We provide a detailed description of a general procedure by which a nano/micro-mechanical resonator can be calibrated using its thermal motion. A brief introduction to the equations of motion for such a resonator is presented, followed by a detailed derivation of the corresponding power spectral density (PSD) function. The effective masses for a number of different resonator geometries are determined using both finite element method (FEM) modeling and analytical calculations.
@article{arxiv.1305.0557,
title = {A general procedure for thermomechanical calibration of nano/micro-mechanical resonators},
author = {B. D. Hauer and C. Doolin and K. S. D. Beach and J. P. Davis},
journal= {arXiv preprint arXiv:1305.0557},
year = {2013}
}