Resonant Excitation-Induced Acoustic Frequency Combs in a Microcantilever Resonator


Mechanical resonators are fundamental tools for scientific endeavors and ideal platforms for developing high-performance devices, including sensors, transducers, filters and oscillators. This can be attributed to their high precision and excellent compatibility with different materials and integrated circuits. In particular, the nonlinear dynamics of microelectromechanical resonators have drawn significant research attention owing to their attractive properties. They consume a low amount of energy and can achieve strong coupling between different modes as well as efficient energy transfer.

Parametric excitation is a common technique for achieving mode coupling in nonlinear systems. To this end, various nonlinear effects like injection locking and mechanical sideband have been demonstrated experimentally in mechanical microresonators. In mechanical microresonators, acoustic frequency combs (AFCs) consisting of a series of equally spaced discrete frequencies have been explored for potential applications in enhanced heat transport, information processing and quantum state manipulation.

A number of AFCs have been reported in previous studies. Most of these AFCs arise from degenerating four-wave mixing of two adjacent modes via cubic nonlinearities. As a result, most of these AFCs display a limited number of “teeth”, less than 20 in most cases, due to the difficulty in managing the required zero-dispersion condition. Nevertheless, despite its potential applications, the generation of nonlinear mode coupling through resonant excitation on a one-end clamped microcantilever resonator remains an underexplored field.

On this account, Yanyan Li, Dr. Wenyao Luo, Zhixin Zhao and led by Professor Duo Liu from Shandong University demonstrated the efficiency and practicability of resonant excitation as a powerful tool for generating nonlinear mode coupling in a cantilever microresonator. This was achieved by moderating resonant driving at the second flexural mode ( f2 ) of the microcantilever. A monocrystalline silicon microcantilever beam mounted on a piezoelectric disc in a vacuum chamber at room temperature was utilized. A Doppler vibrometer equipped with a network analyzer and high-precision low-noise lock-in amplifier was adopted to monitor the cantilever motion. The frequency characteristics of the resonant driving at f2 were detailed. The work is currently published in the journal, Physical Review Applied.

The research team revealed that the microcantilever exhibited two flexural modes for small amplitude excitation, one at f1 = 14.44 kHz and the other at f1 = 90.31 kHz. However, as the drive amplitude was increased beyond a moderate threshold, the resonant driving at  produced red and blue sidebands at the sum ( f2 +f1 ) and difference ( f2 f1 ) frequencies. This was attributed to the mode coupling between the fundamental flexural mode (f1) and f2 With a slight detuning of the drive frequency, a continuous frequency shift of the red and blue sidebands over a frequency span of 220 Hz was observed.

Furthermore, strong resonant driving at f2 produced frequency combs characterized with frequency span across multiple modes ranging from 0 to 500 kHz. This was observed when the drive amplitude increased remarkably higher than the threshold value. It was worth noting that detuning of the drive frequency produced AFCs with different frequency intervals. The authors also demonstrate AFCs with various frequency intervals locked to the fractional multiples of the frequency of the second flexural mode, resembling the Devil’s staircase. The AFCs can be used as a multichannel frequency stabilizer with potentials on high precision and high throughput measurement under complex conditions.

In a nutshell, the manipulation of nonlinear mode coupling in microcantilever beams using resonant excitation was reported. From the results, the proposed method could open a path toward achieving effective parametric control based on injection locking. In a statement to Advances in Engineering, Professor Duo Liu explained that their study contributes to the advancement in the controlled manipulation of multimode mechanical resonator systems.


Li, Y., Luo, W., Zhao, Z., & Liu, D. (2022). Resonant Excitation-Induced Nonlinear Mode Coupling in a Microcantilever ResonatorPhysical Review Applied, 17(5), 054015.

Go To Physical Review Applied

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