Measurement and nonlinear analysis of an inertial sensor with micropillar gap filler under voltage modulation

Abstract

Inertial sensors, particularly capacitive MEMS accelerometers, are indispensable for accurately measuring acceleration and orientation. This study examines the dynamic behavior of a plate positioned on a polymeric micropillar array, such as PDMS, subjected to base excitation through harmonic acceleration and a direct current (DC) bias voltage. The PDMS micropillars are represented through finite deformation theory using a Neo-Hookean approach to account for their quadratic, cubic, and coupled nonlinearities. Governing equations have been formulated to describe the vertical compression and rotational modes of the plate, placing special emphasis on the compression mode resulting from the uniform distribution of both the gap and the mass. The findings from the static analysis reveal that saddle-node bifurcation occurs at a critical voltage. Notably, the pull-in voltage identified is substantially lower than that seen in traditional capacitive systems. ​These characteristics indicate that the design is particularly well-suited for low-voltage applications, highlighting its potential to operate efficiently in such environments. This makes the design suitable for low-voltage applications. The system demonstrates stability for deflections up to 44% of the gap, a notable improvement over the 33% limit observed in conventional designs, thereby extending the operational range. A rise in the dielectric permittivity of the micro pillars, achieved for instance through the incorporation of nanoparticles, results in a reduction of the pull-in voltage while simultaneously enhancing the variation in capacitance. This modification not only reduces the voltage required for operation but also enhances the system’s sensitivity by allowing for more significant capacitance changes. The dynamic analysis reveals a plethora of nonlinear behaviors, including wideband frequency responses, significant 2x harmonic generation, and bifurcations such as period doubling at specific frequencies. The broad frequency response enhances the suitability of the structure for wideband energy harvesting, whereas the bifurcation behaviors offer potential for sensitive switching. These findings provide important insights into the nonlinear interactions in micro-pillar-supported capacitive systems, paving the way for advancements in energy harvesting, actuation, and precision sensing applications.