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NASA NTRS1992

Dominant modes of mechanical systems

To obtain a reduced model of a mechanical system, one can identify the dominant modes and retain those as the reduced model. Two widely used schemes for selection of dominant modes are modal cost analysis (MCA) and balancing, but neither of these methods guarantees that the model error is small, where model error measures the difference between the output of the full model and the output of the reduced model. The authors introduce a set of coordinates called pseudo uncorrelated modal coordinates (PUnc) that can be used in conjunction with component cost analysis to select dominant modes yielding a reduced model with minimum model error. Furthermore, unlike MCA and balancing, the accuracy of the reduced model (the model error) in PUnc coordinates can be evaluated before reduction.

Breida, M.↗
NASA NTRS1992

Dominant modes via model error

Obtaining a reduced model of a stable mechanical system with proportional damping is considered. Such systems can be conveniently represented in modal coordinates. Two popular schemes, the modal cost analysis and the balancing method, offer simple means of identifying dominant modes for retention in the reduced model. The dominance is measured via the modal costs in the case of modal cost analysis and via the singular values of the Gramian-product in the case of balancing. Though these measures do not exactly reflect the more appropriate model error, which is the H2 norm of the output-error between the full and the reduced models, they do lead to simple computations. Normally, the model error is computed after the reduced model is obtained, since it is believed that, in general, the model error cannot be easily computed a priori. The authors point out that the model error can also be calculated a priori, just as easily as the above measures. Hence, the model error itself can be used to determine the dominant modes. Moreover, the simplicity of the computations does not presume any special properties of the system, such as small damping, orthogonal symmetry, etc.

Yousuff, A.↗
NASA NTRS1983

Dominant modes of relationship between U.S. temperature and geomagnetic activity

Eigen-analysis is applied to a matrix of cross-correlation coefficients between the geomagnetic aa-index for 0 to 23-yr lag and the monthly mean temperature at 32 United States stations. About 75 percent of the relationship between the two fields is contained in three dominant modes. A secular trend (about 90 yr) and two 11-yr cycles dominate the mode time series. The month-to-month changes in the temperature anomaly patterns indicate a slow eddy-like motion to the east of the Continental Divide for all three dominant modes.

Prohaska, J. T.↗
NASA NTRS1975

The dominant mode of standing Alfven waves at the synchronous orbit

Low-frequency oscillations of the earth's magnetic field recorded by a magnetometer on board ATS 1 have been examined for the 6-month interval between January and June 1968. Using evidence from OGO 5 and ATS 5 as well as the data from ATS 1, it is argued that the dominant mode at ATS 1 must be the fundamental rather than the second harmonic of a standing Alfven wave. It is concluded that these transverse oscillations are more accurately associated with magnetically disturbed days than with quiet days. From 14 instances when oscillations of distinctly different periods occurred during the same time interval at ATS 1, it is also concluded that higher harmonics can exist. The period ratio in seven of the 14 cases corresponds to the simultaneous occurrence of the second harmonic with the fundamental, and four other cases could be identified as the simultaneous occurrence of the fourth harmonic with the fundamental.

Cummins, W. D.↗
NASA NTRS1975

The dominant mode of standing Alfven waves at synchronous orbit

Low-frequency oscillations of the earth's magnetic field recorded by the UCLA magnetometer on board ATS-1, have been examined for the six-month interval, January-June, 1968. The initial interpretation, that these oscillations represent the second harmonic of a standing Alfven wave, has been re-examined, and it is concluded that this hypothesis must be withdrawn. Using evidence from OGO-5 and ATS-5, as well as the data from ATS-1, it is argued that the dominant mode at the synchronous orbit must be the fundamental rather than the second harmonic. From 14 instances when the oscillations of distinctly different periods occurred during the same time interval at ATS-1 it is concluded that higher harmonics can exist. The period ratio in 7 of the 14 cases corresponds to the simultaneous occurrence of the second harmonic with the fundamental, and 4 other cases could be identified as the simultaneous occurrence of the fourth harmonic with the fundamental.

