Generalization of Den Hartog’s Equal-Peak Method for nonlinear primary systems

G Habiba,T Detroux,G Kerschen,M Belhaq

doi:10.1051/matecconf/20141601005

G Habiba, T Detroux + Show 2 more

Open Access

https://doi.org/10.1051/matecconf/20141601005

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Journal: MATEC Web of Conferences	Publication Date: Jan 1, 2014
Citations: 2	License type: cc-by

Affiliation: University of Liège

Abstract

This study addresses the mitigation of one problem nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a new nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA), is introduced in this paper. One unconventional aspect of the NLTVA is that the mathematical form of its restoring force is tailored according to the nonlinear restoring force of the primary system. The NLTVA parameters are then determined using a nonlinear generalization of Den Hartog’s equal-peak method. The mitigation of the resonant vibrations of a Duffing oscillator is considered to illustrate the proposed developments.

Highlights

With continual interest in expanding the performance envelope of engineering systems, nonlinear components are increasingly utilized in real-world applications
Mitigating the resonant vibrations of nonlinear structures is becoming a problem of great practical significance; it is the focus of the present study
In view of the results presented in the previous section, it is meaningful to examine the performance of nonlinear absorbers for vibration mitigation of nonlinear primary structures

Summary

Introduction

With continual interest in expanding the performance envelope of engineering systems, nonlinear components are increasingly utilized in real-world applications. To improve the performance robustness, damping was introduced in the absorber [13]; Den Hartog [14] and Brock [15] derived approximate analytic formulas for the absorber stiffness and damping in order to minimize the maximal response of the system at the resonant frequencies, which is obtained making the two resonant peaks have the same amplitude. To mitigate a problem nonlinear resonance in an as large as possible range of forcing amplitudes, we introduce the nonlinear tuned vibration absorber (NLTVA). We propose to fully exploit the additional design parameter offered by nonlinear devices and, to synthesize the absorber’s load-deflection curve according to the nonlinear restoring force of the primary structure

Synthesis of the nonlinear restoring force of the absorber

Nonlinear generalization of the equal-peak method

Conclusion