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At least 19 records

Spectral Analysis of Vibrational Harmonic Motion by use of a Continuous-Wave CO2 Doppler Lidar

Vibrational motion of a harmonic oscillator was investigated using a focused continuous wave CO2 Doppler lidar at 9.1 microns wavelength. A continuum of frequencies along with many discrete, equally spaced, resonant frequency modes was observed. The frequency modes are similar in structure to the oscillatory longitudinal modes of a laser cavity and arise because of interference of the natural resonant frequency of the oscillator with specific frequencies within the continuum. The spectra revealed departures from linear motion for vigorous vibrations of the oscillator. Each consecutive resonant frequency mode occurred for a movement of the oscillator much less than the wavelength of incident lidar radiation.

Jarzembski, Maurice A.↗

Unsteady aerodynamic models for maneuvering aircraft

Forced oscillation tests over a large angle-of-attack range for an F-18 model are conducted in the NASA Langley 12-foot low-speed tunnel. The resulting dynamic longitudinal data are analyzed with an unsteady aerodynamic modeling method based on Fourier functional analysis and the indicial formulation. The method is extensively examined and improved to automate the calculation of model coefficients, and to evaluate more accurately the indicial integral. The results indicate that the general model equation obtained from harmonic test data in a range of reduced frequency is capable of accurately modeling the nonlinear responses with large hysteresis effect, except in the region where a delayed flow reattachment occurs at low angles of attack in down strokes. The indicial formulation is used to calculate the response to harmonic motion, harmonic ramp motion, constant-rate pitching motion and smaller-amplitude harmonic motion. The results show that more accurate results can be obtained when the motion starts from a low angle of attack where hysteresis effect is not important.

Hu, Chien-Chung↗

Fourier functional analysis for unsteady aerodynamic modeling

A method based on Fourier analysis is developed to analyze the force and moment data obtained in large amplitude forced oscillation tests at high angles of attack. The aerodynamic models for normal force, lift, drag, and pitching moment coefficients are built up from a set of aerodynamic responses to harmonic motions at different frequencies. Based on the aerodynamic models of harmonic data, the indicial responses are formed. The final expressions for the models involve time integrals of the indicial type advocated by Tobak and Schiff. Results from linear two- and three-dimensional unsteady aerodynamic theories as well as test data for a 70-degree delta wing are used to verify the models. It is shown that the present modeling method is accurate in producing the aerodynamic responses to harmonic motions and the ramp type motions. The model also produces correct trend for a 70-degree delta wing in harmonic motion with different mean angles-of-attack. However, the current model cannot be used to extrapolate data to higher angles-of-attack than that of the harmonic motions which form the aerodynamic model. For linear ramp motions, a special method is used to calculate the corresponding frequency and phase angle at a given time. The calculated results from modeling show a higher lift peak for linear ramp motion than for harmonic ramp motion. The current model also shows reasonably good results for the lift responses at different angles of attack.

Lan, C. Edward↗

Fourier functional analysis for unsteady aerodynamic modeling

A method based on Fourier analysis is developed to analyze the force and moment data obtained in large amplitude forced oscillation tests at high angles of attack. The aerodynamic models for normal force, lift, drag, and pitching moment coefficients are built up from a set of aerodynamic responses to harmonic motions at different frequencies. Based on the aerodynamic models of harmonic data, the indicial responses are formed. The final expressions for the models involve time integrals of the indicial type advocated by Tobak and Schiff. Results from linear two- and three-dimensional unsteady aerodynamic theories as well as test data for a 70-degree delta wing are used to verify the models. It is shown that the present modeling method is accurate in producing the aerodynamic responses to harmonic motions and the ramp type motions. The model also produces correct trend for a 70-degree delta wing in harmonic motion with different mean angles-of-attack. However, the current model cannot be used to extrapolate data to higher angles-of-attack than that of the harmonic motions which form the aerodynamic model. For linear ramp motions, a special method is used to calculate the corresponding frequency and phase angle at a given time. The calculated results from modeling show a higher lift peak for linear ramp motion than for harmonic ramp motion. The current model also shows reasonably good results for the lift responses at different angles of attack.

