Vibration and instability analysis of tubular nano- and micro-beams conveying fluid using nonlocal elastic theory |
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| Affiliation: | 1. Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 1807 Granada, Spain;2. Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain;3. Department of Mathematics, Faculty of Science and Technology, University of the Basque Country UPV-EHU, Bilbao, Spain;1. Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan, ROC;2. Department of Mechanical Engineering, Center for Micro/Nano Science and Technology, National Cheng Kung University, Tainan 701, Taiwan, ROC;3. Department of Mechanical Engineering, Kun Shan University, Tainan 701, Taiwan, ROC;4. Department of Mechanical Engineering, National Chin-Yi University of Technology, Taichung 411, Taiwan, ROC;5. HIWIN Technologies Corporation, Taiwan, ROC;1. Space Research Institute of Netherlands (SRON), Sorbonnelaan 2, 3584 CA Utrecht, the Netherlands;2. Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia;1. Department of Engineering, Persian Gulf University, Bushehr, Iran;2. Department of Engineering, King’s College, 133 N River St., Wilkes-Barre, PA 18702, USA |
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| Abstract: | 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. |
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