The nonlinear dynamic response of a MEMS resonator with a triangular tuning comb is studied. The motion equation with dis-smooth tuning electrostatic force is derived according to Newton’s second law. The analytical solution of the periodic response is obtained using the harmonic balance method and section integral method. The singularity theory is then applied to investigate the bifurcation of the periodic response of the untuned system. The transition sets on the DC-AC voltage plane dividing the planes into several persistent regions are obtained. The bifurcation diagrams’ topological structures and jump phenomena corresponding to different parameter regions are analyzed. We explore the effects of tuning voltage on the response. This demonstrates that the amplitude–frequency curves present more hardening characteristics with increased tuning voltage. Many twists, bifurcation points, and unstable solutions appear, leading to complicated jump phenomena. Two bifurcation points exist on the response curves: the smooth and dis-smooth bifurcation points, with the latter occurring on the switching plane of non-uniform fingers.

The inclination effect caused by fabrication errors on the periodic response of a symmetric MEMS gyroscope is investigated. The dynamic equation is established considering the inclination effect on support stiffness and electrostatic forces. The periodic response is obtained by the averaging method. The two-variable singularity theory is employed to study the bifurcation characteristics and give transition sets on the DC-AC voltage plane, which divide the plane into four persistent regions. The amplitude-frequency curves demonstrate that only the two persistent regions with low voltages are feasible for the gyroscope. Both over-etching and under-etching reduce the feasible region. The effect of parameters on the performance is present. The mechanical sensitivity and nonlinearity increase with the voltages. With the increase in the inclination angle, the mechanical sensitivity and nonlinearity decrease first and then increase. The full temperature stability of the mechanical sensitivity is also considered. The variation in mechanical sensitivity with temperature is small at a large voltage and negative inclination angle. Under-etching, which leads to small nonlinearity and good temperature stability, is more beneficial to the performance of the gyroscope than over-etching.

Magnetic nonlinearity and multi-oscillator coupling are commonly employed to improve the performance of energy harvesters. This study integrates both mechanisms to propose a nested dual-oscillator coupled piezoelectric energy harvester with an external magnet, investigating both repulsive and attractive interactions between the two oscillators. The influence of parameters on static/dynamic characteristics and harvesting performance is analyzed. For the repulsive-type harvester, the response under weak excitation is characterized by small-amplitude in-phase motion within potential wells; under strong excitation, one oscillator exhibits a large-amplitude response while the other remains nearly quiescent, and non-periodic responses may occur. Large magnet spacings effectively enhance the bandwidth and output power. The attractive-type harvester primarily shows in-phase periodic motion, though non-periodic behavior may appear under strong excitation. Small moving-magnet spacing combined with large external-magnet spacing can significantly boost bandwidth and power output. In both configurations, performance declines as the external-magnet spacing exceeds an optimal range. The repulsive-type harvester features a wider potential well, performing well under weak excitation, whereas the attractive-type, with vibration modes aligned to the potential well profile, is more likely to generate large-amplitude responses under strong excitation. Experimental results show excellent agreement with simulation data, confirming the reliability of the proposed design.