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NASA NTRS1984

Standing hydromagnetic oscillations in the magnetosphere

The mechanisms for generating Alfven waves in the magnetosphere are determined, on the basis of a comprehensive survey of satellite magnetometer data. The mechanisms are classified in terms of the physical properties of standing Alfven waves such as the direction of the major axis of polarization, harmonic mode, and the azimuthal wave number. In an analysis of the statistical organization of the pulsations, it is shown that the most common transverse waves seem to be azimuthally polarized waves involving the fundamental and several harmonics, with radially polarized waves excited at the second harmonic. The former are probably driven externally, while the latter are likely to be excited internally through particle-wave interactions.

Takahashi, K.↗

NASA NTRS1985

In-flight acoustic measurements on a light twin-engined turboprop airplane

Four series of flight tests were conducted to measure sound pressure levels inside and outside the cabin of a twin-engined turboprop airplane. Particular emphasis was placed on harmonics of the propeller blade passage frequency. The cabin was unfurnished for the first three flights, when the main objective was to investigate the repeatability of the data. For the fourth flight, the cabin was treated with fiberglass batts. Typically, the exterior sound pressure levels were found to vary 3 to 5 dB for a given harmonic, but variations as high as 8 dB were observed. The variability of harmonic levels within the cabin was slightly higher but depended on control of the relative phase between the propellers; when phase was not controlled the average variability was about 10 dB. Noise reductions provided by the fuselage structure were in the range of 20 to 40 dB, when an exterior microphone in the plane of rotation of the propeller was used as reference.

Wilby, J. F.↗

NASA NTRS1985

Frequency domain solutions to multi-degree-of-freedom, dry friction damped systems under periodic excitation

The anticipated low damping level in large space structures (LSS) has been a major concern for the designers of these structures. Low damping degrades the free response and complicates the design of shape and attitude controllers for flexible spacecraft. Dry friction damping has been considered as a means of increasing the passive damping of LSS, by placing it in the joints and connecting junctures of structures. However, dry friction is highly nonlinear and, hence, analytical investigations are difficult to perform. Here, a multi-harmonic, frequency domain solution technique is developed and applied to a multi-DOF, dry friction damped system. It is seen that the multi-harmonic method is much more accurate than traditional, one harmonic solution methods. The method also compares well with time integration. Finally, comparisons are made with experimental results.

Ferri, A. A.↗

NASA NTRS1987

Multiple-mode nonlinear free and forced vibrations of beams using finite element method

Multiple-mode nonlinear free and forced vibration of a beam is analyzed by the finite element method. The geometric nonlinearity is investigated. Inplane displacement and inertia (IDI) are also considered in the formulation. Harmonic force matrix is derived and explained. Nonlinear free vibration can be simply treated as a special case of the general forced vibration by setting the harmonic force matrix equal to zero. The effect of the higher modes is more pronouced for the clamped supported beam than the simply supported one. Beams without IDI yield more effect of the higher modes than the one with IDI. The effects of IDI are to reduce nonlinearity. For beams with end supports restrained from axial movement (immovable cases), only the hardening type nonlinearity is observed. However, beams of small slenderness ratio (L/R = 20) with movable end supports, the softening type nonlinearity is found. The concentrated force case yields a more severe response than the uniformly distributed force case. Finite element results are in good agreement with the solution of simple elliptic response, harmonic balance method, and Runge-Kutte method and experiment.

Mei, Chuh↗

NASA NTRS1987

A study of methods to predict and measure the transmission of sound through the walls of light aircraft. Numerical method for analyzing the optimal performance of active noise controllers

An optimal active noise controller is formulated and analyzed for three different active noise control problems. The first problem formulated is the active control of enclosed or partially enclosed harmonic sound fields where the noise source strengths and enclosure boundary description are known. The enclosure boundary is described by either pressure, velocity, or impedance boundary conditions. The second problem formulated is the active control of the free field power radiated from a distributed noise source with a known time harmonic surface velocity. The third problem formulated is the active control of enclosed or partially enclosed harmonic sound field where the noise source strengths of enclosure boundary description may not be known. All three formulations are derived using an indirect boundary element technique. Formulation and verification of an indirect boundary element method is presented. The active noise controller formulations for enclosures are capable of analyzing systems with generalized enclosure shapes, point noise sources, and/or locally reacting impedance boundary conditions. For each formulation, representative results of optimal active noise controller case studies are presented, and some general conclusions are drawn.

