Samir A. Nayfeh

Minimax optimization of multi-degree-of-freedom tuned-mass dampers

Abstract Many methods have been developed for the design of a single-degree-of-freedom (SDOF) absorber to damp SDOF vibration. Yet there are few studies for the case where both the absorber and the main system have multiple degrees of freedom. In this paper, an efficient numerical approach based on the descent-subgradient method is proposed to maximize the minimal damping of modes in a prescribed frequency range for general viscous or hysteretic multi-degree-of-freedom (MDOF) tuned-mass systems. Examples are given to illustrate the efficiency of the minimax method and the damping potential of MDOF tuned-mass dampers (TMDs). The performance of minimax, H2, and H∞ optimal TMDs are compared. Finally, the results of an experiment in which a 2-DOF TMD is optimized to damp the first two flexural modes of a free–free beam are presented.

Optimization of the Individual Stiffness and Damping Parameters in Multiple-Tuned-Mass-Damper Systems

The characteristics of multiple tuned-mass-dampers (MTMDs) attached to a single-degree-of-freedom primary system have been examined by many researchers. Several papers have included some parameter optimization, all based on restrictive assumptions. In this paper, we propose an efficient numerical algorithm to directly optimize the stiffness and damping of each of the tuned-mass dampers (TMDs) in such a system. 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 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.

The Dynamics of Lead-Screw Drives: Low-Order Modeling and Experiments

The closed-loop performance of a lead-screw drive is usually limited by a resonance in which the carriage oscillates in the direction of motion as the screw undergoes longitudinal and torsional deformation. In this paper, we develop a model of lead-screw system dynamics that accounts for the distributed inertia of the screw and the compliance and damping of the thrust bearings, nut, and coupling. The distributed-parameter model of the lead-screw drive system is reduced to a low-order model using a Galerkin procedure and verified by experiments performed on a pair of ball-screw systems. The model is found to accurately predict the presence of a finite right-half plane zero in the transfer function from motor torque to carriage position. A viscoelastic damper incorporated into one of the lead-screw support bearings is shown to give rise to significant, deterministic damping in the system transfer functions.

Low order continuous-time filters for approximation of the ISO 2631-1 human vibration sensitivity weightings

Human health and comfort under whole-body vibration depend on the level, frequency, direction, location, and duration of the acceleration. The international standard ISO 2631-1 [1] specifies a method of evaluation of the effect of exposure to vibration on humans by weighting the root-mean square (r.m.s.) acceleration with human vibration sensitivity curves. There are six frequency-weighting curves given as magnitudes Wi at the one-third octave frequencies fi:

The Two-Degree-of-Freedom Tuned-Mass Damper for Suppression of Single-Mode Vibration Under Random and Harmonic Excitation

Whenever a tuned-mass damper is attached to a primary system, motion of the absorber body in more than one degree of freedom (DOF) relative to the primary system can be used to attenuate vibration of the primary system. In this paper, we propose that more than one mode of vibration of an absorber body relative to a primary system be tuned to suppress single-mode vibration of a primary system. We cast the problem of optimization of the multi-degree-of-freedom connection between the absorber body and primary structure as a decentralized control problem and develop optimization algorithms based on the H2 and H-infinity norms to minimize the response to random and harmonic excitations, respectively. We find that a two-DOF absorber can attain better performance than the optimal SDOF absorber, even for the case where the rotary inertia of the absorber tends to zero. With properly chosen connection locations, the two-DOF absorber achieves better vibration suppression than two separate absorbers of optimized mass distribution. A two-DOF absorber with a negative damper in one of its two connections to the primary system yields significantly better performance than absorbers with only positive dampers.