Chin, Suei↗

Wave packet motion in harmonic potential and computer visualization

Wave packet motions of a single electron in harmonic potentials or a magnetic field are obtained analytically. The phase of the wave function which depends on both time and space is also presented explicitly. The probability density of the electron changes its width and central position periodically. These results are visualized using computer animation techniques.

Tsuru, Hideo↗

Development and application of a program to calculate transonic flow around an oscillating three-dimensional wing using finite difference procedures

A finite difference method for solving the unsteady transonic flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. Difference equations are derived for harmonic transonic flow to include a coordinate transformation for swept and tapered planforms. A pilot program is developed for three-dimensional planar lifting surface configurations (including thickness) for the CRAY-XMP at Boeing Commercial Airplanes and for the CYBER VPS-32 at the NASA Langley Research Center. An investigation is made of the effect of the location of the outer boundaries on accuracy for very small reduced frequencies. Finally, the pilot program is applied to the flutter analysis of a rectangular wing.

Weatherill, Warren H.↗

A harmonic analysis method for unsteady transonic flow and its application to the flutter of airfoils

A finite difference method for solving the unsteady transonic flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. A study is presented of the shock motion associated with an oscillating airfoil and its representation by the harmonic procedure. The effects of the shock motion and the resulting pressure pulse are shown to be included in the harmonic pressure distributions and the corresponding generalized forces. Analytical and experimental pressure distributions for the NACA 64A010 airfoil are compared for Mach numbers of 0.75, 0.80 and 0.842. A typical section, two-degree-of-freedom flutter analysis of a NACA 64A010 airfoil is performed. The results show a sharp transonic bucket in one case and abrupt changes in instability modes.

Ehlers, F. E.↗

Systems and methods that use harmonic drives for converting reciprocating axial motion to continuous rotary motion, helical drives for converting reciprocating rotary motion to reciprocating axial motion and combinations thereof for converting reciprocating rotary motion to continuous rotary motion

A harmonic drive assembly and fluid-powered linear motors with both axial pistons are rotary piston arrangements incorporating the harmonic drive assembly are disclosed. The motors may be used in downhole drilling applications, but the drive assembly and/or motors may be used in other applications. The assembly, motors and methods use advanced harmonic drives, advanced helical drives, and combinations thereof with 1) motors with axial pistons and reciprocating linear rings to convert reciprocative axial motion to continuous rotary motion, and 2) motors with rotary pistons and reciprocating linear rings to rectify reciprocative rotary motion to continual rotary motion to improve performance over prior configurations.

Raymond, David W.↗

Systems and methods that use harmonic drives for converting reciprocating axial motion to continuous rotary motion, helical drives for converting reciprocating rotary motion to reciprocating axial motion and combinations thereof for converting reciprocating rotary motion to continuous rotary motion

A harmonic drive assembly and fluid-powered linear motors with both axial pistons are rotary piston arrangements incorporating the harmonic drive assembly are disclosed. The motors may be used in downhole drilling applications, but the drive assembly and/or motors may be used in other applications. The assembly, motors and methods use advanced harmonic drives, advanced helical drives, and combinations thereof with 1) motors with axial pistons and reciprocating linear rings to convert reciprocative axial motion to continuous rotary motion, and 2) motors with rotary pistons and reciprocating linear rings to rectify reciprocative rotary motion to continual rotary motion to improve performance over prior configurations. Axial pistons provide a robust simple solution for generating rotation; Rotational pistons provide increased torque generation as the torque generated is proportional to motor length. Since downhole drills are long, a high-torque motor can be produced using this method.