Cummings, W. D.↗
NASA NTRS1984

Electron-cyclotron maser emission - Relative growth and damping rates for different modes and harmonics

The temporal growth rate and the number of e-folding growths are calculated and compared for the following wave modes due to a loss-cone-driven cyclotron maser: fundamental x, o, and z modes and second harmonic x and o modes. The dominant mode of the maser should be the fastest growing mode for a saturated maser and should be the mode with the greatest number of e-folding growths for an unsaturated maser; this mode is the fundamental x mode) for a plasma frequency to cyclotron frequency ratio of less than about 0.3; it is the z mode (or perhaps the fundamental o mode) for ratios between 0.3 and 1.0, and the z mode (or perhaps the second harmonic x mode) for ratios between 1.0 and 1.3. Two main points are made: the dominance of the z mode over the range of ratios considered and the very weak effect of cyclotron damping. Electron-cyclotron maser emission is seen as responsible for auroral kilometric radiation, decametric radio emission from Jupiter and Saturn, solar microwave spike bursts, and microwave emission from some flare stars.

Melrose, D. B.↗
NASA NTRS1992

Dynamic analysis to evaluate viscoelastic passive damping augmentation for the Space Shuttle Remote Manipulator System

The effectiveness of constrained viscoelastic layer damping treatment designs is evaluated separately as passive control measures for low frequency joint dominated modes and higher frequency boom flexure dominated modes using a NASTRAN finite element analysis. Passive damping augmentation is proposed which is based on a constrained viscoelastic layer damping treatment applied to the surface of the manipulators's flexible booms. It is pointed out that even the joint compliance dominated modes can be damped to some degree through appropriate design of the treatment.

Alberts, Thomas E.↗
NASA NTRS1987

Efficient placement of structural dynamics sensors on the space station

System identification of the space station dynamic model will require flight data from a finite number of judiciously placed sensors on it. The placement of structural dynamics sensors on the space station is a particularly challenging problem because the station will not be deployed in a single mission. Given that the build-up sequence and the final configuration for the space station are currently undetermined, a procedure for sensor placement was developed using the assembly flights 1 to 7 of the rephased dual keel space station as an example. The procedure presented approaches the problem of placing the sensors from an engineering, as opposed to a mathematical, point of view. In addition to locating a finite number of sensors, the procedure addresses the issues of unobserved structural modes, dominant structural modes, and the trade-offs involved in sensor placement for space station. This procedure for sensor placement will be applied to revised, and potentially more detailed, finite element models of the space station configuration and assembly sequence.

Lepanto, Janet A.↗
NASA NTRS2017

Advanced Characterisation of Aerosol Size Properties from Measurements of Spectral Optical Depth Using the GRASP Algorithm

This study evaluates the potential of using aerosol optical depth (τ (sub a)) measurements to characterise the microphysical and optical properties of atmospheric aerosols. With this aim, we used the recently developed GRASP (Generalized Retrieval of Aerosol and Surface Properties) code for numerical testing of six different aerosol models with different aerosol loads. The direct numerical simulations (self-consistency tests) indicate that the GRASP-AOD retrieval provides modal aerosol optical depths (fine and coarse) to within 0.01 of the input values. The retrieval of the fine-mode radius, width and volume concentration are stable and precise if the real part of the refractive index is known. The coarse-mode properties are less accurate, but they are significantly improved when additional a priori information is available. The tests with random simulated errors show that the uncertainty in the bimodal log-normal size distribution parameters increases as the aerosol load decreases. Similarly, the reduction in the spectral range diminishes the stability of the retrieved parameters. In addition to these numerical studies, we used optical depth observations at eight AERONET locations to validate our results with the standard AERONET inversion products. We found that bimodal log-normal size distributions serve as useful input assumptions, especially when the measurements have inadequate spectral coverage and/or limited accuracy, such as moon photometry. Comparisons of the mode median radii between GRASP-AOD and AERONET indicate average differences of 0.013µm for the fine mode and typical values of 0.2–0.3µm for the coarse mode. The dominant mode (i.e. fine or coarse) indicates a 10 % difference in mode radii between the GRASP-AOD and AERONET inversions, and the average of the difference in volume concentration is around 17 % for both modes. The retrieved values of the fine-mode τ(sub a)(500) using GRASP-AOD are generally between those values obtained by the standard AERONET inversion and the values obtained by the AERONET spectral deconvolution algorithm (SDA), with differences typically lower than 0.02 between GRASP-AOD and both algorithms. Finally, we present some examples of application of GRASP-AOD inversion using moon photometry and the airborne PLASMA sun photometer during the ChArMEx summer 2013 campaign in the western Mediterranean.

