Spatial Modulation of Nonlinear Flexural Vibrations of Membrane Resonators

Year: 2019

Authors: Yang F., Rochau F., Huber J.S., Brieussel A., Rastelli G., Weig E.M., Scheer E.

Autors Affiliation: Univ Konstanz, Dept Phys, D-78457 Constance, Germany

Abstract: We study the vibrational motion of mechanical resonators under strong drive in the strongly nonlinear regime. By imaging the vibrational state of rectangular silicon nitride membrane resonators and by analyzing the frequency response using optical interferometry, we show that, upon increasing the driving strength, the membrane adopts a peculiar deflection pattern formed by concentric rings superimposed onto the drum head shape of the fundamental mode. Such a circular symmetry cannot be described as a superposition of a small number of excited linear eigenmodes. Furthermore, different parts of the membrane vibrate at different multiples of the drive frequency, an observation that we denominate as “localization of overtones.” We introduce a phenomenological model that is based on the coupling of a small number of effective nonlinear resonators, representing the different parts of the membrane, and that describes the experimental observations correctly.


Volume: 122 (15)      Pages from: 154301  to: 154301

More Information: The authors thank R. Waitz for help in sample fabrication. We are indebted to W. Belzig, T. Dekorsy, M. Dykman, V. Gusev, M. Hettich, P. Leiderer, S. Shaw, I. Wilson-Rae, R. S. Edwards, L. Q. Zhou, and the SFB767 Nanomechanics Discussion Group for fruitful discussion and comments about the work. The authors gratefully acknowledge financial support from the China Scholarship Council, the European Union´s Horizon 2020 program for Research and Innovation under Grant Agreement No. 732894 (FET Proactive HOT), by the German Excellence Initiative through the Zukunftskolleg of the University of Konstanz, and by the Deutsche Forschungsgemeinschaft (DFG) via the Collaborative Research Center SFB767.
KeyWords: nonlinear mechanical systems
DOI: 10.1103/PhysRevLett.122.154301