Raymond, David W.↗

Unsteady aerodynamic modeling for arbitrary motions

Results indicating that unsteady aerodynamic loads derived under the assumption of simple harmonic motions executed by airfoil or wing can be extended to arbitrary motions are summarized. The generalized Theodorsen (1953) function referable to loads due to simple harmonic oscillations of a wing section in incompressible flow, the Laplace inversion integral for unsteady aerodynamic loads, calculations of root loci of aeroelastic loads, and analysis of generalized compressible transient airloads are discussed.

Edwards, J. W.↗

Ultrasonic Apparatus for Pulverizing Brittle Material

The figure depicts an apparatus that pulverizes brittle material by means of a combination of ultrasonic and sonic vibration, hammering, and abrasion. The basic design of the apparatus could be specialized to be a portable version for use by a geologist in collecting powdered rock samples for analysis in the field or in a laboratory. Alternatively, a larger benchtop version could be designed for milling and mixing of precursor powders for such purposes as synthesis of ceramic and other polycrystalline materials or preparing powder samples for x-ray diffraction or x-ray fluorescence measurements to determine crystalline structures and compositions. Among the most attractive characteristics of this apparatus are its light weight and the ability to function without need for a large preload or a large power supply: It has been estimated that a portable version could have a mass <0.5 kg, would consume less than 1 W h of energy in milling a 1-cm3 volume of rock, and could operate at a preload <10 N. The basic design and principle of operation of this apparatus are similar to those of other apparatuses described in a series of prior NASA Tech Briefs articles, the two most relevant being Ultrasonic/ Sonic Drill/Corers With Integrated Sensors (NPO-20856), Vol. 25, No. 1 (January 2001), page 38 and Ultrasonic/ Sonic Mechanisms for Deep Drilling and Coring (NPO-30291), Vol. 27, No. 9 (September 2003), page 65. As before, vibrations are excited by means of a piezoelectric actuator, an ultrasonic horn, and a mass that is free to move axially over a limited range. As before, the ultrasonic harmonic motion of the horn drives the free-mass in a combination of ultrasonic harmonic and lower-frequency hammering motion. In this case, the free-mass is confined within a hollow cylinder that serves as a crushing chamber, and the free-mass serves as a crushing or milling tool. The hammering of the free-mass against a material sample at the lower end of the chamber grinds the sample into powder in a relatively short time. The restriction of the free-mass to axial motion only makes the grinding very efficient. The free-mass can be fabricated to have teeth on its lower face to enhance the grinding effect. Optionally, there can be a hole at the bottom of the chamber covered with a sieve to tailor the size distribution of the powder leaving the crushing chamber.

Sherrit, Stewart↗

Effective Strength of Sinusoidally-Varying Focussing

Particle beam focussing and other confined physical systems often obey the equation ¨x = kx, where k < 0 implies stable motion. A constant negative value of k yields simple harmonic motion (constant focussing), while positive values give unstable (defocussing) motion. Alternating gradient focussing is the surprising principle that if k(t) is varied periodically, the overall motion can sometimes be stable even if the average value of k is zero or negative. It is used where focussing in one direction implies defocussing in one or more other directions, such as with electromagnetic fields in free space that have to satisfy ∇ · E = 0 and similar.

43 PARTICLE ACCELERATORS↗

Airfoil in sinusoidal motion in a pulsating stream

The forces and moments on a two-dimensional airfoil executing harmonic motions in a pulsating stream are derived on the basis of non-stationary incompressible potential flow theory, with the inclusion of the effect of the continuous sheet of vortices shed from the trailing edge. An assumption as to the form of the wake is made with a certain degree of approximation. A comparison with previous work applicable only to the special case of a stationary airfoil is made by means of a numerical example, and the excellent agreement obtained shows that the wake approximation is quite sufficient. The results obtained are expected to be useful in considerations of forced vibrations and flutter of rotary wing aircraft.

