Research developments in vibration control of structures using passive tuned mass dampers

https://hal.inria.fr/inria-00072297/document

Modeling, stability and control of biped robots-a general framework

Survey of nonlinear vibration of gear transmission systems

Vibration absorption in systems with a nonlinear energy sink: Nonlinear damping

This paper is the second one in the series of two papers devoted to detailed investigation of the response regimes of a linear oscillator with attached nonlinear energy sink (NES) under harmonic external forcing and assessment of possible application of the NES for vibration absorption and mitigation. In this paper, we study the performance of a strongly nonlinear, damped vibration absorber with relatively small mass attached to a periodically excited linear oscillator. We present a nonlinear absorber tuning procedure in the vicinity of (1:1) resonance which provides the best total system energy suppression, using analytical and numerical tools. A linear absorber is also tuned according to the same criterion of total system energy suppression as the nonlinear one. Both optimally tuned absorbers are compared under common parameters of damping, external forcing but different absorber stiffness characteristics; certain cases for which nonlinear absorber is preferable over the linear one are revealed and confirmed numerically.

Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. II: Optimization of a nonlinear vibration absorber

The steady state vibrations of a non-linear dynamic vibration absorber are studied using the method of multiple scales, in conjunction with digital simulations. The main results are concerned with certain dynamic instabilities which can occur if the absorber is designed such that the desired operating frequency is approximately the mean of the two linearized natural frequencies of the system. A combination resonance can occur in this case, resulting in large amplitude almost-periodic vibrations. This motion destroys the effectiveness of the absorber and can coexist with the desired low-amplitude periodic response, which leads to initial condition dependent dynamics.

On the response of the non-linear vibration absorber

The dynamic response of a two-degree-of-freedom impacting system is considered. The system consists of an inverted pendulum whith motion limiting stops attached to a sinusoidally excited mass-spring system. Two types of periodic response for this system are analyzed in detail; existence, stability, and bifurcations of these motions can be explicitly computed using a piecewise linear model

The Onset of Chaos in a Two-Degree-of-Freedom Impacting System

The nonlinear behavior of an unbalanced rotor supported in a fluid film bearing is analyzed. A simplified two dimensional model is adopted which uses the long-bearing approximation with a π-film to account for cavitation. This model has been thoroughly studied by Myers [1] in the balanced case, where it is shown that the whirl instability is the result of a Hopf bifurcation. The implications of imbalance are studied in this paper. This leads to the study of a periodically perturbed Hopf bifurcation. It is shown that the dynamics in this situation can, especially under certain nonlinear resonance conditions, have an extremely complicated dependence on the system parameters and the rotor speed. Complete bifurcation diagrams are presented for a particular rotor model which demonstrate this dependence.

Jinsiang Shaw

Papers

On the response of the non-linear vibration absorber

The Onset of Chaos in a Two-Degree-of-Freedom Impacting System

The effects of unbalance on oil whirl