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The aerodynamic damping in roll of a series of wings has been investigated in the Langley high-speed 7- by 10-foot tunnel at Mach numbers ranging from 0.2 to 0.8 by use of a forced oscillatory-roll technique. Tests were conducted on wings of aspect ratio 6 with sweep angles of 25, 35, and 45 deg and on 35 deg swept wings of aspect ratios 4 and 5.
Wind tunnel tests have been made at angles of attack from about -2 deg to about 22 deg at 0 deg angle of sideslip by using a small-amplitude forced-oscillation technique. Models were tested with upper and lower control flaps both deflected and undeflected. The configuration with flaps deflected has positive damping in both pitch and yaw and is stable in both pitch and yaw except at the higher angles of attack where the tail surfaces are submerged in the wake from the body.
Simple stability methods are used to derive an approximate, closed-form expression for the lead-lag damping of rotor blades in hover. Destabilizing terms are shown to be a result of two dynamic mechanisms. First, the destabilizing aerodynamic forces that can occur when blade lift is higher than a critical value are maximized when the blade motion is in a straight line equidistant from the blade chord and the average direction of the air flow velocity. This condition occurs when the Coriolis terms vanish and when the elastic coupling terms align the blade motion with this least stable direction. Second, the nonconservative stiffness terms that result from pitch-flap or pitch-lag coupling can add or subtract energy from the system depending upon whether the motion of the blade tip is clockwise or counterclockwise.
This article presents an efficient numerical algorithm and a complete listing of the associated computer program, developed for the eigenproblem solution of discrete damped structures, including spinning ones. The numerically stable procedure is based on a combined Sturm sequence and inverse iteration technique, which fully exploits the banded form of the relevant matrices and proves to be most substantially economical when compared to similar existing softwares. Numerical results are presented for representative structures, solved by the present computer program written in FORTRAN V for the JPL UNIVAC 1108 computer.
A set of equations describing the coupled flap-lag-torsional dynamics of a cantilevered rotor blade in hover is presented. This set of equations is used to evaluate the influence of structural damping, preconing and offsets on the linearized aeroelastic stability of some representative blade configurations. A number of examples illustrating the coupled nonlinear flap-lag-torsional response are considered.
Wind tunnel tests were conducted to measure the pitch-, yaw-, and roll-damping characteristics of a modified 089B shuttle orbiter. These tests were conducted for NASA-Langley at the von Karman Gas Dynamics Facility of the Arnold Engineering Development Center. Data were obtained utilizing the small amplitude forced-oscillation technique at angles of attack of -4.9 to 26.5 deg at Reynolds numbers, based on model length, of 1,180,000 to 4,820,000. The orbiter was dynamically stable in pitch, yaw, and roll, and the pitch derivatives were dependent on Reynolds number, while the roll derivatives were independent of Reynolds number.
A tracking filter that includes an output that is logarithmically proportional to the amplitude of the filtered signal is used to measure the damping exponent of a transient decay. This method is analogous to the digital technique referred to as the moving-block or peak-plot method. The method is simple to use and quite accurate, avoids the numerical computations associated with similar digital techniques, but is constrained by the poor time-domain response characteristics of commercial tracking filters presently available.
Brushless tachometer generates signals for moving large and varying loads precisely. Stepper waveform generator sends short sequence of pulses to instruct control logic circuit to perform its function-that is, to select proper windings and directions of excitation to drive and damp motor. Control logic circuit bases decisions on following logic signals, derived from tachometer: rate direction, rate threshold, and position.
Various procedures that might be used in evaluating system response characteristics as involved in subcritical flight and wind-tunnel flutter testing of aircraft are reviewed with emphasis on the means for eliminating or minimizing the contamination effects produced by an unknown noise in the input. Results of a procedure developed for identifying modal frequency and damping values, and a possible way for making a detailed evaluation of system parameters, are also given.
An analysis of one and multidegree of freedom systems with classical damping is presented. Definition and minimization of error functions for each system are discussed. Systems with classical and nonclassical normal modes are studied, and results for first order perturbation are given. An alternative method of matching power spectral densities is provided, and numerical results are reviewed.
Experimental data are presented for the unbalance response of a flexible, ball bearing supported rotor to speeds above the third lateral bending critical. Values of squeeze film damping coefficients obtained from measured data are compared to theoretical values obtained from short bearing approximation over a frequency range from 5000 to 31 000 cycles/min. Experimental response for an undamped rotor is compared to that of one having oil squeeze film dampers at the bearings. Unbalance applied varied from 0.62 to 15.1 gm-cm.
