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Two of the more common procedures for analyzing the stability and forced response of equations with periodic coefficients are reviewed: the use of Floquet methods, and the use of multiblade coordinate and harmonic balance methods. The analysis procedures of these periodic coefficient systems are compared with those of the more familiar constant coefficient systems. Previously announced in STAR as N82-23702
The technique of harmonic splines allows direct estimation of a complete planetary gravity field (geoid, gravity, and gravity gradients) everywhere over the planet's surface. Harmonic spline results of Venus are presented as a series of maps at spacecraft and constant altitudes. Global (except for polar regions) and local relations of gravity to topography are described.
Analysis of geomagnetic field for 1955 by spherical harmonics
Photographic and Doppler tracking of geodetic satellites to determine tesseral harmonics of earth gravitational fields
Higher Harmonic Control reduces helicopter airframe vibration through the exercise of rotor blade pitch control at frequencies that are higher harmonics of rotor rotation. Analysis wind tunnel tests and flight tests of this technology with an OH-6A helicopter have led to vibration reduction levels of the order of more than 80 percent. Blade feathering capability at rotor speed harmonics other than the first also promises the improvement of such rotor characteristics as acoustics, aerodynamic efficiency and ground resonance.
The time dependent governing acoustic-difference equations and boundary conditions are developed and solved for sound propagation in an axisymmetric (cylindrical) hard wall duct with a plug mean flow and spinning acoustic modes. The analysis begins with a harmonic sound source radiating into a quiescent duct. This explicit iteration method then calculates stepwise in real time to obtain the transient as well as the 'steady' state solutions of the acoustic field. The time dependent finite difference analysis has two advantages over the steady state finite difference and finite element techniques: (1)the elimination of large matrix storage requirements, and (2)shorter solution times under most conditions.
The time dependent governing/acoustic-difference equations and boundary conditions are developed and solved for sound propagation in an axisymmetric (cylindrical) hard wall duct with a plug mean flow and spinning acoustic modes. The analysis begins with a harmonic sound source radiating into a quiescent duct. This explicit iteration method then calculates stepwise in real time to obtain the transient as well as the 'steady' state solutions of the acoustic field. The time dependent finite difference analysis has two advantages over the steady state finite difference and finite element techniques: (1) the elimination of large matrix storage requirements, and (2) shorter solution times under most conditions.
This report presents an analysis and performance comparison of five system identification algorithms. The methods are presented in the context of identifying a frequency-domain transfer matrix for the higher harmonic control (HHC) of helicopter vibration. The five system identification algorithms include three previously proposed methods: (1) the weighted-least- squares-error approach (in moving-block format), (2) the Kalman filter method, and (3) the least-mean-squares (LMS) filter method. In addition there are two new ones: (4) a generalized Kalman filter method and (5) a generalized LMS filter method. The generalized Kalman filter method and the generalized LMS filter method were derived as extensions of the classic methods to permit identification by using more than one measurement per identification cycle. Simulation results are presented for conditions ranging from the ideal case of a stationary transfer matrix and no measurement noise to the more complex cases involving both measurement noise and transfer-matrix variation. Both open-loop identification and closed- loop identification were simulated. Closed-loop mode identification was more challenging than open-loop identification because of the decreasing signal-to-noise ratio as the vibration became reduced. The closed-loop simulation considered both local-model identification, with measured vibration feedback and global-model identification with feedback of the identified uncontrolled vibration. The algorithms were evaluated in terms of their accuracy, stability, convergence properties, computation speeds, and relative ease of implementation.
The basic theoretical work required to understand sound transmission into an enclosed space (that is, one closed by the transmitting structure) is developed for random pressure fields and for harmonic (tonal) excitation. The analysis is used to predict the noise reducton of unpressurized unstiffened cylinder, and also the interior response of the cylinder given a tonal (plane wave) excitation. Predictions and measurements are compared and the transmission is analyzed. In addition, results for tonal (harmonic) mechanical excitation are considered.
