Significant damping can be introduced to a closed structure by filling the structure with a moderately lossy, low-wave-speed medium, such as a foam or a low-density powder. In this paper, we study the damping in long, thin-walled, cylindrical tubes filled with a low-density powder. Experimental results show that significant damping can be attained in tube bending (n=1) modes as well as shell bending (n=2 and higher) modes. To predict the damping in such systems, we develop a model based on three-dimensional shell equations including shear deformation and in-plane inertia, and treat the powder as a compressible fluid with a complex speed of sound. By studying the spatial decay of steady harmonic motion in an infinitely long tube, we obtain estimates for the loss factor of vibration for various numbers of circumferential nodes as a function of driving frequency.
We propose a modified LMS algorithm for adaptive feedforward control
with actuator limits. Unlike the leaky LMS method, which limits the controller effort by introducing an auxiliary cost, in the proposed algorithm we maintain the cost as the performance measurement. We derive the true stochastic gradient of the cost for systems with saturation with respect to the filter coefficients and obtain an adaptation rule very close to that of the filtered-x algorithm, but in the proposed algorithm, the reference filter is a time-varying modification of the secondary channel. In simulations of an active vibration isolation system with actuator limits, the proposed algorithm attains better performance than that attained by the leaky LMS algorithm.
Norna Robertson, Benjamin Abbott, R. Abbott, R. Adhikari, Graham Allen, Helena Armandula, Stuart Aston, A. Baglino, Mark Barton, B. Bland, Rolf Bork, J. Bogenstahl, Gianpietro Cagnoli, C. Campbell, C. Cantley, K. Carter, D. Cook, D. Coyne, David Crooks, Edward Daw, Daniel DeBra, E. Elliffe, J. Faludi, Peter Fritschel, A. Ganguli, Joseph Giaime, S. Gossler, A. Grant, J. Greenhalgh, M. Hammond, Jonathan Hanson, C. Hardham, Gregory Harry, Alistair Heptonstall, Jay Heefner, James Hough, D. Hoyland, Wensheng Hua, L. Jones, R. Jones, Jonathan Kern, J. LaCour, Brian Lantz, K. Lilienkamp, N. Lockerbie, Harald Lueck, M. MacInnis, K. Mailand, Ken Mason, R. Mittleman, Samir Nayfeh, J. Nichol, David Ottaway, H. Overmier, M. Perreur-Lloyd, J. Phinney, M. Plissi, W. Rankin, D. Robertson, J. Romie, Sheila Rowan, R. Scheffler, David Shoemaker, P. Sarin, Peter Sneddon, Clive Speake, O. Spjeld, G. Stapfer, Kenneth Strain, C. Torrie, G. Traylor, J. van Niekerk, Alberto Vecchio, Shirong Wen, P. Willems, I. Wilmut, Harry Ward, M. Zucker, Lei Zuo
To meet the overall isolation and alignment requirements for the optics in Advanced LIGO, the planned upgrade to LIGO, the US laser interferometric gravitational wave observatory, we are developing three sub-systems: a hydraulic external pre-isolator for low frequency alignment and control, a two-stage active isolation platform designed to give a factor of ~1000 attenuation at 10 Hz, and a multiple pendulum suspension system that provides passive isolation above a few hertz. The hydraulic stage uses laminar-flow quiet hydraulic actuators with millimeter range, and provides isolation and alignment for the optics payload below 10 Hz, including correction for measured Earth tides and the microseism. This stage supports the in-vacuum two-stage active isolation platform, which reduces vibration using force feedback from inertial sensor signals in six degrees of freedom. The platform provides a quiet, controlled structure to mount the suspension system. This latter system has been developed from the triple pendulum suspension used in GEO 600, the German/UK gravitational wave detector. To meet the more stringent noise levels required in Advanced LIGO, the baseline design for the most sensitive optics calls for a quadruple pendulum, whose final stage consists of a 40 kg sapphire mirror suspended on fused silica ribbons to reduce suspension thermal noise.