Greenberg, J Mayo↗

Linear Wave Motion from Concentrated Harmonic Sources in Blasius Flow

The motion of individual linear instability waves in shear flows is well described by existing theoretical and numerical methods. However, naturally occuring sources produce coherent wave motions with broadband spanwise wavenumber and frequency spectra, and the different spectral components interact both linearly and nonlinearily. This paper describes a series of calculations for the parameters of three different experiments using locally parallel linear stability theory (LST), the Parabolized Stability Equations (PSE), and Direct Numerical Simulation (DNS). The calculations illustrate the strengths and weaknesses of the different methods, the extent to which the methods agree or disagree, and, finally the extent to which agreement with the measurements can be attained, given that the experiments also have their own difficulties.

linear↗

Localized, Non-Harmonic Active Flap Motions for Low Frequency In-Plane Rotor Noise Reduction

A first-of-its-kind demonstration of the use of localized, non-harmonic active flap motions, for suppressing low frequency, in-plane rotor noise, is reported in this paper. Operational feasibility is verified via testing of the full-scale AATD/Sikorsky/UTRC active flap demonstration rotor in the NFAC's 40- by 80-Foot anechoic wind tunnel. Effectiveness of using localized, non-harmonic active flap motions are compared to conventional four-per-rev harmonic flap motions, and also active flap motions derived from closed-loop acoustics implementations. All three approaches resulted in approximately the same noise reductions over an in-plane three-by-three microphone array installed forward and near in-plane of the rotor in the nearfield. It is also reported that using an active flap in this localized, non-harmonic manner, resulted in no more that 2% rotor performance penalty, but had the tendency to incur higher hub vibration levels.

FLAPS(CONTROL SURFACES)↗

Wind tunnel tests of a blade subjected to midchord torsional oscillation at high subsonic stall flutter conditions

A mechanical drive system for oscillating blades in a wind tunnel at frequencies up to 767 hertz and amplitudes of + or - 1.2 deg is described. High-speed motion pictures of schlieren images of the flow over a double-circular arc blade oscillating in harmonic motion about the midchord revealed extensive shock patterns at a nominal free stream Mach number of 0.7, a mean angle of attack of 4 deg, and reduced frequency of about 0.7. A phase lag resulting from the slow response of the flow to the motion of the blade increased with increasing reduced frequency. This phase lag, based on the difference between the time the blade attained its maximum angle of attack and the time required for the normal shock to reach its extreme downstream position, was nominally 100 deg at the above conditions.

Boldman, D. R.↗

Rates of change of the earth's magnetic field measured by recent analyses

Typical rates of change of the earth's magnetic field are presented as a function of the earth's spherical harmonics. Harmonics up to the eight degree are analyzed. With the increase in the degree of the harmonics an increase in the relative rate of change can be observed. For higher degrees, the rate of change can be predicted. This enables a differentiation between harmonics originating in the core and harmonics caused by crustal magnetization. The westward drift of the magnetic field depends on the longitudinal gradient of the field. In order to determine the longitudinal motions, harmonics up to degree 20 can be utilized. The average rate of secular acceleration increases with the degree of harmonics from 0.001 deg/sq yr for a dipole term to an average of 0.05 deg/sq yr for degree eight harmonics.

Harrison, C. G. A.↗

Modeling of aircraft unsteady aerodynamic characteristics. Part 1: Postulated models

A short theoretical study of aircraft aerodynamic model equations with unsteady effects is presented. The aerodynamic forces and moments are expressed in terms of indicial functions or internal state variables. The first representation leads to aircraft integro-differential equations of motion; the second preserves the state-space form of the model equations. The formulations of unsteady aerodynamics is applied in two examples. The first example deals with a one-degree-of-freedom harmonic motion about one of the aircraft body axes. In the second example, the equations for longitudinal short-period motion are developed. In these examples, only linear aerodynamic terms are considered. The indicial functions are postulated as simple exponentials and the internal state variables are governed by linear, time-invariant, first-order differential equations. It is shown that both approaches to the modeling of unsteady aerodynamics lead to identical models.

Klein, Vladislav↗