Torres, Benjamin↗
NASA NTRS1995

Vibration Analysis of a Split Path Gearbox

Split path gearboxes can be attractive alternatives to the common planetary designs for rotorcraft, but because they have seen little use, they are relatively high risk designs. To help reduce the risk of fielding a rotorcraft with a split path gearbox, the vibration and dynamic characteristics of such a gearbox were studied. A mathematical model was developed by using the Lagrangian method, and it was applied to study the effect of three design variables on the natural frequencies and vibration energy of the gearbox. The first design variable, shaft angle, had little influence on the natural frequencies. The second variable, mesh phasing, had a strong effect on the levels of vibration energy, with phase angles of 0 deg and 180 deg producing low vibration levels. The third design variable, the stiffness of the shafts connecting the spur gears to the helical pinions, strongly influenced the natural frequencies of some of the vibration modes, including two of the dominant modes. We found that, to achieve the lowest level of vibration energy, the natural frequencies of these two dominant modes should be less than those of the main excitation sources.

Krantz, Timothy L.↗
NASA NTRS1989

Analysis of a second-order-accurate finite-volume method for temporally-growing compressible shear layers

A finite-volume method for solving the compressible laminar Navier-Stokes equation in two dimensions is assessed for use in the simulation of transitional flows. The method is second-order-accurate, uses alternating-direction-implicit time integration, and a total-variation-diminishing smoothing operator in the inviscid flux terms. The test problem was a free shear layer with a forced periodicity in x at a specified wavelength and with the parallel mean flow specified as a hyperbolic-tangent profile. A grid refinement investigation verified this method to be second-order-accurate with less than 4 percent error in the growth rate of isolated modes on a 32 by 64 grid. The interaction between modes of similar amplitude was small, less than 1 percent. However, in cases where there was a dominant mode, numerical phase error pumped energy into all other modes. This error results in nonphysical growth rate for modes whose energy content is several orders of magnitude below the dominant mode. In the case when the dominant mode saturates, the pumping action stops and the growth rate of the next largest growing mode regains physical significance.

Atkins, H. L.↗
NASA NTRSDate not supplied

Reduced Dimensionality Analysis of TEMPO Ozone Profile Retrievals Using the Compact Phase Space (CPSR) Algorithm

TEMPO ozone (O 3 ) profile retrievals are expected to have fidelity in the troposphere due the sensitivities of the associated averaging kernels. However, those averaging kernels are severely rank deficiency meaning that a visual inspection of the vertical structure of the averaging kernel profile sensitivities is misleading due linear dependencies in the profile. The Compact Phase Space Retrieval (CPSR) algorithm use singular value decompositions of the averaging kernels and the ‘compressed’ retrieval solution error covariance to project the transformed averaging kernels into a space that removes the linear dependencies and accounts for the solution error uncertainties. In this oral presentation and poster, we apply the CPSR dimensional reduction analysis to TEMPO and TROPOMI O 3 profile retrievals for 13:45 UTC March 29, 2024 to study the phase space characteristics of the transformed averaging kernels as a function of latitude for North America. Our results show that TEMPO generally has more phase space vertical structure in the troposphere than TROPOMI. TEMPO has four to five dominant modes, and TROPOMI has five to six dominant modes. That means that dimensional reduction can reduce the TEMPO resource requirements by ~77% and the TROPOMI requirements by ~81%. Finally, we found that after removing linear dependences and after accounting for solution uncertainties TEMPO still has sensitivities throughout the troposphere.

TEMPO↗
NASA NTRS1991

The stability to two-dimensional wakes and shear layers at high Mach numbers

This study is concerned with the stability properties of laminar free-shear-layer flows, and in particular symmetric two-dimensional wakes, for the supersonic through the hypersonic regimes. Emphasis is given to the use of proper wake profiles that satisfy the equations of motion at high Reynolds numbers. In particular the inviscid stability of a developing two-dimensional wake is studied as it accelerates at the trailing edge of a splitter plate. The nonparallelism of the flow is a leading-order effect in the calculation of the basic state, which is obtained numerically. Neutral stability characteristics are computed and the hypersonic stability is obtained by increasing the Mach number. It is found that the stability characteristics are altered significantly as the wake develops. Multiple modes (secondary modes) are found in the near wake that are closely related to the corresponding Blasius ones, but as the wake develops mode multiplicity is delayed to higher and higher Mach numbers. At a distance of about one plate length from the trailing edge, there is only one mode in a Mach number range of 0-20. The dominant mode emerging at all wake stations, and for high enough Mach numbers, is the so-called vorticity mode that is centered around the generalized inflection point layer. The structure of the dominant mode is also obtained analytically for all streamwise wake locations and it is shown how the far-wake limit is approached. Asymptotic results for the hypersonic mixing layer given by a tanh and a Lock distribution are also given.