This report presents, in two parts, a dynamic aeroelastic stability (flutter) analysis of a cascade of blades in supersonic axial flow. Each blade of the cascade is modeled as a typical section having pitching and plunging degrees of freedom. Aerodynamic forces are obtained from a time accurate, unsteady, two-dimensional cascade solver based on the Euler equations. The solver uses a time marching flux-difference splitting (FDS) scheme. Flutter stability is analyzed in the frequency domain. The unsteady force coefficients required in the analysis are obtained by harmonically oscillating (HO) the blades for a given flow condition, oscillation frequency, and interblade phase angle. The calculated time history of the forces is then Fourier decomposed to give the required unsteady force coefficients. An influence coefficient (IC) method and a pulse response (PR) method are also implemented to reduce the computational time for the calculation of the unsteady force coefficients for any phase angle and oscillation frequency. Part 1, this report, presents these analysis methods and their validation by comparison with results obtained from linear theory for a selected flat plate cascade geometry. A typical calculation for a rotor airfoil is also included to show the applicability of the present solver for airfoil configurations. The predicted unsteady aerodynamic forces for a selected flat plate cascade geometry and flow conditions correlated well with those obtained from linear theory for different interblade phase angles and oscillation frequencies. All the three methods of predicting unsteady force coefficients, namely, HO, IC, and PR, showed good correlations with each other. It was established that only a single calculation with four blade passages is required to calculate the aerodynamic forces for any phase angle for a cascade consisting of any number of blades, for any value of the oscillation frequency. Flutter results, including mistuning effects, for a cascade of stator airfoils are presented in Part 2 of the report.
The all-sky interplanetary Lyman-alpha pattern is sensitive to the latitude distribution of the solar wind because of destruction of neutral H by charge-exchange with solar wind protons. Lyman-alpha intensities recorded by Prognoz 5 and 6 in 1976 in a few parts of the sky were demonstrating a decrease of solar wind mass flux by about 30 % from equator to pole, when assuming a sinusoidal variation of this mass flux (harmonic distribution). A new analysis with a discrete variation with latitude has shown a decrease from 0 to 30 deg and then a plateau of constant mass flux up to the pole. This distribution bears a striking resemblance with Ulysses in-situ measurements, showing a clear similarity at 19 years interval. The Ulysses measurements were then used as a model input to calculate an all-sky Lyman-alpha pattern, either with a discrete model or with a harmonic solar wind variation with the same Ulysses equator-to-pole variation. There are conspicuous differences between the two Lyman-alpha patterns, in particular in the downwind region which are discussed in the context of future all-sky measurements with SWAN experiment on SOHO.
A time dependent numerical solution of the linearized continuity and momentum equation is developed for sound propagation in a two-dimensional straight hard or soft wall duct with a sheared mean flow. The time dependent governing acoustic-difference equations and boundary conditions are developed along with a numerical determination of the maximum stable time increments. The analysis begins with a harmonic noise source radiating into a quiescent duct. This explicit iteration method then calculates stepwise in real time to obtain the transient as well as the 'steady' state solution of the acoustic field. Example calculations are presented for sound propagation in hard and soft wall ducts, with no flow and with plug flow. Although the problem with sheared flow has been formulated and programmed, sample calculations have not yet been examined. So far, the time dependent finite difference analysis has been found to be superior to the steady state finite difference and finite element techniques because of shorter solution times and the elimination of large matrix storage requirements.
Excessive vibration of turbomachinery blades causes high cycle fatigue problems which require damping treatments to mitigate vibration levels. One method is the use of piezoelectric materials as passive or active dampers. Based on the technical challenges and requirements learned from previous turbomachinery rotor blades research, an effort has been made to investigate the effectiveness of a shunted piezoelectric for the turbomachinery rotor blades vibration control, specifically for a condition with centrifugal rotation. While ample research has been performed on the use of a piezoelectric material with electric circuits to attempt to control the structural vibration damping, very little study has been done regarding rotational effects. The present study attempts to fill this void. Specifically, the objectives of this study are: (a) to create and analyze finite element models for harmonic forced response vibration analysis coupled with shunted piezoelectric circuits for engine blade operational conditions, (b) to validate the experimental test approaches with numerical results and vice versa, and (c) to establish a numerical modeling capability for vibration control using shunted piezoelectric circuits under rotation. Study has focused on a resonant damping control using shunted piezoelectric patches on plate specimens. Tests and analyses were performed for both non-spinning and spinning conditions. The finite element (FE) shunted piezoelectric circuit damping simulations were performed using the ANSYS Multiphysics code for the resistive and inductive circuit piezoelectric simulations of both conditions. The FE results showed a good correlation with experimental test results. Tests and analyses of shunted piezoelectric damping control, demonstrating with plate specimens, show a great potential to reduce blade vibrations under centrifugal loading.
