Dynamical Performances of a Vibration Absorber for Continuous Structure considering Time-Delay Coupling

Xiuting Sun,Youshuo Song

doi:10.1155/2016/5039796

Xiuting Sun, Youshuo Song

Open Access

https://doi.org/10.1155/2016/5039796

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Abstract

The nonlinear effect incurred by time delay in vibration control is investigated in this study via a vibration absorber coupled with a continuous beam structure. The stability of the vibration absorber coupled structure system with time-delay coupling is firstly studied, which provides a general guideline for the potential time delay to be introduced to the system. Then it is shown that there is a specific region for the time delay which can bring bifurcation modes to the dynamic response of the coupling system, and the vibration energy at low frequencies can be transferred or absorbed due to the bifurcation mode and the vibration in the corresponding frequency range is thus suppressed. The nonlinear mechanism of this vibration suppression incurred by the coupling time delay is discussed in detail, which provides a novel and alternative approach to the analysis, design, and control of vibration absorbers in engineering practice.

Highlights

Vibration absorbers including passive and active dynamic vibration absorbers received increasing attention in structural vibration control in the past several years [1,2,3,4,5]
Kobori et al [12] proposed a concept of active variable stiffness in active vibration control and explored the potential benefits of nonlinear dynamics incurred by time delay in vibration control
The mode bifurcated by the time delay could absorb the vibration energy of external excitation

Summary

Introduction

Vibration absorbers including passive and active dynamic vibration absorbers received increasing attention in structural vibration control in the past several years [1,2,3,4,5]. Some preliminary results have shown that the nonlinear dynamics incurred by time delay in the coupling of slave and master structures could be advantageous in absorbing vibration energy, a systematic and theoretical study on the nonlinear mechanism in affecting the stability of continuous structures and absorbing vibration energy is still yet to be further developed. The geometry of the slave structure and the coupling strength should be carefully designed so that the frequency of vibration modes bifurcated by the introduced time delay could be proportional to the excitation frequency In this way, it is known that the coupled modes of nonlinear systems can realize energy transmission and possible suppression [23]. The nonlinear mechanism of this vibration suppression incurred by the coupling time delay is discussed in detail This provides a novel and alternative insight into the analysis, design, and control of vibration absorbers in engineering practice.

The Nonlinear Vibration and Its Modeling

Natural Frequency and Stability of the System

The Vibration Response of the Nonlinear Vibration Absorber with Time Delay

Conclusions