In this article, we address the model identication of nonlinear vibratory systems, with a specic focus on systems modeled with distributed nonlinearities, such as geometrically nonlinear mechanical structures. The proposed strategy theoretically relies on the concept of nonlinear modes of the underlying conservative unforced system and the use of normal forms. Within this framework, it is shown that without internal resonance, a valid reduced order model for a nonlinear mode is a single Dung oscillator. We then propose an ecient experimental strategy to measure the backbone curve of a particular nonlinear mode and we use it to identify the free parameters of the reduced order model. The experimental part relies on a Phase-Locked Loop (PLL) and enables a robust and automatic measurement of backbone curves as well as forced responses. It is theoretically and experimentally shown that the PLL is able to stabilize the unstable part of Dung-like frequency responses, thus enabling its robust experimental measurement. Finally, the whole procedure is tested on three experimental systems: a circular plate, a chinese gong and a piezoelectric cantilever beam. It enable to validate the procedure by comparison to available theoretical models as well as to other experimental identication methods.

a b s t r a c tTuned 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.