Stress-Induced Variations in the Stiffness of Micro- and Nanocantilever Beams

摘要

The effect of surface stress on the stiffness of cantilever beams remains an outstanding problem in theudphysical sciences. While numerous experimental studies report significant stiffness change due to surfaceudstress, theoretical predictions are unable to rigorously and quantitatively reconcile these observations. Inudthis Letter, we present the first controlled measurements of stress-induced change in cantilever stiffnessudwith commensurate theoretical quantification. Simultaneous measurements are also performed onudequivalent clamped-clamped beams. All experimental results are quantitatively and accurately predictedudusing elasticity theory. We also present conclusive experimental evidence for invalidity of the longstandingudand unphysical axial force model, which has been widely applied to interpret measurementsudusing cantilever beams. Our findings will be of value in the development of micro- and nanoscale resonantudmechanical sensors.