Effective Mass Calculations Using COMSOL Multiphysics® for Thermomechanical Calibration
Over the past few decades, nano/micro-mechanical resonators have experienced tremendous improvements in measurement sensitivity. In order to ensure accuracy, it is crucial that each nano/micro-mechanical device is properly calibrated. Thermomechanical calibration provides a noninvasive calibration method by which scaling issues can be circumvented. Each resonator is modeled as a damped harmonic oscillator, while accounting for its extended structure by introducing a single, mode-dependent quantity: its effective mass. Though the effective mass can be calculated analytically for a number of simple cases, the finite element method (FEM) capabilities in COMSOL Multiphysics® were used for modeling more complex geometries. I will present the results of these calculations, which when combined with thermomechanical calibration, provide a recipe by which any nano/micro-mechanical resonator can be calibrated using COMSOL.