Elastic properties and vibration of micro-machined structures subject to residual stresses

This paper presents a theoretical derivation of the changes in resonant frequencies for micro-machined beams due to residual stress. It was found that the frequency increases with increasing strain: the change in the square of the frequency was proportional to the strain, and long slender beams show larger frequency changes. A method for determining Young´s Modulus and strain from multiple frequency measurements is presented. The results are compared both to FEM analysis, as well as to experimental results from the literature.