We study the dynamics of servomechanisms in which power is transmitted
from the motor to payload using a flat steel belt. The bandwidth of
control in such systems is usually limited by a resonance in which
the payload and motor oscillate out of phase and the belt undergoes
longitudinal strains. In this paper, we conduct experiments on
a linear positioning system, show that significant damping
in the drive resonance can be attained by attaching a layer of
low-wave-speed foam to the belt, and develop a simple model of this
damping phenomenon.
In this paper we propose a new robust control algorithm for
skyhook isolation using an integral sliding surface. Unlike
conventional sliding control based on reference tracking, a
dynamic sliding surface is directly defined in state space, and
the target dynamics are achieved by driving the system onto this
surface. Such an algorithm eliminates the need for measurement of
base vibration, and also yields an equivalent control exactly
equal to that obtained by inverse dynamics. We further examine the
effect of geophone sensor dynamics on the practical
implementation, and design an electric circuit to correct the
low-frequency characteristics of the sensor. We implement the
proposed control in a realistic plant, and compare the performance
to that of direct velocity feedback and conventional sliding
control.
The characteristics of multiple tuned-mass dampers (MTMDs) attached to
a single-degree-of-freedom primary system have been examined by many
researchers, and several papers have included some parameter
optimization. In this paper, we propose an efficient numerical
algorithm to optimize the stiffness and damping of each of the
tuned-mass dampers (TMDs) in such a system directly. We formulate the
parameter optimization as a decentralized H2 control problem where
the block-diagonal feedback gain matrix is composed of the stiffness
and damping coefficients of the TMDs. The gradient of the
root-mean-square (RMS) response with respect to the design parameters
is evaluated explicitly, and the optimization can be carried out
efficiently.
The effects of the mass distribution, number of dampers, total mass
ratio, and uncertainties in system parameters are studied. Numerical
results indicate that the optimal designs have neither uniformly
spaced tuning frequencies nor identical damping coefficients, and that
optimization of the individual parameters in the MTMD system yields a
substantial improvement in performance. We also find that the
distribution of mass among the TMDs has little impact on the
performance of the system provided that the stiffness and damping can
be individually optimized.
In this paper, we study vibration damping in structures coupled to low-density media (such as powder or foam) in which the speed of sound propagation is relatively low. The results of several experiments in which flexural vibration of aluminum beams over a broad frequency range is damped by the introduction of a layer of lossy low-wave-speed foam are presented. We find that at frequencies high enough to set up standing waves through the thickness of the foam, damping coefficients as high as 0.07 can be obtained with a foam layer whose mass is 3.9% of that of the beam. Next, a model is presented for the flexural dynamics of coupled beam-foam systems in which we treat the foam material as a continuum in which waves of dilatation and distortion can propagate. Approximate solutions for the frequency response of the primary beam are obtained by means of a modal expansion, and the results are in close agreement with the measured responses.
Many methods have been developed for the design of a single-degree-of-freedom (SDOF) vibration absorber to damp SDOF vibration since Den Hartog presented his fixed points method in 1928. But a rigid body employed as a vibration absorber will in general have six degrees of freedom relative to a structure. By taking full advantage of the inertia of the body, we can damp as many as six modes, or make the system more robust or compact. In this paper, we present a two-step method for optimization of the stiffness and damping of a multi-degree-of-freedom connection between a reaction mass and a vibrating structure: First, treating the reaction mass as a perturbation to the vibrating structure, we obtain an approximate design. Second, we adapt a descent-subgradient method to fine-tune the design by maximizing the minimal damping over a prescribed frequency range.
Heavy structures (such as machine-tool bases) are
sometimes filled with granular materials (such as sand, gravel, or
lead shot) to increase their damping. Traditionally, relatively dense
granular fills have been selected for such applications in order
to obtain strong coupling between the structure and the granular
material. But recent experiments indicate that a low-density
granular fill can provide high damping of structural vibration if the
speed of sound in the fill is sufficiently low. We describe a
set of experiments in which aluminum beams are filled with a granular
material whose total mass is three per cent of that of the
unfilled beam and damping coefficients as high as 0.04 are
obtained. The experiments indicate that the damping at high
frequencies is essentially a linear phenomenon.
We present a simple model that qualitatively explains the
essentially linear high-frequency damping observed in the
experiments.
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