Nonlinear Generalization of Den Hartog's Equal-Peak Method

Abstract

This study addresses the mitigation of a nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA), is introduced in this paper. An 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.

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• $H_{\infty }$ optimization of multiple tuned mass dampers for multimodal vibration control
• Analysis and design of nonlinear resonances via singularity theory
• Effects of modal energy scattering and friction on the resonance mitigation with an impact absorber
• Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators