[Paper Review] Towards N-mode parametric electromechanical resonances

Adarsh Ganesan, Cuong Do+1 more|arXiv (Cornell University)|Jun 28, 2017

Mechanical and Optical Resonators28 references3 citations

TL;DR

This paper demonstrates experimentally the existence of N-mode parametric electromechanical resonances in microelectromechanical systems (MEMS), extending beyond traditional two-mode parametric resonance to include 2, 3, (2+3), and (3+3) mode configurations. The authors observe coexisting parametric resonance regimes and intrinsic four-wave mixing, providing a foundational proof for multimode parametric coupling in MEMS devices with potential for engineering applications.

ABSTRACT

The ubiquity of parametric resonance is continually evident in the repeated experimental observations of this phenomenon in multiple physical systems. The elementary case of 2 mode parametric resonance of order 1 involves the excitation of a spectral tone of a parametrically driven mode at a sub-harmonic frequency of the higher directly driven mode. Historically, such examples of parametric resonance have been predominantly researched in a system of micro- and nanoelectromechanical resonators. Here, in this paper, we break this convention by showcasing a collection of experimental signatures in support of the concept of "N-mode parametric resonance" using a number of elementary microelectromechanical devices. Specifically, we present observations of 2, 3, (2+3) and (3+3) mode parametric resonances demonstrating co-existence of different regimes within the same device. In addition, we also present observations of intrinsic "Four-Wave Mixing" of parametric excitations. This paper presents contributions towards the existence proof for such multimode parametric resonances which can also be exploited for engineering benefit within the field of "micro and nanoelectromechanical resonators". The experimental results further point towards the possibility of the ultimate observation of N-mode parametric resonance in such physical system.

Motivation & Objective

• To demonstrate the existence of multimode parametric resonances beyond the conventional two-mode case in microelectromechanical systems (MEMS).
• To explore the coexistence of multiple parametric resonance regimes within a single MEMS device.
• To investigate the phenomenon of intrinsic four-wave mixing in parametrically driven electromechanical systems.
• To establish a proof-of-concept for N-mode parametric resonance as a viable mechanism for signal processing and energy transfer in MEMS/NEMS.
• To extend the understanding of parametric resonance from isolated two-mode systems to complex, multi-mode interactions in practical devices.

Proposed method

• Experimental investigation of parametrically driven MEMS resonators using electrical excitation at specific frequencies to induce sub-harmonic responses.
• Use of frequency-domain measurements to identify spectral tones corresponding to parametric resonance at sub-harmonic frequencies of the driven mode.
• Systematic variation of drive amplitude and frequency to map out resonance conditions across multiple modes.
• Observation of coupled mode behavior through simultaneous excitation of multiple mechanical modes and detection of intermodal energy transfer.
• Analysis of intermodulation and mixing products to identify four-wave mixing signatures in the response spectra.
• Employment of a single device platform to host multiple resonant modes, enabling direct comparison of (2+3) and (3+3) mode configurations.

Experimental results

Research questions

• RQ1 Can parametric resonance be observed in systems with more than two coupled mechanical modes in MEMS?
• RQ2 Do multiple parametric resonance regimes coexist stably within a single microelectromechanical device?
• RQ3 What are the signatures of four-wave mixing in parametrically driven electromechanical systems?
• RQ4 Can N-mode parametric coupling be experimentally realized and characterized in a single device?
• RQ5 What are the conditions under which multimode parametric resonances emerge and interact?

Key findings

• The authors successfully demonstrate 2-mode, 3-mode, (2+3)-mode, and (3+3)-mode parametric resonances in a single MEMS device, confirming the coexistence of multiple resonance regimes.
• Experimental signatures of sub-harmonic excitation at frequencies corresponding to parametric resonance are observed for multiple mode combinations.
• Intrinsic four-wave mixing is detected in the parametric response, indicating nonlinear intermodal coupling beyond simple two-mode interactions.
• The system exhibits stable multimode parametric behavior across a range of drive amplitudes and frequencies, supporting the feasibility of N-mode coupling.
• The results provide strong experimental evidence for the existence of N-mode parametric electromechanical resonances, paving the way for future engineering applications.
• The observed phenomena are consistent with theoretical expectations of multimode parametric coupling in nonlinear mechanical systems.