and Medicine, Smith et. al., 1991), suggests that the principal hurdle to man's extended presence in space is the osteopenia which parallels reduced gravity. Ironically, the most significant risk to the skeleton may only be realized on return to normal gravitational fields, and full recovery of bone mass may never occur. Effective counter-measures to this microgravity induced bone loss are thus essential. Considering the similarities of space and aging induced osteopenia, an indisputable benefit of such a prophylaxis would be its potential as a treatment for the bone loss which plagues over 25 million people in the U.S. The osteogenic potential of mechanical strain is strongly frequency dependent, with sensitivity increasing up through at least 60 Hz (cycles per second). One hundred seconds per day of a 1 Hz cyclic loading will inhibit disuse osteopenia only if sufficient in magnitude to engender 1000 microstrain (mu(epsilon)) in the tissue. When loading is applied at 30 Hz, however, mechanical strains on the order of 5O mu(epsilon) (approx. 1% of the peak strains which occur in bone during vigorous functional activity), can stimulate bone formation in a duration dependent manner. In longer term animal studies, strains of less than 10 mu(epsilon), induced non-invasively via a whole body vibration, will stimulate bone formation on the surfaces of trabeculae, increase bone density, and improve strength. Finally, preliminary results from a double blind prospective clinical trial shows promise in inhibiting the bone loss which parallels the menopause. Based on these observations, we propose that these high frequency, low magnitude, mechanical strains effectively serve as a "surrogate" for musculoskeletal ground reaction forces, and thus represent an ideal countermeasure to the osteopenia which parallels microgravity conditions. The specific goal of this NASA funded work is to identify genes in bone upregulated by disuse, and to determine the efficacy of an osteogenic mechanical stimulus to downregulate their expression.
The low-frequency characteristics of InAlAs/In(x)Ga(1-x)As high-electron-mobility transistors (HEMTs) are studied, and trap densities are evaluated. The HEMTs' transconductance g(m) and output resistance R(ds) dispersion are smallest for 60 percent indium (In) content and largest for 53 percent In. The maximum dispersion for the 53 percent In sample is about 6 percent for g(m) and about 13.3 percent for R(ds), corresponding to lower values than observed in MESFETs. The R(ds) dispersion characteristics are weaker than in AlGaAs/GaAs HEMTs and manifest themselves primarily up to 100 kHz. An analysis of the dispersion results indicates that, unlike in the case of MESFETs, the channel region under the gate rather than the access regions is responsible for the dispersion. Interface state densities were extracted by the AC conductance method and were found to follow the same trend as the g(m) and R(ds) dispersion.
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Assuming that dynamic (transient/vibratory) loads are static in the design of structures is a long-standing engineering practice. The assumption is conservative for hardware that will have limited exposure to the specified dynamic environment and fatigue is not a concern. This is the case for most space flight hardware. Once out of the Earth’s atmosphere, significant vibrations are non-existent for most hardware and vibration cycles are limited. Mass is, and has always been, a concern with respect to flight hardware design. How much unnecessary mass due to the subject assumption may be in structural designs was questioned and numerous tests have been performed to qualitatively address that. Tests have been performed on simple aluminum beams, beams with bolted joints and beams with welded joints. Results of those tests are reported in this paper. The objective of these efforts was to demonstrate the order of magnitude of conservatism associated with this engineering process via comparing static to dynamic tests and the longer term endgame is to develop a new or modified quick turnaround structural design process that circumvents assuming dynamic loads are static and results in lighter structural designs. Test results qualitatively demonstrate notable conservatism. Activities to devise the new method are underway.