Mollo, Christopher G.↗

NASA NTRS1987

Component mode synthesis and large deflection vibration of complex structures. Volume 2: Single-mode large deflection vibrations of beams and plates using finite element method

A finite element method is presented for the large amplitude vibrations of complex structures that can be modelled with beam and rectangular plate elements subjected to harmonic excitation. Both inplane deformation and inertia are considered in the formulation. Derivation of the harmonic force and nonlinear stiffness matrices for a beam and a rectangular plate element are presented. Solution procedures and convergence characteristics of the finite element method are described. Nonlinear response to uniform and concentrated harmonic loadings and improved nonlinear free vibration results are presented for beams and rectangular plates of various boundary conditions.

Mei, Chuh↗

NASA NTRS1986

Observations concerning the generation and propagation of Type III solar bursts

A number of Type III bursts were observed during the Helios missions in which the burst exciter passed over the spacecraft, as evidenced by strong electric field fluctuations near the plasma frequency. Six of these were suitable for detailed study. Of the six events, one was ambiguous, one showed what is interpreted as a switchover from harmonic to fundamental, and the rest all generated fundamental at onset. This would be expected if both fundamental and harmonic are generated, as, at a fixed frequency, the fundamental will be generated earlier. For the event which seems to show both fundamental and harmonic emission, the frequency ratio is not exactly 2. This is explained in terms of a time delay of the fundamental, due to scattering and diffusion in the source region. A time delay of the order of 600 seconds at 1 AU and 20 kHz, and inversely proportional to frequency, is required to explain the observations. Crude estimates show that delay times at least this long may be attributed to trapping and scattering.

Kellogg, P. J.↗

NASA NTRS1988

Accuracy of analytic energy level formulas applied to hadronic spectroscopy of heavy mesons

Linear and harmonic potential models are used in the nonrelativistic Schroedinger equation to obtain article mass spectra for mesons as bound states of quarks. The main emphasis is on the linear potential where exact solutions of the S-state eigenvalues and eigenfunctions and the asymptotic solution for the higher order partial wave are obtained. A study of the accuracy of two analytical energy level formulas as applied to heavy mesons is also included. Cornwall's formula is found to be particularly accurate and useful as a predictor of heavy quarkonium states. Exact solution for all partial waves of eigenvalues and eigenfunctions for a harmonic potential is also obtained and compared with the calculated discrete spectra of the linear potential. Detailed derivations of the eigenvalues and eigenfunctions of the linear and harmonic potentials are presented in appendixes.

Badavi, Forooz F.↗

NASA NTRS1989

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.↗

NASA NTRS1989

Active Control of the Forced and Transient Response of a Finite Beam

When studying structural vibrations resulting from a concentrated source, many structures may be modelled as a finite beam excited by a point source. The theoretical limit on cancelling the resulting beam vibrations by utilizing another point source as an active controller is explored. Three different types of excitation are considered, harmonic, random, and transient. In each case, a cost function is defined and minimized for numerous parameter variations. For the case of harmonic excitation, the cost function is obtained by integrating the mean squared displacement over a region of the beam in which control is desired. A controller is then found to minimize this cost function in the control interval. The control interval and controller location are continuously varied for several frequencies of excitation. The results show that control over the entire beam length is possible only when the excitation frequency is near a resonant frequency of the beam, but control over a subregion may be obtained even between resonant frequencies at the cost of increasing the vibration outside of the control region. For random excitation, the cost function is realized by integrating the expected value of the displacement squared over the interval of the beam in which control is desired. This is shown to yield the identical cost function as obtained by integrating the cost function for harmonic excitation over all excitation frequencies. As a result, it is always possible to reduce the cost function for random excitation whether controlling the entire beam or just a subregion, without ever increasing the vibration outside the region in which control is desired. The last type of excitation considered is a single, transient pulse. A cost function representative of the beam vibration is obtained by integrating the transient displacement squared over a region of the beam and over all time. The form of the controller is chosen a priori as either one or two delayed pulses. Delays constrain the controller to be causal. The best possible control is then examined while varying the region of control and the controller location. It is found that control is always possible using either one or two control pulses. The two pulse controller gives better performance than a single pulse controller, but finding the optimal delay time for the additional controllers increases as the square of the number of control pulses.

