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. arXiv:1902.01270v1 [cond-mat.mes-hall]

Dynamically-enhanced strain in atomically thin resonators

“…2 – 4 cannot be understood as a simple geometrical effect arising from the time-averaged harmonic oscillations of mode profile that remains smooth over the whole drum area. Instead, the enhancement of ε d could arise from so-called localisation of harmonics, a phenomenon recently observed in larger and thicker (~500 μm wide, ~500 nm thick) SiN membranes 51 showing RMS displacement saturation similar to Fig. 3 a.…”

“…As the resonator enters the saturation regime, non-linearities (either intrinsic 44 , geometrical 50 , 52 or electrostatically-induced 5 , 7 , 53 ) may lead to internal energy transfer towards harmonics of the driven mode (Supplementary Fig. 17 ) and, crucially, to the emergence of ring-shaped patterns over length scales significantly smaller than the size of the membrane 51 . The large displacement gradients associated with these profiles thus enhance ε d (Supplementary Note 7 ).…”

Fabry–Perot interferometric calibration of van der Waals material-based nanomechanical resonators

“…From a practical standpoint, monitoring vibrational amplitude is essential in avoiding dynamic pull-in instability 13 when driving the NMR at high amplitude, which limits the actuation ranges for electromotive-driven NMRs. Furthermore, the vibrational resonant amplitude enables understanding of nonlinear regime of motion 14,15 and optomechanical effects on driven mechanics 8,16,17 , both of which are accessible for mechanical resonators with nanoscale dimensions, and embedded in motionsensitive interferometric platforms.…”

Mechanically Modulated Sideband and Squeezing Effects of Membrane Resonators

“…Such a tunable sideband response offers a new possibility for future device applications. Our results may also give insight into other sideband related phenomena such as the energy transfer via mode coupling in the nonlinear and the chaotic regime [19,[24][25][26][27].…”