Thermal Effects on Modified Beam Structures with Enhanced Sensitivity for Resonant Sensing Applications

Micromechanical resonators are widely used in precision sensing applications due to their high stability and sensitivity. Traditional clamped-clamped (C-C) beam resonators, while popular in resonant sensors, suffer from limitations in thermal stability and sensitivity. In this paper, we explore the thermal behavior of resonators with modified boundary conditions-specifically Free-Free (F-F) beams-and demonstrate their advantages over conventional C-C designs. A combination of finite element simulations and experimental characterization is employed to analyze resonance frequency shifts under varying temperature and axial loading conditions. Our results indicate that F-F beam resonators exhibit enhanced thermal stability and higher sensitivity to applied forces, making them promising for high-precision sensing. For example, over a 50 K temperature increase, an F-F beam showed ~23% less frequency drift than an equivalent C-C beam. Moreover, under an applied axial force (simulating a constant acceleration, such as gravity), the sensitivity of the F-F resonator to temperature and material changes is further reduced compared to the C-C case. This reduced thermal sensitivity under load is highly beneficial for applications requiring stable performance under varying thermal and mechanical conditions. The findings suggest that adopting F-F boundary conditions in resonator design can lead to superior performance in inertial sensing, gravimetry, and force measurement systems.