Damping constant of Fraunhofer lines.
Solar photosphere collisional damping by hydrogen atoms larger than electron damping for Fraunhofer lines
Swamy, K. S. K.↗
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Damping factor for the least-squares method of optical design.
Damping factor automatic determination by use of second derivatives of residuals for damped least squares method of optical design
Buchele, D. R.↗
An evaluation of random analysis methods for the determination of panel damping
An analysis is made of steady-state and non-steady-state methods for the measurement of panel damping. Particular emphasis is placed on the use of random process techniques in conjunction with digital data reduction methods. The steady-state methods considered use the response power spectral density, response autocorrelation, excitation-response crosspower spectral density, or single-sided Fourier transform (SSFT) of the response autocorrelation function. Non-steady-state methods are associated mainly with the use of rapid frequency sweep excitation. Problems associated with the practical application of each method are evaluated with specific reference to the case of a panel exposed to a turbulent airflow, and two methods, the power spectral density and the single-sided Fourier transform methods, are selected as being the most suitable. These two methods are demonstrated experimentally, and it is shown that the power spectral density method is satisfactory under most conditions, provided that appropriate corrections are applied to account for filter bandwidth and background noise errors. Thus, the response power spectral density method is recommended for the measurement of the damping of panels exposed to a moving airflow.
Bhat, W. V.↗
Design and testing of a magnetic suspension and damping system for a space telescope
The basic equations of motion are derived for a two dimensional, three degree of freedom simulation of a space telescope coupled to a spacecraft by means of a magnetic suspension and isolation system. The system consists of paramagnetic or ferromagnetic discs confined to the magnetic field between two Helmholtz coils. Damping is introduced by varying the magnetic field in proportion to a velocity signal derived from the telescope. The equations of motion are nonlinear, similar in behavior to the one-dimensional Van der Pol equation. The computer simulation was verified by testing a 264-kilogram air bearing platform which simulates the telescope in a frictionless environment. The simulation demonstrated effective isolation capabilities for disturbance frequencies above resonance. Damping in the system improved the response near resonance and prevented the build-up of large oscillatory amplitudes.
Ockman, N. J.↗
Development of procedures for calculating stiffness and damping properties of elastomers in engineering applications. Part 1: Verification of basic methods
The primary aim of this investigation was verification of basic methods which are to be used in cataloging elastomer dynamic properties (stiffness and damping) in terms of viscoelastic model constants. These constants may then be used to predict dynamic properties for general elastomer shapes and operating conditions, thereby permitting optimum application of elastomers as energy absorption and/or energy storage devices in the control of vibrations in a broad variety of applications. The efforts reported involved: (1) literature search; (2) the design, fabrication and use of a test rig for obtaining elastomer dynamic test data over a wide range of frequencies, amplitudes, and preloads; and (3) the reduction of the test data, by means of a selected three-element elastomer model and specialized curve fitting techniques, to material properties. Material constants thus obtained have been used to calculate stiffness and damping for comparison with measured test data. These comparisons are excellent for a number of test conditions and only fair to poor for others. The results confirm the validity of the basic approach of the overall program and the mechanics of the cataloging procedure, and at the same time suggest areas in which refinements should be made.
Chiang, T.↗
Evaluation of flexible ring baffles for damping liquid oscillations
An experimental study was undertaken of damping produced by single flexible-ring baffles in a 396-cm diameter tank of liquid nitrogen. Two 24.8-cm wide baffles were tested. One baffle was 0.00635 cm thick type 301 stainless steel and the other 0.0254 cm thick Teflon FEP. Each baffle produced damping of liquid oscillations equal to or greater than that expected from rigid baffles of the same size. The equations used to determine the baffle thickness required were found to be adequate baffle design equations.
Bugg, F.↗
Sinusoidal response of composite-material plates with material damping.
A general forced-vibration analysis is presented for laminated anisotropic rectangular plates including material damping. The theory used is the laminated version of the Mindlin plate theory and includes thickness-shear flexibility and rotatory and coupling inertia. A solution is obtained by the Rayleigh-Ritz method, extended to include the energy dissipated and the work done by the excitation. The analysis is applied to prediction of the resonant frequencies and associated nodal patterns and damping ratios of the first five modes for a series of rectangular plates with free edges. The plates considered consist of unidirectional boron-fiber/epoxy composite material with respective fiber orientations of 0, 10, 30, 45, 60, and 90 deg.
Siu, C. C.↗
Radiative damping of trapped gravity waves in the solar atmosphere.
The radiative damping of trapped gravity waves in an optically thin atmosphere is studied for a stratified Boussinesq fluid. The character of the atmospheric eigenmodes depends on the distribution of the Brunt-Vaisala frequency N and the radiative relaxation time tau. The calculations for simple layer models show that if N x tau is large over some finite fraction of the trapping region, then modes of long lifetime can exist. In order to suppress gravity waves entirely, it is necessary that N x tau be less than or equal to 1 over the entire trapping region. Qualitative application of the results to the solar atmosphere leads to the conclusion that gravity wave eigenmodes of the solar atmosphere, although damped, are by no means eliminated by radiative effects.
Clark, P. A.↗
The application of Riegels' rule and time-like damping to transonic flow calculations
Finite difference relaxation solutions of the nonlinear small perturbation equations have proven reliable and successful in determining the transonic flowfields about thin airfoils. However, application of the small perturbation approach to thick airfoils usually results in an accuracy less than desirable. The incorporation of Riegels' Rule and time-like damping into the small perturbation approach and their application to thick and thin airfoils in transonic flow are discussed. Studies for thick and thin airfoils are presented. It is concluded that Riegels' Rule and damping should both be included in small perturbation transonic flow calculations.
