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The use of spline-based inverse procedures to estimate damping coefficients for flexible structures in distributed-parameter systems is reported. Damping models involving viscous (air) damping and Kelvin-Voigt damping in an Euler-Bernoulli framework are used to analyze data from vibration experiments with composite material beams.
Using a high-temperature optically based displacement measurement system, a foil air bearing's stiffness and damping characteristics were experimentally determined. Results were obtained over a range of modified Sommerfeld Number from 1.5E6 to 1.5E7, and at temperatures from 25 to 538 C. An Experimental procedure was developed comparing the error in two curve fitting functions to reveal different modes of physical behavior throughout the operating domain. The maximum change in dimensionless stiffness was 3.0E-2 to 6.5E-2 over the Sommerfeld Number range tested. Stiffness decreased with temperature by as much as a factor of two from 25 to 538 C. Dimensionless damping was a stronger function of Sommerfeld Number ranging from 20 to 300. The temperature effect on damping being more qualitative, showed the damping mechanism shifted from viscous type damping to frictional type as temperature increased.
Point vibration dampers whose basic energy absorption mechanism is elastoplastic hysteresis, supplemented by rubber damping elements
A method of estimating the distributed damping parameters based on the measured modal parameters (frequency and damping ratios) was derived. Three different mathematical models were used to model the damping mechanism of a quasi-isotropic pultruded cantilevered beam. These three models were (1) viscous (air) damping, (2) strain rate damping, and (3) both viscous and strain rate damping. The eigenvalues of the partial differential equation model were found to be uninfluenced by any of the three assumed damping models. Values were obtained for each of the damping models as well as the modulus of elasticity of the beam. It was found that the two-parameter damping model provided the best fit to measured modal data. However, the two-parameter damping model could only reproduce the measured damping ratios to within 85 percent.
A method of estimating the distributed damping parameters of a beam based on measured modal parameters (frequency and damping ratios) is derived. Three different mathematical models were used to model the damping mechanism of a quasi-isotropic pultruded cantilevered beam. These three models were (1) viscous (air) damping, (2) strain-rate damping, and (3) both viscous and strain-rate damping. Values were obtained for each of the damping models as well as the modulus of elasticity of the beam. It is found that the two-parameter damping model provides the best fit to measure modal data. However, the two-parameter damping model can only reproduce the measured damping ratios to within 85 percent.
Engineering preliminary design methods for approximating and predicting the effects of viscous or equivalent viscous-type damping treatments on the free and forced vibration of lightly damped aircraft-type structures are developed. Similar developments are presented for dynamic hysteresis viscoelastic-type damping treatments. It is shown by both engineering analysis and numerical illustrations that the intermodal coupling of the undamped modes arising from the introduction of damping may be neglected in applying these preliminary design methods, except when dissimilar modes of these lightly damped, complex aircraft-type structures have identical or nearly identical natural frequencies. In such cases, it is shown that a relatively simple, additional interaction calculation between pairs of modes exhibiting this 'modal response' phenomenon suffices in the prediction of interacting modal damping fractions. The accuracy of the methods is shown to be very good to excellent, depending on the normal natural frequency separation of the system modes, thereby permitting a relatively simple preliminary design approach. This approach is shown to be a natural precursor to elaborate finite element, digital computer design computations in evaluating the type, quantity, and location of damping treatment.
The estimation of material and patch parameters for a system involving a circular plate, to which piezoceramic patches are bonded, is considered. A partial differential equation (PDE) model for the thin circular plate is used with the passive and active contributions form the patches included in the internal and external bending moments. This model contains piecewise constant parameters describing the density, flexural rigidity, Poisson ratio, and Kelvin-Voigt damping for the system as well as patch constants and a coefficient for viscous air damping. Examples demonstrating the estimation of these parameters with experimental acceleration data and a variety of inputs to the experimental plate are presented. By using a physically-derived PDE model to describe the system, parameter sets consistent across experiments are obtained, even when phenomena such as damping due to electric circuits affect the system dynamics.
A simple engineering approximation using undamped modes is shown to be valid for determining the effect of small viscous or equivalent viscous-type damping forces on the forced vibration response of a lightly damped linear systems. It is shown that intermodal coupling of the undamped modes may be neglected with negligible error, except when the system has degenerate or quasi-degenerate modes. This can occur in complex structural systems such as aircraft or spacecraft. In such cases, one of these two modes has virtually no damping, whereas the other effectively has the damping of both.
Nonconservative loading on linear two-degree of freedom elastic system, discussing damping effects on equilibrium stability
Destabilization of linear system with N degrees of freedom without damping subjected to nonconservative forces
Nonconservative loading on linear two-degree of freedom elastic system, discussing damping effects on equilibrium stability
Cantilevered continuous pipe conveying fluid at constant velocity, showing that internal and external damping and Coriolis forces may have destabilizing effect
Cantilevered continuous pipe conveying fluid at constant velocity, showing that internal and external damping and Coriolis forces may have destabilizing effect
This validation study examines the effect on vibroacoustic response resulting from the installation of cable bundles on a curved orthogrid panel. Of interest is the level of damping provided by the installation of the cable bundles and whether this damping could be potentially leveraged in launch vehicle design. The results of this test are compared with baseline acoustic response tests without cables. Damping estimates from the measured response data are made using a new software tool that leverages a finite element model of the panel in conjunction with advanced optimization techniques. While the full test series is not yet complete, the first configuration of cable bundles that was assessed effectively increased the viscous critical damping fraction of the system by as much as 0.02 in certain frequency ranges.
Viscous ring damper for removing wobble motion of spin-stabilized satellite analyzed by studying energy dissipation
Dynamic behaviors of structures analyzed interactively. Interactive steadystate vibration-response program, VIBRA, developed. Frequency-response analyses commonly used in evaluating dynamic behaviors of structures subjected to cyclic external forces. VIBRA calculates frequency response using modalsuperposition approach. Method applicable to single or multiple forces applied to linear, proportionally damped structure in which damping is viscous or structural. VIBRA written in FORTRAN 77 for interactive execution.
This paper deals with the dynamic response of anisotropic laminated composite flat panels exposed to sonic boom and explosive blast-type loadings. The pertinent governing equations incorporating transverse shear deformation, transverse normal stress, the higher order effects as well as the viscous structural damping are solved by using the integral-transform technique. The obtained results are compared with their counterparts obtained within the framework of the first order transverse shear deformation and the classical plate theories and some conclusions concerning their range of applicability are outlined. The paper also contains a detailed analysis of the influence played by the various parameters characterizing the considered pressure pulses as well as the material and geometry of the plate.
The Aquarius Instrument s large radar reflector dish needed to be stowed for launch, and then deployed on-orbit. The Deployment Subsystem consisted of a cantilevered boom structure and two single-axis hinge mechanisms to accurately deploy and position the reflector dish relative to the radar feed horns. The cantilevered design demanded high stiffness and accuracy from the deployment mechanism at the root of the boom. A preload-generating end-of-travel latch was also required. To largely eliminate the need for control systems, each deployment mechanism was actuated by a passive spring motor with viscous-fluid damping. Tough requirements and adaptation of a heritage actuator to the new application resulted in numerous challenges. Fabrication, assembly, and testing encountered additional problems, though ultimately the system was demonstrated very successfully. This paper revisits the development to highlight which design concepts worked and the many important lessons learned.