Sketch of the experimental setups showing the membrane chip carrying a free-standing SiN membrane, the piezoelectric ring and drive, the objective of the imaging white light interferometer (IWLI) and the laser beam of the Michelson interferometer (MI).

Project A07: Phys. Rev. Lett. 2019

Spatial Modulation of Nonlinear Flexural Vibrations of Membrane Resonators

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.

Fan Yang, Felix Rochau, Jana S. Huber, Alexandre Brieussel, Gianluca Rastelli, Eva M. Weig, Elke Scheer
Phys. Rev. Lett. 122, 154301 (2019)
DOI: 10.1103/PhysRevLett.122.154301