Herron, D. L.↗
Electronic damping of mechanical vibrations
The conditions required for measuring and recording the patterns of vibration of a process are discussed. It is stated that the frequency of the process being investigated must be an order of magnitude lower than the natural frequency of the sensitive receiving element for sufficient accuracy. The elastic element must damp so the frequency range of the vibrational patterns being investigated can be expanded. This is especially true of the tensile stresses of a moving signal carrier. A method is proposed for damping mechanical vibrations of elastic sensitive elements with semiconductor strain gages, based on electronic compensation of the natural vibrations. A schematic diagram is provided to show the conditions.
Vasilyev, P.↗
Investigation of a vibration-damping unit for reduction in low-frequency vibrations of electric motors
The vibroacoustical characteristics of different types of electric motors are discussed. It is shown that the basic source of low frequency vibrations is rotor unbalance. A flexible damping support, with an antivibrator, is used to obtain the vibroacoustical effect of reduction in the basic harmonic of the electric motor. A model of the electric motor and the damping apparatus is presented. Mathematical models are developed to show the relationships of the parameters. The basic purpose in using a calculation model id the simultaneous replacement of the exciting force created by the rotor unbalance and its inertial rigidity characteristics by a limiting kinematic disturbance.
Grigoryey, N. V.↗
Effect of damping on excitability of high-order normal modes
The effect of localized structural damping on the excitability of higher-order large space telescope spacecraft modes is investigated. A preprocessor computer program is developed to incorporate Voigt structural joint damping models in a finite-element dynamic model. A postprocessor computer program is developed to select critical modes for low-frequency attitude control problems and for higher-frequency fine-stabilization problems. The selection is accomplished by ranking the flexible modes based on coefficients for rate gyro, position gyro, and optical sensor, and on image-plane motions due to sinusoidal or random PSD force and torque inputs.
Merchant, D. H.↗
The effects of localized damping on structural response
The effect of localized structural damping on the excitability of higher order normal modes of the large space telescope was investigated. A preprocessor computer program was developed to incorporate Voigt structural joint damping models in a NASTRAN finite-element dynamic model. A postprocessor computer program was developed to select critical modes for low-frequency attitude control problems and for higher frequency fine-stabilization problems. The mode selection is accomplished by ranking the flexible modes based on coefficients for rate gyro, position gyro, and optical sensors, and on image-plane motions due to sinusoidal or random power spectral density force and torque inputs.
Merchant, D. H.↗
Langevin equation with stochastic damping - Possible application to critical binary fluid
We solve the familiar Langevin equation with stochastic damping to represent the motion of a Brownian particle in a fluctuating medium. A connection between the damping and the random driving forces is proposed which preserves quite generally the Einstein relation between the diffusion and mobility coefficients. We present an application to the case of a Brownian particle in a critical binary mixture.
Jasnow, D.↗
Development of procedures for calculating stiffness and damping properties of elastomers. Part 3: The effects of temperature, dissipation level and geometry
Effects of temperature, dissipation level and geometry on the dynamic behavior of elastomer elements were investigated. Force displacement relationships in elastomer elements and the effects of frequency, geometry and temperature upon these relationships are reviewed. Based on this review, methods of reducing stiffness and damping data for shear and compression test elements to material properties (storage and loss moduli) and empirical geometric factors are developed and tested using previously generated experimental data. A prediction method which accounts for large amplitudes of deformation is developed on the assumption that their effect is to increase temperature through the elastomers, thereby modifying the local material properties. Various simple methods of predicting the radial stiffness of ring cartridge elements are developed and compared. Material properties were determined from the shear specimen tests as a function of frequency and temperature. Using these material properties, numerical predictions of stiffness and damping for cartridge and compression specimens were made and compared with corresponding measurements at different temperatures, with encouraging results.
Smalley, A. J.↗
Determination of subcritical damping by moving-block/randomdec applications
Two techniques are described which allow the determination of subcritical dampings and frequencies during aeroelastic testing of flight vehicles. The moving-block technique is shown to have the advantage of being able to provide damping and frequency information for each mode which might be present in a signal trace, but it has the disadvantage of requiring that the structure be excited transiently. The randomdec technique requires only random turbulence for excitation, but the randomdec signature is difficult to analyze when more than one mode is present. It is shown that by using the moving-block technique to analyze the randomdec signatures, the best features of both methods are gained. Examples are presented illustrating the direct application of the moving-block method to model helicopter rotor testing and application of the combined moving-block/randomdec method to flutter studies of two fixed-wing models.
Hammond, C. E.↗
Turbulence excited frequency domain damping measurement and truncation effects
Existing frequency domain modal frequency and damping analysis methods are discussed. The effects of truncation in the Laplace and Fourier transform data analysis methods are described. Methods for eliminating truncation errors from measured damping are presented. Implications of truncation effects in fast Fourier transform analysis are discussed. Limited comparison with test data is presented.
Soovere, J.↗
Neutrino damping of nonradial pulsations in gravitational collapse
Using simple classical neutron-gas models, it is shown that neutrino radiation may in some cases be more efficient than gravitational radiation for damping out nonradial pulsations during gravitational collapse. This implies that previous estimates of gravitational radiation from neutron-star or black-hole formation following supernovae may have been overly optimistic. Final conclusions for any particular model await detailed hydrodynamic calculations. However, this paper shows that neutrino damping is potentially important in such calculations and must be taken into account.
Kazanas, D.↗