https://hal-ensta-paris.archives-ouvertes.fr/hal-03882270Gobat, GiorgioGiorgioGobatPOLIMI - Politecnico di Milano [Milan]Zega, ValentinaValentinaZegaPOLIMI - Politecnico di Milano [Milan]Fedeli, PatrickPatrickFedeliST-CORNAREDO - STMicroelectronics [Cornaredo]Touzé, CyrilCyrilTouzéENSTA Paris - École Nationale Supérieure de Techniques AvancéesIP Paris - Institut Polytechnique de ParisUME - Unité de Mécanique - ENSTA Paris - École Nationale Supérieure de Techniques AvancéesIMSIA - UMR 9219 - Institut des Sciences de la mécanique et Applications industrielles - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - ENSTA Paris - École Nationale Supérieure de Techniques Avancées - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique - EDF R&D - EDF R&D - EDF - EDFFrangi, AttilioAttilioFrangiPOLIMI - Politecnico di Milano [Milan]Frequency combs in a MEMS resonator featuring 1:2 internal resonance: ab initio reduced order modelling and experimental validationHAL CCSD2022[SPI.NANO] Engineering Sciences [physics]/Micro and nanotechnologies/Microelectronics[SPI.MECA.VIBR] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Vibrations [physics.class-ph][SPI.MECA.STRU] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph][NLIN] Nonlinear Sciences [physics][MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Touzé, Cyril2022-12-02 12:25:322023-02-08 17:11:262022-12-19 08:28:14enJournal articleshttps://hal-ensta-paris.archives-ouvertes.fr/hal-03882270/document10.1007/s11071-022-08029-7application/pdf1Abstract This paper is devoted to a detailed analysis of the appearance of frequency combs in the dynamics of a micro-electro-mechanical systems (MEMS) resonator featuring 1:2 internal resonance. To that purpose, both experiments and numerical predictions are reported and analysed to predict and follow the appearance of the phononic frequency comb arising as a quasi-periodic regime between two Neimark-Sacker bifurcations. Numerical predictions are based on a reduced-order model built thanks to an implicit condensation method, where both mechanical nonlinearities and electrostatic forces are taken into account. The reduced order model is able to predict a priori, i.e. without the need of experimental calibration of parameters, and in real time, i.e. by solving one or two degrees-of-freedom system of equations, the nonlinear behaviour of the MEMS resonator. Numerical predictions show a good agreement with experiments under different operating conditions, thus proving the great potentiality of the proposed simulation tool. In particular, the bifurcation points and frequency content of the frequency comb are carefully predicted by the model, and the main features of the periodic and quasi-periodic regimes are given with accuracy, underlining that the complex dynamics of such MEMS device is effectively driven by the characteristics of the 1:2 internal resonance.