Abstract
Micro- and nano-resonators have been studied extensively both for the scientific viewpoint to understand basic interactions at small scales as well as for applied research to build sensors and mechanical signal processors. Majority of the resonant microsystems, particularly those manufactured at a large scale, have employed simple mechanical structures with one dominant resonant mode, such as in timing resonators, or linearly coupled resonant modes, as in vibratory gyroscopes. There is an increasing interest in the development of models and methods to better understand the nonlinear interactions at micro- and nano-scales and also to potentially improve the performance of the existing devices in the market beyond limits permissible by the linear effects. Internal resonance is a phenomenon that allows for nonlinear coupling and energy transfer between different vibration modes of a properly designed system. Herein, for the first time, we describe and experimentally demonstrate the potential for employing internal resonance for detection of angular rate signals, where the Coriolis effect modifies the energy coupling between the distinct drive and sense vibration modes. In doing so, in addition to providing a robust method of exciting the desired mode, the proposed approach further alleviates the mode-matching requirements and reduces instabilities due to the cross-coupling between the modes in current linear vibratory gyroscopes.
Highlights
Micro- and nano-fabricated resonators are used in numerous applications including timing and frequency references, filters, chemical sensing, and physical sensing
There can be a nonlinear coupling of vibration energy from the forced vibrations along www.nature.com/scientificreports the spring direction to the pendulum mode through 2:1 internal resonance because of the inherent quadratic nonlinearities in the system
There has been a significant level of interest in understanding the nonlinear dynamics of micro- and nano-structures
Summary
Micro- and nano-fabricated resonators are used in numerous applications including timing and frequency references, filters, chemical sensing, and physical sensing. Internal resonance may occur when the linear natural frequencies of a system are commensurate or nearly commensurate (e.g., ω2 = kω[1] or ω2 ≈ kω[1] where k = 2, 3, ...) and there exist nonlinear coupling terms between the vibration modes[12]. When the vibrational amplitude of this mode reaches a threshold value, it saturates and the additional energy from the input source is transferred to the lower natural frequency mode due to the nonlinear coupling between them. To maximize the sensitivity of MEMS Coriolis vibratory gyroscopes (CVGs), the natural frequencies of the sense and drive modes are designed to match. The proposed design exploits the 2:1 internal resonance within a microresonator with 2 DOF such that the sense mode bandwidth is widened to the extent to circumvent the requirement for mode matching. The phenomenon is self-initiating once the excitation amplitude exceeds a threshold level without a need for a controller, electrostatic tuning, or additional DOF
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