Dynamic Synthesis of Microsystems Using the Segment Rayleigh–Ritz Method

Microsystem development requires accurate and parametric-based modeling as well as experimental validation of the effects of multiphysics influences such as electrostatic, thermal, and mechanical on microsystems in a systematic manner. This work attempts to synthesize the influence of electrothermomechanical influences on microsystems using an energy-based method, namely, the segment Rayleigh-Ritz (SRR), thereby making it possible to study the multiphysics influences on the dynamic behavior of microsystems in a simplified and unified way. Electrostatic, thermal, and geometrical influences along with microfabrication limitations related to the boundary support are studied on cantilever-based microsystems. Silicon-on-insulator-based technology is used for demonstration purposes. The SRR energy method was developed in order to improve the theoretical formulation for microsystems with nonuniform properties. The method of artificial springs is employed to model the boundary support, electrostatic influences, and intersegmental boundaries. The microfabricated support conditions were quantified through a rotational stiffness, and its invariance with geometry, temperature, and electrostatic field was verified through dynamic testing under electrothermal influences. Comparison with test results validates the dynamic synthesis modeling for microstructures. This approach can be expanded further to nondimensional design optimization and for targeted performance tuning of the static and dynamic behavior of microsystems.