The emergence of graphene and other two-dimensional materials overcomes the limitation in the characteristic size of silicon-based micro-resonators and paved the way in the realization of nano-mechanical resonators. In this paper, we review the progress to date of the research on the fabrication methods, resonant performance, and device applications of graphene-based nano-mechanical resonators, from theoretical simulation to experimental results, and summarize both the excitation and detection schemes of graphene resonators. In recent years, the applications of graphene resonators such as mass sensors, pressure sensors, and accelerometers gradually moved from theory to experiment, which are specially introduced in this review. To date, the resonance performance of graphene-based nano-mechanical resonators is widely studied by theoretical approaches, while the corresponding experiments are still in the preliminary stage. However, with the continuous progress of the device fabrication and detection technique, and with the improvement of the theoretical model, suspended graphene membranes will widen the potential for ultralow-loss and high-sensitivity mechanical resonators in the near future.

In this paper, a novel two-axis differential resonant accelerometer based on graphene with transmission beams is presented. This accelerometer can not only reduce the cross sensitivity, but also overcome the influence of gravity, realizing fast and accurate measurement of the direction and magnitude of acceleration on the horizontal plane. The simulation results show that the critical buckling acceleration is 460 g, the linear range is 0–89 g, while the differential sensitivity is 50,919 Hz/g, which is generally higher than that of the resonant accelerometer reported previously. Thus, the accelerometer belongs to the ultra-high sensitivity accelerometer. In addition, increasing the length and tension of graphene can obviously increase the critical linear acceleration and critical buckling acceleration with the decreasing sensitivity of the accelerometer. Additionally, the size change of the force transfer structure can significantly affect the detection performance. As the etching accuracy reaches the order of 100 nm, the critical buckling acceleration can reach up to 5 × 10⁴ g, with a sensitivity of 250 Hz/g. To sum up, a feasible design of a biaxial graphene resonant accelerometer is proposed in this work, which provides a theoretical reference for the fabrication of a graphene accelerometer with high precision and stability.

Reliable calibration that converts transduced signals into physical displacement is essential for quantitative studies and applications of nanoelectromechanical resonators, including nonlinear dynamics, precision sensing, and optomechanical and electromechanical coupling. Existing harmonic calibration based on nonlinear optical transduction is generally restricted to systems with optically thin suspended layers and highly reflective substrates. Their weak higher-order harmonic signals are also susceptible to noise, drift, and inconsistencies between separately acquired frequency sweeps. Here, we generalize this approach to hexagonal boron nitride/graphene (h-BN/Gra) heterostructure resonators without local metallic reflectors. Multilayer thin-film interference calculations show that a branch-local phase correction enables the effective two-beam inversion to recover vibration amplitude and local static gap within acceptable error bounds. Experimentally, we use multi-demodulator lock-in detection to acquire the ω, 2ω, and 3ω optical responses simultaneously at each frequency point. Ratios among these harmonics then yield frequency-resolved vibration amplitude and local static gap. Repeated frequency sweeps at a constant gate bias simultaneously track the resonance characteristics and local static gap, revealing a time-dependent relaxation of approximately 24 nm in the local device configuration. This work provides a practical in situ route for simultaneously resolving resonance characteristics and configurational evolution across a broader range of nanomechanical resonator architectures.