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

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.