The paper outlines the theory, design, and application of an apparatus based on the single beam resonant dwell technique to determine the damping capacity of metallic materials by measuring the response of a structural element to excitation at a modal frequency. In this apparatus, a cantilever beam specimen of a test material is clamped to a bar which is connected at one end to an electromagnetic shaker and at the other to a heavy base. The thickness of the bar at the base end is reduced by two saw cuts to provide a pivot around which the remainder of the bar can rotate when excited by the shaker which is connected to the bar by a rod passing through a hole in the base. The response of the supporting system to shaker excitation is measured with an accelerometer mounted on the bar at the root of the specimen. Specimen response is measured optically with a low-power microscope with a reticle. Specimen loss factor is determined in terms of acceleration at the beam root, beam tip displacement, and the beam natural frequency.
A test rig to measure the dynamic stiffness and damping of elastomer O rings was described. Test results for stiffness and loss coefficient in the frequency range from 50 Hz to 1000 Hz are presented. Results are given for three different materials, for five temperatures, for three amplitudes, for five values of squeeze for three values of stretch for three values of cross-section diameter and for three values of groove width. All test data points were plotted. In addition, trend summary plots were presented which compare the effect of material, temperature, amplitude, squeeze, stretch, cross-section diameter, and groove width. O ring deflections under a static load for different material were presented; and effective static stiffness values were compared with dynamic values.
General expressions for computing time constants for radiative decay of harmonic temperature perturbations in planetary atmospheres are developed. Four spatial scales are shown to be generally important: the scale height of the atmospheric absorber, the absorption mean free path for thermal radiation, the altitude above the planetary surface, and the wavelength of the temperature perturbation. Atmospheric inhomogeneity is particularly important when the radiation mean free path and the vertical wavelength divided by 2 pi both exceed the absorber scale height. The surface is very important for wave decay at altitudes less than a few radiation mean free paths, and its effect depends on a comparison of the surface response time and the lifetime of the atmospheric perturbation. The surface response time depends on the conducting and emitting properties of the surface material and on the strength of turbulence in the planetary boundary layer. The additional influence of chemical reactions and phase changes on radiative damping is discussed, and several assumptions inherent in the development of the general expressions for time constants are evaluated. Terrestrial examples are used for purposes of illustration, but the development is kept sufficiently general so that the results remain applicable to most situations on other planets.
Bayliss (1975) has studied the question whether in the case of linear differential equations the relationship between the stability of the homogeneous equations and the existence of almost periodic solutions to the inhomogeneous equation is preserved by finite difference approximations. In the current investigation analogous properties are considered for the case in which the damping is quadratic rather than linear. The properties of the considered equation for arbitrary forcing terms are examined and the validity is proved of a theorem concerning the characteristics of the unique solution. By using the Lipschitz continuity of the mapping and the contracting mapping principle, almost periodic solutions can be found for perturbations of the considered equation. Attention is also given to the Lipschitz continuity of the solution operator and the results of numerical tests which have been conducted to test the discussed theory.
Experimental data are presented for the unbalance response of a flexible, ball bearing supported rotor to speeds above the third lateral bending critical. Values of squeeze film damping coefficients obtained from measured data are compared to theoretical values obtained from short bearing approximation over a frequency range from 5000 to 31,000 cycles/min. Experimental response for an undamped rotor is compared to that of one having oil squeeze film dampers at the bearings. Unbalances applied varied from 0.62 to 15.1 gm-cm.
Tests were performed on elastomer specimens of the material polybutadiene to determine the performance limitations imposed by strain, temperature, and frequency. Three specimens were tested: a shear specimen, a compression specimen, and a second compression specimen in which thermocouples were embedded in the elastomer buttons. Stiffness and damping were determined from all tests, and internal temperatures were recorded for the instrumented compression specimen. Measured results are presented together with comparisons between predictions of a thermo-viscoelastic analysis and the measured results. Dampers of polybutadiene and Viton were designed, built, and tested. Vibration measurements were made and sensitivity of vibration to change in unbalance was also determined. Values for log decrement were extracted from the synchronous response curves. Comparisons were made between measured sensitivity to unbalance and log decrement and predicted values for these quantities.
Recent measurements by the Pioneer 10 and Helios 1 spacecraft show that the leading edge of a corotating structure spreads as it moves from 0.3 AU to the orbit of the earth and steepens again farther out. By including Landau damping effects in the dynamical behavior of the streams, the above qualitative features can be accounted for.