Papageorgiou, Demetrios T.↗
NASA NTRS1994

Climatology and natural variability of the global hydrologic cycle in the GLA atmospheric general circulation model

Time average climatology and low-frequency variabilities of the global hydrologic cycle (GHC) in the Goddard Laboratory for Atmospheres (GLA) general circulation model (GCM) were investigated in the present work. A 730-day experiment was conducted with the GLA GCM forced by insolation, sea surface temperature, and ice-snow undergoing climatological annual cycles. Ifluences of interactive soil moisture on time average climatology and natural variability of the GHC were also investigated by conducting 365-day experiments with and without interactive soil moisture. Insolation, sea surface temperature, and ice-snow were fixed at their July levels in the latter two experiments. Results show that the model's time average hydrologic cycle variables for July in all three experiments agree reasonably well with observations. Except in the case of precipitable water, the zonal average climates of the annual cycle experiment and the two perpetual July experiments are alike, i.e., their differences are within limits of the natural variability of the model's climate. Statistics of various components of the GHC, i.e., water vapor, evaporation, and precipitation, are significantly affected by the presence of interactive soil moisture. A long-term trend is found in the principal empirical modes of variability of ground wetness, evaporation, and sensible heat. Dominant modes of variability of these quantities over land are physically consistent with one another and with land surface energy balance requirements. The dominant mode of precipitation variability is found to be closely related to organized convection over the tropical western Pacific Ocean. The precipitation variability has timescales in the range of 2 to 3 months and can be identified with the stationary component of the Madden-Julian Oscillation. The precipitation mode is not sensitive to the presence of interactive soil moisture but is closely linked to both the rotational and divergent components of atmospheric moisture transport. The present results indicate that globally coherent natural variability of the GHC in the GLA GCM has two basic timescales in the absence of annual cycles of external forcings: a long-term trend associated with atmosphere-soil moisture interaction which affects the model atmosphere mostly over midlatitude continental regions and a large-scale 2- to 3-month variability associated with atmospheric moist processes over the western Pacific Ocean.

Lau, K.-M.↗
NASA NTRS1990

Cyclotron maser and plasma wave growth in magnetic loops

Cyclotron maser and plasma wave growth which results from electrons accelerated in magnetic loops are studied. The evolution of the accelerated electron distribution is determined by solving the kinetic equation including Coulomb collisions and magnetic convergence. It is found that for modest values of the column depth of the loop the growth rates of instabilities are significantly reduced and that the reduction is much larger for the cyclotron modes than for the plasma wave modes. The large decrease in the growth rate with column depth suggests that solar coronal densities must be much lower than commonly accepted in order for the cyclotron maser to operate. The density depletion has to be similar to that which occurs during auroral kilometric radiation events in the magnetosphere. The resulting distributions are much more complicated than the idealized distributions used in many theoretical studies, but the fastest growing mode can still simply be determined by the ratio of electron plasma to gyrofrequency, U=omega(sub p)/Omega(sub e). However, the dominant modes are different than for the idealized situations with growth of the z-mode largest for U approximately less than 0.5, and second harmonic x-mode (s=2) or fundamental o-mode (s=1) the dominant modes for 0.5 approximately less than U approximately less than 1. The electron distributions typically contain more than one inverted feature which could give rise to wave growth. It is shown that this can result in simultaneous amplification of more than one mode with each mode driven by a different feature and can be observed, for example, by differences in the rise times of the right and left circularly polarized components of the associated spike bursts.

Hamilton, Russell J.↗
NASA NTRS1994

Effect of density gradients in confined supersonic shear layers. Part 2: 3-D modes

The effect of basic flow density gradients on the supersonic wall modes were investigated in Part 1 of this analysis. In that investigation only the 2-D modes were studied. Tam and Hu investigated the 3-D modes in a confined vortex sheet and reported that the first 2-D Class A mode (A01) had the highest growth rate compared to all other 2-D and 3-D modes present in the vortex sheet for that particular set of flow patterns. They also showed that this result also held true for finite thickness shear layers with delta(sub w) less than 0.125. For free shear layers, Sandham and Reynolds showed that the 3-D K-H mode became the dominant mode for M(sub c) greater than 0.6. Jackson and Grosch investigated the effect of crossflow and obliqueness on the slow and fast odes present in a M(sub c) greater than 1 environment and showed that for certain combination of crossflow and wave angles the growth rates could be increased by up to a factor of 2 with respect to the 2-D case. The case studied here is a confined shear layer shown in Part 1. All solution procedures and basic low profiles are the same as in Part 1. The effect of density gradients on the 3-D modes present in the density ratios considered in Part 1 are investigated.

Peroomian, Oshin↗