Dynamics of microscale pipes containing internal fluid flow: Damping, frequency shift, and stability

• Published in: Journal of sound and vibration Vol. 329; no. 8; pp. 1081 - 1088
• Main Authors: Rinaldi, Stephanie, Prabhakar, Sairam, Vengallatore, Srikar, Païdoussis, Michael P.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 12.04.2010; Elsevier
• Subjects: Applied sciences; Exact sciences and technology; Flows in ducts, channels, nozzles, and conduits; Fluid dynamics; Fundamental areas of phenomenology (including applications); Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Mechanical engineering. Machine design; Mechanical instruments, equipment and techniques; Micromechanical devices and systems; Physics; Precision engineering, watch making; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Internal friction; Vibration; Pipe flow; Elastomer; Mechanical properties; Boundary condition; Continuum; Frequency shift; Vibration damping; Internal flow; Flow(fluid); Size effect; Dynamic stability; Internal fluid; Thermoelasticity; Flow velocity; Continuum mechanics; Hollow beam; Microelectromechanical device; Microfluidics
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2009.10.025

This paper initiates the theoretical analysis of microscale resonators containing internal flow, modelled here as microfabricated pipes conveying fluid, and investigates the effects of flow velocity on damping, stability, and frequency shift. The analysis is conducted within the context of classical continuum mechanics, and the effects of structural dissipation (including thermoelastic damping in hollow beams), boundary conditions, geometry, and flow velocity on vibrations are discussed. A scaling analysis suggests that slender elastomeric micropipes are susceptible to instability by divergence (buckling) and flutter at relatively low flow velocities of ∼10 m/s.