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1. Strong internal resonance in a nonlinear, asymmetric microbeam resonator

   https://doi.org/10.1038/s41378-020-00230-1  

   Asadi, Keivan ; Yeom, Junghoon ; Cho, Hanna ( December 2021 , Microsystems & Nanoengineering)

   Abstract Exploiting nonlinear characteristics in micro/nanosystems has been a subject of increasing interest in the last decade. Among others, vigorous intermodal coupling through internal resonance (IR) has drawn much attention because it can suggest new strategies to steer energy within a micro/nanomechanical resonator. However, a challenge in utilizing IR in practical applications is imposing the required frequency commensurability between vibrational modes of a nonlinear micro/nanoresonator. Here, we experimentally and analytically investigate the 1:2 and 2:1 IR in a clamped–clamped beam resonator to provide insights into the detailed mechanism of IR. It is demonstrated that the intermodal coupling between the second and third flexural modes in an asymmetric structure (e.g., nonprismatic beam) provides an optimal condition to easily implement a strong IR with high energy transfer to the internally resonated mode. In this case, the quadratic coupling between these flexural modes, originating from the stretching effect, is the dominant nonlinear mechanism over other types of geometric nonlinearity. The design strategies proposed in this paper can be integrated into a typical micro/nanoelectromechanical system (M/NEMS) via a simple modification of the geometric parameters of resonators, and thus, we expect this study to stimulate further research and boost paradigm-shifting applications exploring the various benefitsmore »of IR in micro/nanosystems.« less
2. Nonlinear mode coupling in a MEMS resonator

   https://doi.org/10.1117/12.2551883  

   Czaplewski, David ; López, Daniel ; Shoshani, Oriel ; Shaw, Steven ( March 2020 , Proceedings of SPIE)

   A single micro-electromechanical (MEMS) resonator can be shown to exhibit behaviors unexpected in a simple resonant structure. For small driving forces, the resonator displays typical simple harmonic oscillator re- sponse. As the driving force is increased, the resonator shows the slightly more complex, but well understood, Duffing response. Rather unexpected response behavior can appear when the resonator frequency is detuned by nonlinear- ity to where two oscillatory modes of the resonator begin to interact through nonlinear coupling due to an internal resonance. The paper focuses on how the resonator response changes as the internal resonance is approached in the operating parameter space and how that behavior is conveniently represented in a bifurcation diagram. This behavior is accurately captured by a generic mathematical model. We describe an analysis of the model which shows how this coupled response varies with the system and drive parameters, especially focusing on the nonlinear coupling strength between the two modes.
3. Nonlinear Modal Interactions and Internal Resonance in a Micromachined Disk Resonator

   https://doi.org/10.1109/MEMS46641.2020.9056349  

   Sun, Jiangkun ; Zhang, Hemin ; Chen, Dongyang ; Pandit, Milind ; Sobreviela, Guillermo ; Xiao, Dingbang ; Zhuo, Ming ; Gerrard, Dustin D. ; Kwon, Ryan ; Vukasin, Gabrielle ; et al ( January 2020 , 2020 IEEE 33rd International Conference on Micro Electro Mechanical Systems (MEMS))
4. Strong Nonlinear Coupling in a ${\mathrm{Si}}_3{\mathrm{N}}_4$ Ring Resonator

   https://doi.org/10.1103/PhysRevLett.122.153906  

   Ramelow, Sven ; Farsi, Alessandro ; Vernon, Zachary ; Clemmen, Stephane ; Ji, Xingchen ; Sipe, J. E. ; Liscidini, Marco ; Lipson, Michal ; Gaeta, Alexander L. ( April 2019 , Physical Review Letters)
5. FREQUENCY COMB GENERATION IN A NONLINEAR RESONATOR THROUGH MODE COUPLING USING A SINGLE TONE DRIVING SIGNAL

   https://doi.org/10.31438/trf.hh2018.21  

   David A. Czaplewski, Steven W. ( July 2018 , Technical digest - Solid-State Sensor, Actuator, and Microsystems Workshop)

   In this paper, we demonstrate bursting behavior in a nonlinear microelectromechanical (MEMS) resonator that creates a frequency comb in the corresponding spectral response. The bursting behavior occurs for a single driving tone applied to the resonator. The bursting behavior arises from the non-linear analog of “level anti-crossing” in a 1:3 internal resonance that can efficiently transfer energy between two modes of a resonator at low excitation amplitudes. The internal resonance creates a region in parameter space where stable oscillations do not exist, resulting in a forbidden zone of operation.