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.

The framework of nonlinear normal modes gives a remarkable insight into the dynamics of nonlinear vibratory systems exhibiting distributed nonlinearities. In the case of Chinese opera gongs, geometrical nonlinearities lead to a pitch glide of several vibration modes in playing situation. This study investigates the relationship between the nonlinear normal modes formalism and the ascendant pitch glide of the fundamental mode of a xiaoluo gong. In particular, the limits of a single nonlinear mode modeling for describing the pitch glide in playing situation are examined. For this purpose, the amplitude-frequency relationship (backbone curve) and the frequency-time dependency (pitch glide) of the fundamental nonlinear mode is measured with two excitation types, in free vibration regime: first, only the fundamental nonlinear mode is excited by an experimental appropriation method resorting to a phase-locked loop; second, all the nonlinear modes of the instrument are excited with a mallet impact (playing situation). The results show that a single nonlinear mode modeling fails at describing the pitch glide of the instrument when played because of the presence of 1:2 internal resonances implying the nonlinear fundamental mode and other nonlinear modes. Simulations of two nonlinear modes in 1:2 internal resonance confirm qualitatively the experimental results.

Instruments that belong to the gong family exhibit nonlinear dynamics at large amplitudes of vibration. In the specific case of the xiaoluo gong, this nonlinear behavior results in a pitch glide of several modes of the instrument in addition to harmonic distortion and internal resonances. This study applies a linear modal active control to a xiaoluo gong in an attempt to change its sound properties. First, a modal damping control of the fundamental mode based on a linear identification and a state space controller is applied in the small amplitude regime (no pitch glide). Results indicate that modal control influences not only the controlled mode but also the frequency components involved in distortion or internal resonance phenomena. Second, a modal damping control is performed in the large amplitude regime (in the presence of pitch glide). Results show that modal control does not affect the pitch glide. However, the controller becomes effective at a time trigger which is related to the instantaneous frequency.