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Results for “VIBRATING STRING”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Nonreflective boundary control of a vibrating string

One of the important applications in the developing Large Space Systems Technology will be the electrostatically controlled membrane mirror antenna. A high level of surface quality is achievable using electrostatically tensioned membranes in which surface accuracy is obtained through active control. Electrostatic actuators behind the membrane surface would provide a means of obtaining the prescribed surface shape and also be utilized to suppress the structural vibrations in the system. The surface quality, in this case, would be limited by the size, force field shape, and the number of the electrostatic actuators. An additional control capability is to introduce boundary control at the membrane perimeter. Using this additional control mechanism, structural vibrations can be absorbed at the boundary without being reflected back into the interior regions of the membrane antenna. In this paper, boundary control of a vibrating string is studied. For this system, a nonreflective boundary control is developed in which waves reaching the boundary are absorbed by the appropriate control movement of the boundary. The control is closed-loop and utilizes a single measurement close to the boundary. The closed-loop control is a delay of the measurement. The delay is determined by the velocity of wave propagation in the string and the location of the sensor.

Caglayan, A. K.↗
NASA NTRS1972

On coherent oscillations of a string.

Vibrations of an elastic string when the separation between the ends varies randomly are studied. The emphasis is on the evolution of the coherent, or ordered, oscillations of the string. Using a perturbation technique borrowed from quantum field theory and the modified Kryloff-Bogoliuboff method, the 'multiple scattering' effect of the random separation between the ends on the linear and nonlinear coherent oscillations are investigated. It is found that due to the random interactions the coherent fundamental oscillation as well as the harmonies are damped. Their frequencies are also modified.

Liu, C. H.↗
NASA NTRS1985

Stiffness control of large space structures

A method of using internal force producing dual element/actuators for vibration suppression of large space structures is proposed. The technique is applied to a vibrating string and to a low order system. Response feedback control for the vibrating string and selected modal control are used for achieving the modal damping. The actuators may be electrically powered and are suitable for structures with extremely low rigidity.

Chen, J. C.↗
NASA NTRS1985

Stiffness control of large space structures

A method of using internal force producing dual element/actuators for vibration suppression of large space structures is proposed. This technique is applied to a vibrating string as well as a low order system. Response feedback control for the vibrating string and selected modal control are used for achieving the modal damping. The actuators used in this method may be electrically powered and are suitable for structures with extremely low rigidity.

Chen, J.-C.↗
DOE OSTI2022

Helmholtz vibrations in bowed strings

We report for almost 160 years, it has been known that Helmholtz oscillations, unique to vibrating strings in bowed instruments (violin, cello, etc.), have two distinct regimes: “slip” and “stick.” During the slip regime, the force at the bow-string interaction is attributed to friction between the sliding bow hair and the vibrating string, with a friction coefficient that decreases with increasing relative velocity. Yet the hair-string interaction during the stick regime is less understood. We propose that the interaction force during the stick regime is proportional to the product of the longitudinal acoustic impedance of the bow hair to the relative bow-string velocity. We validate this hypothesis by solving the string's differential equation of motion, including an enhanced formulation to avoid parasitic high-frequency oscillations. This physical model enables us to analyze, in real time, the characteristics of the Helmholtz oscillations, including the string shape, excitation of harmonics, Schelleng ripples, and string energy, showing that the bowed string gains energy during the stick regime and loses energy during the slip regime.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Micro-/nanosized cantilever beams and mass sensors under applied axial tensile/compressive force vibrating in vacuum and viscous fluid

Vibrating micro-/nanosized cantilever beams under an applied axial force are the key components of various devices used in nanotechnology. In this study, we perform a complete theoretical investigation of the cantilever beams under an arbitrary value of the axial force vibrating in a specific environment such as vacuum, air or viscous fluid. Based on the results easy accessible expressions enabling one the fast and highly accurate estimations of changes in the Q-factor and resonant frequencies of beam oscillating in viscous fluid caused by the applied axial force are derived and analyzed. It has been also shown that for beam-to-string and string vibrational regimes the mode shape starts to significantly deviate from the one known for a beam without axial force. Moreover, a linear dependency of the vibrational amplitude in resonance on the dimensionless tension parameter has been found. We revealed that only a large axial force, i.e. the string vibrational regime, significantly improves the Q-factor of beams submerged in fluid, while an increase of the axial force in beam and beam-to-string transition regimes has a negligibly small impact on the Q-factor enhancement. Experiments carried out on the carbon nanotubes and nanowires are in a good agreement with present theoretical predictions.

42 ENGINEERING↗
NASA NTRS1971

Two examples in the time optimal control theory of distributed parameter systems.

The behavior of hyperbolic and parabolic partial differential equations is contrasted by studying the point-to-point time-optimal control problem for the equation of heat conduction and the equation of motion of a vibrating string. A maximal principle is obtained for the time-optimal control of the one-dimensional heat equation, and it is proven that time optimal controls are weakly bang-bang. The bang-bang principle is proven to be invalid for hyperbolic equations because of the finite speed of wave propagation. In the case of boundary value control of the vibrating spring, the latter is demonstrated by deriving an explicit formula for the time optimal control.

Quinn, J. P.↗
NASA NTRS1971

A traverse gravimeter for the lunar surface

A semi-automatic, self-levelling lunar gravimeter was designed for the purpose of measuring gravity at predetermined stops along the route of a lunar rover vehicle to obtain a gravity profile. The traverse gravimeter is completely self-contained and is powered by an internal battery. The gravity sensor is a vibrating string accelerometer (VSA) which is enclosed in a precision oven. Gravity data are obtained by initiating a measurement. After the gravimeter has levelled, the VSA difference frequency is counted down and a gate is generated to enable a crystal-controlled clock to a BCD counter. The BCD counter stores the data which are a measurement of gravity. These data, displayed upon command by the astronaut, are transmitted by voice back to earth. It is expected that the accuracy of the gravimeter will be better than one milligal. Low power, light weight, reliability, and simplicity of operation are major considerations in the design of the gravimeter.