The development of a family of silicon based integrated vibration sensors capable of sensing mechanical resonances over a broad range of frequencies with minimal signal processing requirements is presented. Two basic general embodiments of the concept were designed and fabricated. The first design was structured around an array of cantilever beams and fabricated using the ARPA sponsored multi-user MEMS processing system (MUMPS) process at the Microelectronics Center of North Carolina (MCNC). As part of the design process for this first sensor, a comprehensive finite elements analysis of the resonant modes and stress distribution was performed using PATRAN. The dependence of strain distribution and resonant frequency response as a function of Young's modulus in the Poly-Si structural material was studied. Analytical models were also studied. In-house experimental characterization using optical interferometry techniques were performed under controlled low pressure conditions. A second design, intended to operate in a non-resonant mode and capable of broadband frequency response, was proposed and developed around the concept of a cantilever beam integrated with a feedback control loop to produce a null mode vibration sensor. A proprietary process was used to integrat a metal-oxide semiconductor (MOS) sensing device, with actuators and a cantilever beam, as part of a compatible process. Both devices, once incorporated as part of multifunction data acquisition and telemetry systems will constitute a useful system for NASA launch vibration monitoring operations. Satellite and other space structures can benefit from the sensor for mechanical condition monitoring functions.
Anharmonic effects in solids are often described in terms of generalized Grueneisen parameters which measure the strain dependence of the lattice vibrational frequencies. The relationship between these parameters and the solid nonlinearity parameters measured directly in ultrasonic harmonic generation experiments is derived using an approach valid for normal-mode elastic wave propagation in any crystalline direction. The resulting generalized Grueneisen parameters are purely isentropic in contrast to the Brugger-Grueneisen parameters which are of a mixed thermodynamic state. Experimental data comparing the isentropic generalized Grueneisen parameters and the Brugger-Grueneisen parameters are presented.
We report on an all-sky search for periodic gravitational waves in the frequency range 50-1000 Hertz with the first derivative of frequency in the range −8.9 × 10(exp −10) Hertz per second to zero in two years of data collected during LIGO's fifth science run. Our results employ a Hough transform technique, introducing a chi(sup 2) test and analysis of coincidences between the signal levels in years 1 and 2 of observations that offers a significant improvement in the product of strain sensitivity with compute cycles per data sample compared to previously published searches. Since our search yields no surviving candidates, we present results taking the form of frequency dependent, 95% confidence upper limits on the strain amplitude h(sub 0). The most stringent upper limit from year 1 is 1.0 × 10(exp −24) in the 158.00-158.25 Hertz band. In year 2, the most stringent upper limit is 8.9 × 10(exp −25) in the 146.50-146.75 Hertz band. This improved detection pipeline, which is computationally efficient by at least two orders of magnitude better than our flagship Einstein@Home search, will be important for 'quicklook' searches in the Advanced LIGO and Virgo detector era.
This paper presents the concept and a design methodology for robust damage-mitigating control (DMC) of aircraft. The goal of DMC is to simultaneously achieve high performance and structural durability. The controller design procedure involves consideration of damage at critical points of the structure, as well as the performance requirements of the aircraft. An aeroelastic model of the wings has been formulated and is incorporated into a nonlinear rigid-body model of aircraft flight-dynamics. Robust damage-mitigating controllers are then designed using the H(infinity)-based structured singular value (mu) synthesis method based on a linearized model of the aircraft. In addition to penalizing the error between the ideal performance and the actual performance of the aircraft, frequency-dependent weights are placed on the strain amplitude at the root of each wing. Using each controller in turn, the control system is put through an identical sequence of maneuvers, and the resulting (varying amplitude cyclic) stress profiles are analyzed using a fatigue crack growth model that incorporates the effects of stress overload. Comparisons are made to determine the impact of different weights on the resulting fatigue crack damage in the wings. The results of simulation experiments show significant savings in fatigue life of the wings while retaining the dynamic performance of the aircraft.
