Numerical antiresonance continuation of structural systems

Tuned dynamic absorbers are usually used to counteract vibrations at a given frequency. Presence of non-linearities causes energy-dependent relationship of their resonance and antiresonance frequencies at large amplitude of motion, which consequently leads to a detuning of the absorber from the targeted frequency. This paper presents a procedure to track an extremum point (minimum or maximum) of nonlinear frequency responses, based on a numerical continuation technique coupled to the harmonic balance method to follow periodic solutions in forced steady-state. It thus enable to track a particular antiresonance. The procedure is tested and applied on some application cases to highlight the resonance and antiresonance behavior in presence of geometrically non-linear and/or inertial interactions.