Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades

The equations of motion are developed by two complementary methods, Hamilton's principle and the Newtonian method. The resulting equations are valid to second order for long, straight, slender, homogeneous, isotropic beams undergoing moderate displacements. The ordering scheme is based on the restriction that squares of the bending slopes, the torsion deformation, and the chord/radius and thickness/radius ratios are negligible with respect to unity. All remaining nonlinear terms are retained. The equations are valid for beams with mass centroid axis and area centroid (tension) axis offsets from the elastic axis, nonuniform mass and stiffness section properties, variable pretwist, and a small precone angle. The strain-displacement relations are developed from an exact transformation between the deformed and undeformed coordinate systems. These nonlinear relations form an important contribution to the final equations. Several nonlinear structural and inertial terms in the final equations are identified that can substantially influence the aeroelastic stability and response of hingeless helicopter rotor blades

Nonlinear Dynamics of a Helicopter Model in Ground Resonance

An approximate theoretical method is presented which determined the limit cycle behavior of a helicopter model which has one or two nonlinear dampers. The relationship during unstable ground resonance oscillations between lagging motion of the blades and fuselage motion is discussed. An experiment was carried out on using a helicopter scale model. The experimental results agree with those of the theoretical analysis

Scanamorphos: a map-making software for Herschel and similar scanning bolometer arrays

Scanamorphos is one of the public softwares available to post-process scan observations performed with the Herschel photometer arrays. This post-processing mainly consists in subtracting the total low-frequency noise (both its thermal and non-thermal components), masking high-frequency artefacts such as cosmic ray hits, and projecting the data onto a map. Although it was developed for Herschel, it is also applicable with minimal adjustment to scan observations made with some other imaging arrays subjected to low-frequency noise, provided they entail sufficient redundancy; it was successfully applied to P-Artemis, an instrument operating on the APEX telescope. Contrary to matrix-inversion softwares and high-pass filters, Scanamorphos does not assume any particular noise model, and does not apply any Fourier-space filtering to the data, but is an empirical tool using purely the redundancy built in the observations -- taking advantage of the fact that each portion of the sky is sampled at multiple times by multiple bolometers. It is an interactive software in the sense that the user is allowed to optionally visualize and control results at each intermediate step, but the processing is fully automated. This paper describes the principles and algorithm of Scanamorphos and presents several examples of application.Comment: This is the final version as accepted by PASP (on July 27, 2013). A copy with much better-quality figures is available on http://www2.iap.fr/users/roussel/herschel

A Multi-Wavelength Study of Sgr A*: The Role of Near-IR Flares in Production of X-ray, Soft γ\gamma-ray and Sub-millimeter Emission

(abridged) We describe highlights of the results of two observing campaigns in 2004 to investigate the correlation of flare activity in Sgr A* in different wavelength regimes, using a total of nine ground and space-based telescopes. We report the detection of several new near-IR flares during the campaign based on {\it HST} observations. The level of near-IR flare activity can be as low as $\sim0.15$ mJy at 1.6 $\mu$m and continuous up to about 40% of the total observing time. Using the NICMOS instrument on the {\it HST}, the {\it XMM-Newton} and CSO observatories, we also detect simultaneous bright X-ray and near-IR flare in which we observe for the first time correlated substructures as well as simultaneous submillimeter and near-IR flaring. X-ray emission is arising from the population of near-IR-synchrotron-emitting relativistic particles which scatter submillimeter seed photons within the inner 10 Schwarzschild radii of Sgr A* up to X-ray energies. In addition, using the inverse Compton scattering picture, we explain the high energy 20-120 keV emission from the direction toward Sgr A*, and the lack of one-to-one X-ray counterparts to near-IR flares, by the variation of the magnetic field and the spectral index distributions of this population of nonthermal particles. In this picture, the evidence for the variability of submillimeter emission during a near-IR flare is produced by the low-energy component of the population of particles emitting synchrotron near-IR emission. Based on the measurements of the duration of flares in near-IR and submillimeter wavelengths, we argue that the cooling could be due to adiabatic expansion with the implication that flare activity may drive an outflow.Comment: 48 pages, 12 figures, ApJ (in press

Submillimeter Imaging of NGC 891 with SHARC

The advent of submillimeter wavelength array cameras operating on large ground-based telescopes is revolutionizing imaging at these wavelengths, enabling high-resolution submillimeter surveys of dust emission in star-forming regions and galaxies. Here we present a recent 350 micron image of the edge-on galaxy NGC 891, which was obtained with the Submillimeter High Angular Resolution Camera (SHARC) at the Caltech Submillimeter Observatory (CSO). We find that high resolution submillimeter data is a vital complement to shorter wavelength satellite data, which enables a reliable separation of the cold dust component seen at millimeter wavelengths from the warmer component which dominates the far-infrared (FIR) luminosity.Comment: 4 pages LaTeX, 2 EPS figures, with PASPconf.sty; to appear in "Astrophysics with Infrared Surveys: A Prelude to SIRTF

Recent results from proton capture to giant resonances built on highly-excited states

