Journal
PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES
Volume 41, Issue 10, Pages 1835-1840Publisher
ELSEVIER
DOI: 10.1016/j.physe.2009.07.011
Keywords
Nano-beam conveying fluid; Micro-beam conveying fluid; Vibration; Instability; Critical flow velocity; Natural frequency
Funding
- National Natural Science Foundation of China [10802031, 10772071]
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A nonlocal Euler-Bernoulli elastic beam model is developed for the vibration and instability of tubular micro- and nano-beams conveying fluid using the theory of nonlocal elasticity. Based on the Newtonian method, the equation of motion is derived, in which the effect of small length scale is incorporated. With this nonlocal beam model, the natural frequencies and critical flow velocities for the case of simply supported system and for the case of cantilevered system are obtained. The effect of small length scale (i.e., the nonlocal parameter) on the properties of vibrations is discussed. It is demonstrated that the natural frequencies are generally decreased with increasing values of nonlocal parameter, both for the supported and cantilevered systems. More significantly, the effect of small length scale on the critical flow velocities is visible for fluid-conveying beams with nano-scale length; however, this effect may be neglected for micro-beams conveying fluid. (C) 2009 Elsevier B.V. All rights reserved.
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