Reduced dimensional analysis on dynamic characteristics of microcantilever beams in the fluid environment and application to atomic force microscopy

This paper is mainly aimed to investigate the dynamic characteristics of a microbeam structure located at the neighborhood of a wall inside the chamber filled with different fluids. Firstly, by solving the Reynolds equation and the Euler beam equation, specific dynamic characteristics of the entire system such as the resonant frequency, the frequency shift, and the damping ratio can be obtained. Secondly, by relating the calculated dynamic characteristics to the frequency response of a reduced dimensional system, the effective mass, damping and stiffness can be evaluated for the beam structure in the fluid near the chamber wall. The coupling dynamic behavior can be understood by analyzing these extended physical parameters, namely, the effective mass, damping and stiffness. Finally, the preceding analytic procedure is used to demonstrate the limitation on the tip size of the probe of an atomic force microscope operated in non-contact mode within fluid environment.