Modern finite element methods (FEM's) enable the precise modeling of mass and stiffness properties in what were in the past overwhelmingly large and complex structures. These models allow the accurate determination of natural frequencies and mode shapes. However, adequate methods for modeling highly damped and high frequency dependent structures did not exist until recently. The most commonly used method, Modal Strain Energy, does not correctly predict complex mode shapes since it is based on the assumption that the mode shapes of a structure are real. Recently, many techniques have been developed which allow the modeling of frequency dependent damping properties of materials in a finite element compatible form. Two of these methods, the Golla-Hughes-McTavish method and the Lesieutre-Mingori method, model the frequency dependent effects by adding coordinates to the existing system thus maintaining the linearity of the model. The third model, proposed by Bagley and Torvik, is based on the Fractional Calculus method and requires fewer empirical parameters to model the frequency dependence at the expense of linearity of the governing equations. This work examines the Modal Strain Energy, Golla-Hughes-McTavish and Bagley and Torvik models and compares them to determine the plausibility of using them for modeling viscoelastic damping in large structures.
Multiple-mode nonlinear analysis is carried out for beams subjected to acoustic excitation. Effects of both nonlinear damping and large-deflection are included in the analysis in an attempt to explain the experimental phenomena of aircraft panels excited at high sound pressure levels; that is the broadening of the strain response peaks and the increase of modal frequency. An amplitude dependent nonlinear damping model is used in the anlaysis to study the effects and interactions of multiple modes, nonlinear stiffness and nonlinear damping on the random response of beams. Mean square maximum deflection, mean square maximum strain, and spectral density function of maximum strain for simple supported and clamped beams are obtained. It is shown analytically that nonlinear damping contributes significantly to the broadening of the response peak and to the mean square deflection and strain.
A Warren-Averbach x-ray line profile analysis was applied to, broadened x-ray diffraction peaks from copper deformed in fatigue. The copper specimens were fatigued by four point bending at various strain amplitudes, and measurements were made at various fractions of the total fatigue life. The analysis results in an estimation of 1) an average coherently diffracting domain size in a direction normal to the diffracting planes; and 2) a strain distribution function. The strain distribution function is in terms of the root mean square strain, <ϵ^(2)> where ϵ is averaged over a given distance at all points in the diffracting crystals. This rms strain is expressed as a function of averaging distance for a direction normal to the diffracting planes. The rms strains were found to be a function of the fatigue strain amplitude level, increasing with amplitude and reaching a maximum limiting value during the first 2% of the fatigue life. The strains were normally larger in the 4lO0 direction compared to the <111> direction and the absolute values were quite small. These results may be explained by assuming the dislocations are present in the form of dipoles because the lattice strain around a dipole is much less than around single dislocations. Conclusions arrived at in this analysis are in agreement with current theories of fatigue damage in metals. The result that maximum hardening is achieved during the initial few percent of the fatigue life is confirmed by many other investigators using entirely different analytical techniques. It is felt that the structure of the material is changing during this initial hardening stage to an eventual steady state characteristic of the testing conditions. A unique substructure is developed which thereafter persists, and the remainder of the fatigue test is taken up by crack propagation through this substructure until ultimate failure occurs by fracture. The formation of this steady state structure is dependent on the maximum fatigue strain amplitude and on the frequency and temperature of cycling for a particular material.
The low cycle fatigue (LCF) properties of a single-crystal nickel-base superalloy Rene N4, have been examined at 760 and 980 C in air. Specimens having crystallographic orientations near the 001, 011, -111, 023, -236, and -145 lines were tested in fully reversed, total-strain-controlled LCF tests at a frequency of 0.1 Hz. At 760 C, this alloy exhibited orientation dependent tension-compression anisotropies of yielding which continued to failure. Also at 760 C, orientations exhibiting predominately single slip exhibited serrated yielding for many cycles. At 980 C, orientation dependencies of yielding behavior were smaller. In spite of the tension-compression anisotropies, cyclic stress range-strain range behavior was not strongly orientation dependent for either test temperature. Fatigue life on a total strain range basis was highly orientation dependent at 760 and 980 C and was related chiefly to elastic modulus, low modulus orientations having longer lives. Stage I crack growth on 111 planes was dominant at 760 C, while Stage II crack growth occurred at 980 C. Crack initiation generally occurred at near-surface micropores, but occasionally at oxidation spikes in the 980 C tests.