Material modelling and dynamic analysis of functionally graded-MEMS accelerometer subjected to thermal shock loads

Micro-accelerometers are employed in several high-frequency engineering applications for vibration measurements. A major limitation of conventional silicon-based microelectromechanical systems (MEMS) accelerometers is their functionality at higher temperatures (>500°C). In the present work, temperature-compensating functionally graded (FG) porous microstructural elements are introduced in MEMS accelerometer design to improve the sensitivity and dynamic response under thermal shock loads. The sigmoid bi-directional functional grading law is employed to obtain the material properties in axial and thickness directions. The dynamic characteristics of the FG-MEMS accelerometer considering the temperature effects, gap pressure and squeeze film damping, are comprehensively evaluated through developed semi-analytical formulation and numerical simulation. The size effects of the device are accounted for using the modified couple stress theory (MCST). The influence of material and design parameters such as grading indices, porosity, finger gap spacing, and aspect ratio on the dynamic performance is investigated. Finally, the optimal configuration of the FG-MEMS accelerometer is obtained through a multi-objective formulation, and the dynamic sensitivity has increased by 111.92% compared to a conventional silicon-based accelerometer. The novelty of the present work lies in the integration of sigmoid bi-directional functional grading and porosity into the MEMS accelerometer to simultaneously address thermal shock, size-dependent effects, and squeeze-film damping. Unlike conventional silicon-based designs, the proposed FG porous architecture, combined with multi-objective optimization, provides enhanced thermal stability and electromechanical dynamic sensitivity.