Resonant frequency and flutter instability of a nanocantilever with the surface effects

Nanorods and nanotubes are widely used as biosensors and reinforced fibers. Surface effects should be considered due to their nano-meter order dimension in at least one direction. This paper studies vibration and stability of a nanocantilever carrying mass under non-conservative loading. Special emphasis is placed on determination of flutter loads and resonant frequencies of a nanocantilever-mass system subjected to a generalized follower force. An exact characteristic equation is derived. For various concrete cases, the load-frequency interaction curves are displayed and the influences of surface elasticity and residual surface tension are analyzed for both conservative and non-conservative forces. The resonant frequencies are calculated for bending vibration of a sensor with attached mass. Flutter loads are obtained under a generalized follower force. Beck's column with the surface effects is a special case of the present. Surface influences from residual surface tension and surface elasticity on the resonant frequencies and critical loads are examined. It is found that there exists the lowest flutter load independent of the tip mass through which all force-frequency interaction curves passes at a given frequency for any generalized follower force in possible direction.