Post, John Theodore↗

NASA NTRS1989

An Approximate Model for the Performance and Acoustic Predictions of Counterrotating Propeller Configurations

An approximate method was developed to analyze and predict the acoustics of a counterrotating propeller configuration. The method employs the analytical techniques of Lock and Theodorsen as described by Davidson to predict the steady performance of a counterrotating configuration. Then, a modification of the method of Lesieutre is used to predict the unsteady forces on the blades. Finally, the steady and unsteady loads are used in the numerical method of Succi to predict the unsteady acoustics of the propeller. The numerical results are compared with experimental acoustic measurements of a counterrotating propeller configuration by Gazzaniga operating under several combinations of advance ratio, blade pitch, and number of blades. In addition, a constant-speed commuter-class propeller configuration was designed with the Davidson method and the acoustics analyzed at three advance ratios. Noise levels and frequency spectra were calculated at a number of locations around the configuration. The directivity patterns of the harmonics in both the horizontal and vertical planes were examined, with the conclusion that the noise levels of the even harmonics are relatively independent of direction whereas the noise levels of the odd harmonics are extremely dependent on azimuthal direction in the horizontal plane. The equations of Succi are examined to explain this behavior.

Denner, Brett William↗

NASA NTRS1990

Active control of the forced and transient response of a finite beam

Structural vibrations from a point force are modelled on a finite beam. This research explores the theoretical limit on controlling beam vibrations utilizing another point source as an active controller. Three different types of excitation are considered, harmonic, random, and transient. For harmonic excitation, control over the entire beam length is possible only when the excitation frequency is near a resonant frequency of the beam. Control over a subregion may be obtained even between resonant frequencies at the cost of increasing the vibration outside of the control region. For random excitation, integrating the expected value of the displacement squared over the required interval, is shown to yield the identical cost function as obtained by integrating the cost function for harmonic excitation over all excitation frequencies. As a result, it is always possible to reduce the cost function for random excitation whether controlling the entire beam or just a subregion, without ever increasing the vibration outside the region in which control is desired. The last type of excitation considered is a single, transient pulse. The form of the controller is specified as either one or two delayed pulses, thus constraining the controller to be casual. The best possible control is examined while varying the region of control and the controller location. It is found that control is always possible using either one or two control pulses.

Post, John T.↗

NASA NTRS1989

Downward continuation of the free-air gravity anomalies to the ellipsoid using the gradient solution and terrain correction: An attempt of global numerical computations

The formulas for the determination of the coefficients of the spherical harmonic expansion of the disturbing potential of the earth are defined for data given on a sphere. In order to determine the spherical harmonic coefficients, the gravity anomalies have to be analytically downward continued from the earth's surface to a sphere-at least to the ellipsoid. The goal is to continue the gravity anomalies from the earth's surface downward to the ellipsoid using recent elevation models. The basic method for the downward continuation is the gradient solution (the g sub 1 term). The terrain correction was also computed because of the role it can play as a correction term when calculating harmonic coefficients from surface gravity data. The fast Fourier transformation was applied to the computations.

Wang, Y. M.↗

NASA NTRS1989

Analytical and experimental study of high phase order induction motors

Induction motors having more than three phases were investigated to determine their suitability for electric vehicle applications. The objective was to have a motor with a current rating lower than that of a three-phase motor. The name chosen for these is high phase order (HPO) motors. Motors having six phases and nine phases were given the most attention. It was found that HPO motors are quite suitable for electric vehicles, and for many other applications as well. They have characteristics which are as good as or better than three-phase motors for practically all applications where polyphase induction motors are appropriate. Some of the analysis methods are presented, and several of the equivalent circuits which facilitate the determination of harmonic currents and losses, or currents with unbalanced sources, are included. The sometimes large stator currents due to harmonics in the source voltages are pointed out. Filters which can limit these currents were developed. An analysis and description of these filters is included. Experimental results which confirm and illustrate much of the theory are also included. These include locked rotor test results and full-load performance with an open phase. Also shown are oscillograms which display the reduction in harmonic currents when a filter is used with the experimental motor supplied by a non-sinusoidal source.

