Multimodal vibration damping of nonlinear structures using multiple nonlinear absorbers

This paper presents a tuning methodology for multiple nonlinear vibration absorbers that mitigate several nonlinear resonances simultaneously. Specifically, the objective is to maintain equal peaks in the frequency response for all controlled resonances in an as large as possible range of forcing amplitudes. Relying on an all-equal-peak design for linear regimes of motion and adopting a principle of similarity for nonlinear regimes, a semi-analytical expression of the absorber coefficients is derived using first-order harmonic balance and a series expansion of the harmonic coefficients. The proposed methodology is demonstrated numerically using two spring-mass systems.