New measurements of the (p,..gamma..) reaction on natural targets of K and Ca at intermediate proton energies (E/sub p/ = 11 to 36 MeV) reveal excitation functions that are dominated by excited-state giant dipole resonances (ESGDR's) built upon single-particle states in /sup 40/Ca and /sup 41/Sc. These ESGDR's all peak near E/sub ..gamma../ = 20 MeV and have widths which increase monotonically with the final state's excitation energy. The integrated, inverse (..gamma..,P/sub 0/) cross sections are shown to be proportional to the known single-particle spectroscopic strengths indicating a semi-direct mechanism for the capture process. 12 references, 13 figures

Flutter Analysis of the Thermal Protection Layer on the NASA HIAD

A combination of classical plate theory and a supersonic aerodynamic model is used to study the aeroelastic flutter behavior of a proposed thermal protection system (TPS) for the NASA HIAD. The analysis pertains to the rectangular configurations currently being tested in a NASA wind-tunnel facility, and may explain why oscillations of the articles could be observed. An analysis using a linear flat plate model indicated that flutter was possible well within the supersonic flow regime of the wind tunnel tests. A more complex nonlinear analysis of the TPS, taking into account any material curvature present due to the restraint system or substructure, indicated that significantly greater aerodynamic forcing is required for the onset of flutter. Chaotic and periodic limit cycle oscillations (LCOs) of the TPS are possible depending on how the curvature is imposed. When the pressure from the base substructure on the bottom of the TPS is used as the source of curvature, the flutter boundary increases rapidly and chaotic behavior is eliminated

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part II: Nonlinear Theory and Extended Aerodynamics

Conical shell theory and a supersonic potential flow aerodynamic theory are used to study the nonlinear pressure buckling and aeroelastic limit cycle behavior of the thermal protection system for NASA's Hypersonic Inflatable Aerodynamic Decelerator. The structural model of the thermal protection system consists of an orthotropic conical shell of the Donnell type, resting on several circumferential elastic supports. Classical Piston Theory is used initially for the aerodynamic pressure, but was found to be insufficient at low supersonic Mach numbers. Transform methods are applied to the convected wave equation for potential flow, and a time-dependent aerodynamic pressure correction factor is obtained. The Lagrangian of the shell system is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the governing differential-algebraic equations of motion. Aeroelastic limit cycle oscillations and buckling deformations are calculated in the time domain using a Runge-Kutta method in MATLAB. Three conical shell geometries were considered in the present analysis: a 3-meter diameter 70 deg. cone, a 3.7-meter 70 deg. cone, and a 6-meter diameter 70 deg. cone. The 6-meter configuration was loaded statically and the results were compared with an experimental load test of a 6-meter HIAD. Though agreement between theoretical and experimental strains was poor, the circumferential wrinkling phenomena observed during the experiments was captured by the theory and axial deformations were qualitatively similar in shape. With Piston Theory aerodynamics, the nonlinear flutter dynamic pressures of the 3-meter configuration were in agreement with the values calculated using linear theory, and the limit cycle amplitudes were generally on the order of the shell thickness. The effect of axial tension was studied for this configuration, and increasing tension was found to decrease the limit cycle amplitudes when the circumferential elastic supports were neglected, but resulted in more complex behavior when the supports were included. The nominal flutter dynamic pressure of the 3.7-meter configuration was significantly lower than that of the 3-meter, and it was found that two sets of natural modes coalesce to flutter modes near the same dynamic pressure. This resulted in a significant drop in the limit cycle frequencies at higher dynamic pressures, where the flutter mode with the lower frequency becomes more critical. Pre-buckling pressure loads and the aerodynamic pressure correction factor were studied for all geometries, and these effects resulted in significantly lower flutter boundaries compared with Piston Theory alone. The maximum dynamic pressure predicted by aerodynamic simulations of a proposed 3.7-meter HIAD vehicle was still lower than any of the calculated flutter dynamic pressures, suggesting that aeroelastic effects for this vehicle are of little concern

Nonlinear Aeroelastic Analysis of the HIAD TPS Coupon in the NASA 8' High Temperature Tunnel: Theory and Experiment

The purpose of this work is to develop a set of theoretical and experimental techniques to characterize the aeroelasticity of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). A square TPS coupon experiences trailing edge oscillatory behavior during experimental testing in the 8' High Temperature Tunnel (HTT), which may indicate the presence of aeroelastic flutter. Several theoretical aeroelastic models have been developed, each corresponding to a different experimental test configuration. Von Karman large deflection theory is used for the plate-like components of the TPS, along with piston theory for the aerodynamics. The constraints between the individual TPS layers and the presence of a unidirectional foundation at the back of the coupon are included by developing the necessary energy expressions and using the Rayleigh Ritz method to derive the nonlinear equations of motion. Free vibrations and limit cycle oscillations are computed and the frequencies and amplitudes are compared with accelerometer and photogrammetry data from the experiments

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part I: Linear Theory

Conical shell theory and piston theory aerodynamics are used to study the aeroelastic stability of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). Structural models of the TPS consist of single or multiple orthotropic conical shell systems resting on several circumferential linear elastic supports. The shells in each model may have pinned (simply-supported) or elastically-supported edges. The Lagrangian is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the equations of motion. The natural modes of vibration and aeroelastic stability boundaries are found by calculating the eigenvalues and eigenvectors of a large coefficient matrix. When the in-flight configuration of the TPS is approximated as a single shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case. Aeroelastic models that consider the individual TPS layers as separate shells tend to flutter asymmetrically at high dynamic pressures relative to the single shell models. Several parameter studies also examine the effects of tension, orthotropicity, and elastic support stiffness