Spatial modulation of nonlinear flexural vibrations of membrane resonators

Abstract

We study the vibrational motion of membrane resonators upon strong drive in the strongly nonlinear regime. By imaging the vibrational state of rectangular siliconnitride 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, the different parts of the membrane oscillate 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 very small number of effective nonlinear oscillators, representing the different parts of the membrane, and that describes the experimental observations.

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• Fabry-Perot Interferometric Calibration of 2D Nanomechanical Plate Resonators
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• Spatial mapping of intrinsic and readout nonlinearities in a strongly-driven micromechanical membrane
• Geometrical Nonlinearity of Circular Plates and Membranes: an Alternative Method
• Mechanically Modulated Sideband and Squeezing Effects of Membrane Resonators