Vibration analysis of suspended microchannel resonators characterized as cantilevered micropipes conveying fluid and nanoparticle

This paper performs a theoretical analysis of suspended microchannel resonators (SMRs) containing one single or two parallel channels, modeled here as cantilevered micropipes conveying fluid and nanoparticle, and investigates the effects of flow velocity and nanoparticle’s instantaneous position on natural frequency, stability, and damping. For two-channel micropipes (TCMPs), the governing equation is derived using the Newtonian approach by essentially accounting for the flow-induced tensile force due to the fact that the flow reverses direction near the free end of the micropipe. Results of eigenvalue analysis show that the presence of a moving nanoparticle can make originally stable micropipe systems become unstable. The stability of both single-channel micropipes (SCMPs) and TCMPs is strongly dependent on the instantaneous position of the moving nanoparticle. For a TCMP system, of particular interest is that in the absence of external damping, flutter instability may concurrently occurs in several modes even for infinitesimal flow velocity. The same TCMP system but with consideration of external damping, however, can retain stability at low flow velocity. These results highlight the importance of considering fluid–structure interactions in the design of SMRs containing internal flow and nanoparticle.