Mamon, G.↗
NASA NTRS1972

A traverse gravimeter for the lunar surface.

A semiautomatic, self-leveling lunar gravimeter has been designed for the purpose of measuring gravity at predetermined stops along the route of a Lunar Rover Vehicle to obtain a gravity profile. The Traverse Gravimeter is completely self-contained and is powered by an internal battery. The gravity sensor is a vibrating string accelerometer (VSA) which is enclosed in a precision oven. Gravity data are obtained by initiating a measurement. After the gravimeter has leveled, the VSA difference frequency is counted down and a gate is generated to enable a crystal-controlled clock to a BCD counter. The BCD counter stores the data which are a measurement of gravity. These data, displayed upon command by the astronaut, are transmitted by voice back to earth.

Mamon, G.↗
NASA NTRS1973

Traverse gravimeter experiment

A semiautomatic self-leveling lunar gravimeter has been designed for the Apollo 17 mission. This traverse gravimeter, which is completely self-contained and powered by an internal battery, was used to measure gravity at predetermined stops along the route of the Lunar Rover Vehicle. The gravity sensor is a vibrating string accelerometer (VSA) enclosed in a temperature-controlled oven and gimballed leveling assembly. This instrument is capable of resolving gravity differences as small as 0.035 milligal (1 mgal = 0.001 cm/s) on the moon and yet also is able to measure the earth's gravity field of 980,000 milligals. Twenty-two measurements were taken on the moon during the Apollo 17 mission, during which the VSA temperature never varied more than 0.005 C. The flight results indicate an instrument accuracy of better than 2 mgal.

Buck, S. W.↗
NASA NTRS1980

Vibration characteristics of a steadily rotating slender ring

Partial differential equations are derived to describe the structural vibrations of a uniform homogeneous ring which is very flexible because the radius is very large compared with the cross sectional dimensions. Elementary beam theory is used and small deflections are assumed in the derivation. Four sets of structural modes are examined: bending and compression modes in the plane of the ring; bending modes perpendicular to the plane of the ring; and twisting modes about the centroid of the ring cross section. Spatial and temporal characteristics of these modes, presented in terms of vibration frequencies and ratios between vibration amplitudes, are demonstrated in several figures. Given a sufficiently high rotational rate, the dynamics of the ring approach those of a vibrating string. In this case, the velocity of traveling wave in the material of the ring approaches in velocity of the material relative to inertial space, resulting in structural modes which are almost stationary in space.

Lallman, F. J.↗
NASA NTRS1989

Terrestrial gravity instrumentation in the 20th Century: A brief review

At the turn of the century, only pendulum apparatuses and torsion balances were available for general exploration work. Both of these early techniques were cumbersome and time-consuming. It was no wonder that the development of the gravity meter was welcomed with a universal sigh of relief. By 1935 potential field measurements with gravity meters supplanted gradient measurements with torsion balances. Potential field measurements are generally characterized by three types: absolute - measurements are made in fundamental units, traceable to national standards of length and time at each observation site; relative with absolute scale - differences in gravity are measured in fundamental units traceable to national standards of length and time; and relative - differences in gravity are measured with arbitrary scale. Improvements in the design of gravity meters since their introduction has led to a significant reduction in size and greatly increased precision. As the precision increased, applications expanded to include the measurement of crustal motion, the search for non-Newtonian forces, archeology, and civil engineering. Apart from enhancements to the astatic gravity meter, few developments in hardware were achieved. One of these was the vibrating string gravity meter which was developed in the 1950s and was employed briefly for marine and borehole applications. Another is the cryogenic gravity meter which utilizes the stability of superconducting current to achieve a relative instrument with extremely low drift suitable for tidal and secular gravity measurements. An advance in performing measurements from a moving platform was achieved with the development of the straight-line gravity meter. The latter part of the century also saw the rebirth of gradient measurements which offers advantages for observations from a moving platform. Definitive testing of the Bell gradiometer was recently reported.

Valliant, H. D.↗
NASA NTRS1989

GPS-aided gravimetry at 30 km altitude from a balloon-borne platform

A balloon-borne experiment, flown at 30 km altitude over New Mexico, was used to test dynamic differential Global Positioning System (GPS) tracking in support of gravimetry at high-altitudes. The experiment package contained a gravimeter (Vibrating String Accelerometer), a full complement of inertial instruments, a TI-4100 GPS receiver and a radar transponder. The flight was supported by two GPS receivers on the ground near the flight path. From the 8 hour flight, about a forty minute period was selected for analysis. Differential GPS phase measurements were used to estimate changes in position over the sample time interval, or average velocity. In addition to average velocity, differential positions and numerical averages of acceleration were obtained in three components. Gravitational acceleration was estimated by correcting for accelerations due to translational motion, ignoring all rotational effects.

Lazarewicz, Andrew R.↗
NASA NTRS1990

Graphics applications utilizing parallel processing

The results are presented of research conducted to develop a parallel graphic application algorithm to depict the numerical solution of the 1-D wave equation, the vibrating string. The research was conducted on a Flexible Flex/32 multiprocessor and a Sequent Balance 21000 multiprocessor. The wave equation is implemented using the finite difference method. The synchronization issues that arose from the parallel implementation and the strategies used to alleviate the effects of the synchronization overhead are discussed.

Rice, John R.↗