Klingshirn, Eugene A.↗

NASA NTRS1989

Nonlinear interactions in mixing layers and compressible heated round jets

The nonlinear interactions between a fundamental instability mode and both its harmonics and the changing mean flow are studied using the weakly nonlinear stability theory of Stuart and Watson, and numerical solutions of coupled nonlinear partial differential equations. The first part focuses on incompressible cold (or isothermal; constant temperature throughout) mixing layers, and for these, the first and second Landau constants are calculated as functions of wavenumber and Reynolds number. It is found that the dominant contribution to the Landau constants arises from the mean flow changes and not from the higher harmonics. In order to establish the range of validity of the weakly nonlinear theory, the weakly nonlinear and numerical solutions are compared and the limitation of each is discussed. At small amplitudes and at low-to-moderate Reynolds numbers, the two results compare well in describing the saturation of the fundamental, the distortion of the mean flow, and the initial stages of vorticity roll-up. At larger amplitudes, the interaction between the fundamental, second harmonic, and the mean flow is strongly nonlinear and the numerical solution predicts flow oscillations, whereas the weakly nonlinear theory yields saturation. In the second part, the weakly nonlinear theory is extended to heated (or nonisothermal; mean temperature distribution) subsonic round jets where quadratic and cubic nonlinear interactions are present, and the Landau constants also depend on jet temperature ratio, Mach number and azimuthal mode number. Under exponential growth and nonlinear saturation, it is found that heating and compressibility suppress the growth of instability waves, that the first azimuthal mode is the dominant instability mode, and that the weakly nonlinear solution describes the early stages of the roll-up of an axisymmetric shear layer. The receptivity of a typical jet flow to pulse type input disturbance is also studied by solving the initial value problem and then examining the behavior of the long-time solution.

Jarrah, Yousef Mohd↗

NASA NTRS1990

Ion cyclotron bands in VLF saucers

In the wideband VLF data obtained by the polar orbiting DE-1 satellite over the polar night ion trough region of the upper ionosphere, conspicuous frequency-band structures are found to occur both in absorption and emission, particularly associating with VLF saucers. The attenuation bands indicate that the ions of atomic hydrogen from the polar ionosphere are accelerated by the ac electric fields of VLF waves oscillating normal to the static magnetic field, analogous to a cyclotron accelerator. The observed frequencies of the cyclotron harmonics suggest that the acceleration is taking place in the layer below the satellite at a geocentric distance of less than about 1.5 earth radii. This example indicates the existence of upward propagating hiss at those altitudes inside the auroral zone. On the other hand, the frequency shifts of the emission bands are attributed to a combination of two different types of Doppler shift, one due to the orbital motion of the satellite and the other due to the upward motion of the medium at the emission source. This indicates the existence of an upward plasma flow at the source, with a velocity of the order of 20 km/s inside the saucer. The amount of this frequency shift decreases with increasing harmonic order, indicating a higher phase velocity for the electrostatic waves of higher harmonic order.

Maeda, Kaichi↗

NASA NTRS1990

The vibrational frequencies of ozone

The singles and doubles coupled-cluster (CCSD) method is used, together with the recently proposed CCSD(T) and CCSDT-1 methods, to determine the equilibrium structure and harmonic frequencies of ozone at various levels, on the basis of large one-particle basis sets. It is demonstrated that f-type functions are required in order to obtain quantitative accuracy for the equilibrium structure and harmonic frequencies. The CCSD(T) level of theory, in conjunction with a (4s 3p 2d 1f) atomic natural orbital set, yields an equilibrium geometry and harmonic frequencies that are in excellent agreement with experimental results; an effort has accordingly been made to determine the cubic and quartic force constants, and evaluate the anharmonic corrections to the fundamental vibrational frequencies.

Lee, Timothy J.↗

NASA NTRS1990

Acoustic and aerodynamic study of a pusher-propeller aircraft model

An aerodynamic and acoustic study was made of a pusher-propeller aircraft model in the NASA-Ames 7 x 10 ft Wind Tunnel. The test section was changed to operate as an open jet. The 591 mm diameter unswept propeller was operated alone and in the wake of three empennages: an I tail, Y tail, and a V tail. The radiated noise and detailed wake properties were measured. Results indicate that the unsteady blade loading caused by the blade interactions with the wake mean velocity distribution had a strong effect on the harmonics of blade passage noise. The blade passage harmonics above the first were substantially increased in all horizontal directions by the empennage/propeller interaction. Directivity in the plane of the propeller was maximum perpendicular to the blade surface. Increasing the tail loading caused the propeller harmonics to increase 3 to 5 dB for an empennage/propeller spacing of 0.38 mean empennage chords. The interaction noise became weak as empennage propeller spacing was increased beyond 1.0 mean empennage chord lengths. Unlike the mean wake deficit, the wake turbulence had only a small effect on the propeller noise, that effect being a small increase in the broadband noise.

Soderman, Paul T.↗