NASA has employed high-throughput molecular assays to identify sub-cellular changes impacting human physiology during spaceflight. Machine learning (ML) methods hold the promise to improve our ability to identify important signals within highly dimensional molecular data. However, the inherent limitation of study subject numbers within a spaceflight mission minimizes the utility of ML approaches. To overcome the sample power limitations, data from multiple spaceflight missions must be aggregated while appropriately addressing intra- and inter-study variabilities. Here we describe an approach to log transform, scale and normalize data from six heterogeneous, mouse liver derived transcriptomics datasets (ntotal=137) which enabled ML-methods to perform well (AUC ≥ 0.87) in classifying spaceflown vs ground control animals rather than mission-of-origin. Concordance was found between liver-specific biological processes identified from harmonized ML-based analysis and study-by-study classical omics analysis. This work demonstrates the feasibility of applying ML methods on integrated, heterogeneous datasets of small sample size.
This report examines cybersecurity standards for Distributed Energy Resources (DERs) in light of their rapid growth and increasing integration into energy systems. It identifies critical gaps in existing frameworks, including inadequate coverage of DER-specific challenges, complexities in implementing comprehensive standards, integration issues with legacy systems, adoption hurdles for newer standards, and a lack of harmonization across regulatory landscapes. The analysis highlights vulnerabilities such as data integrity risks, unauthorized device control, and denial-of-service attacks across various DER technologies like solar PV, wind turbines, energy storage systems, and hydrogen fuel cells. The report proposes a harmonization strategy to address these deficiencies by developing unified cybersecurity requirements, certification programs, and training resources while fostering collaboration among stakeholders such as government agencies, industry groups, DER operators, manufacturers, and research institutions. A phased roadmap is outlined to refine and implement these measures through pilot testing and widespread adoption. Ultimately, the report underscores the urgent need for coordinated efforts to enhance DER cybersecurity and ensure the reliable operation of future energy systems.
Abstract Because of their large surface areas, nanotubes and nanowires demonstrate exquisite mechanical coupling to their surroundings, promising advanced sensors and nanomechanical devices. However, this environmental sensitivity has resulted in several ambiguous observations of vibrational coupling across various experiments. Herein, we demonstrate a temperature-dependent Radial Breathing Mode (RBM) frequency in free-standing, electron-diffraction-assigned Double-Walled Carbon Nanotubes (DWNTs) that shows an unexpected and thermally reversible frequency downshift of 10 to 15%, for systems isolated in vacuum. An analysis based on a harmonic oscillator model assigns the distinctive frequency cusp, produced over 93 scans of 3 distinct DWNTs, along with the hyperbolic trajectory, to a reversible increase in damping from graphitic ribbons on the exterior surface. Strain-dependent coupling from self-tensioned, suspended DWNTs maintains the ratio of spring-to-damping frequencies, producing a stable saturation of RBM in the low-tension limit. In contrast, when the interior of DWNTs is subjected to a water-filling process, the RBM thermal trajectory is altered to that of a Langmuir isobar and elliptical trajectories, allowing measurement of the enthalpy of confined fluid phase change. These mechanisms and quantitative theory provide new insights into the environmental coupling of nanomechanical systems and the implications for devices and nanofluidic conduits.
Theory of statistical analysis of data distributed over sphere
Covariance analysis of Mars gravity harmonics, ephemeris and radiation pressure from Mariner 1971 range and Doppler radio tracking data