STRUCTURED H2 OPTIMIZATION OF VEHICLE SUSPENSIONS BASED ON MULTI-WHEEL MODELS

Summary Various control techniques, especially LQG optimal control, have been applied to the design of active and semi-active vehicle suspensions over the past several decades. However passive suspensions remain dominant in the automotive marketplace because they are simple, reliable, and inexpensive. The force generated by a passive suspension at a given wheel can depend only on the relative displacement and velocity at that wheel, and the suspension parameters for the left and right wheels are usually required to be equal. Therefore, a passive vehicle suspension can be viewed as a decentralized feedback controller with constraints to guarantee suspension symmetry. In this paper, we cast the optimization of passive vehicle suspensions as structure-constrained LQG/H2 optimal control problems. Correlated road random excitations are taken as the disturbance inputs; ride comfort, road handling, suspension travel, and vehicle-body attitude are included in the cost outputs. We derive a set of necessary conditions for optimality and then develop a gradient-based method to efficiently solve the structure-constrained H2 optimization problem. An eight-DOF four-wheel-vehicle model is studied as an example to illustrate application of the procedure, which is useful for design of both passive suspensions and active suspensions with controller-structure constraints.

Design and Analysis of a New Type of Electromagnetic Damper With Increased Energy Density

configuration of eddy current dampers. An analytical model for this eddy current damper is derived based on electromagnetic theory, and the eddy current density is computed using finiteelement analysis FEA. The predictions of both the analytical model and finite-element analysis agree reasonably well with experimental studies. The results show that the new configuration of eddy current damper has significantly higher efficiency than current implementations. We developed the prototype and demonstrated that the eddy current damper of 100150140 mm 3 can achieve a damping constant 2230 N s /m, whose damping density 1061 kNs/m /m 3 is 5 times more than the typical value 11, and the dimensionless coefficient C0 is also several times higher than the traditional configuration found in the literature. The dependence of damping coefficients on the velocity and frequency is also explored.

Damping of Flexural Vibration by Coupling to Low-Density Granular Materials

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.

Damping of Flexural Vibration by Low-Density Foams and Granular Materials

The damping of flexural vibration by introduction of a layer of low-density foam or powder into a structure is investigated. First, we report on experiments in which a layer of foam attached to an aluminum beam gives rise to significant damping at frequencies high enough to induce standing waves in the foam layer. Next, we provide a simple model for such vibration in which the foam is treated as a two-dimensional elastic continuum in which waves can propagate and find that the model is in good agreement with the experiments. Then the results of experiments in which aluminum beams are filled with a low-density powder are presented. The powder-filled beams exhibit behavior qualitatively like that of the foam-filled beams, but we find that the powder can be adequately modeled as an inviscid compressible fluid.Copyright

Aerodynamic-Rotordynamic Interaction in Axial Compression Systems—Part II: Impact of Interaction on Overall System Stability

This paper presents an integrated treatment of the dynamic coupling between the flow field (aerodynamics) and rotor structural vibration (rotordynamics) in axial compression systems. This work is motivated by documented observations of tip clearance effects on axial compressor flow field stability, the destabilizing effect of fluid-induced aerodynamic forces on rotordynamics, and their potential interaction. This investigation is aimed at identifying the main nondimensional design parameters governing this interaction, and assessing its impact on overall stability of the coupled system. The model developed in this work employs a reduced-order Moore-Greitzer model for the flow field, and a Jeffcott-type model for the rotordynamics. The coupling between the fluid and structural dynamics is captured by incorporating a compressor pressure rise sensitivity to tip clearance, together with a momentum based model for the aerodynamic forces on the rotor (presented in Part I of this paper). The resulting dynamic model suggests that the interaction is largely governed by two nondimensional parameters: the sensitivity of the compressor to tip clearance and the ratio of fluid mass to rotor mass. The aerodynamic-rotordynamic coupling is shown to generally have an adverse effect on system stability. For a supercritical rotor and a typical value of the coupling parameter, the stability margin to the left of the design point is shown to decrease by about 5% in flow coefficient (from 20% for the uncoupled case). Doubling the value of the coupling parameter not only produces a reduction of about 8% in the stability margin at low flow coefficients, but also gives rise to a rotordynamic instability at flow coefficients 7% higher than the design point.