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Structural Engineering and Mechanics Volume 72, Number 1, October10 2019 , pages 71-81 DOI: https://doi.org/10.12989/sem.2019.72.1.071 |
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Frequency response of initially deflected nanotubes conveying fluid via a nonlinear NSGT model |
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Ali Farajpour, Mergen H. Ghayesh and Hamed Farokhi
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| Abstract | ||
| The objective of this paper is to develop a size-dependent nonlinear model of beams for fluid-conveying nanotubes with an initial deflection. The nonlinear frequency response of the nanotube is analysed via an Euler-Bernoulli model. Size influences on the behaviour of the nanosystem are described utilising the nonlocal strain gradient theory (NSGT). Relative motions at the inner wall of the nanotube is taken into consideration via Beskok–Karniadakis model. Formulating kinetic and elastic energies and then employing Hamilton\'s approach, the nonlinear motion equations are derived. Furthermore, Galerkin\'s approach is employed for discretisation, and then a continuation scheme is developed for obtaining numerical results. It is observed that an initial deflection significantly alters the frequency response of NSGT nanotubes conveying fluid. For small initial deflections, a hardening nonlinearity is found whereas a softening-hardening nonlinearity is observed for large initial deflections. | ||
| Key Words | ||
| nonlinear frequency response; nanotubes; fluid flow; initial deflection | ||
| Address | ||
| Ali Farajpour1,2, Mergen H. Ghayesh1 and Hamed Farokhi2 1School of Mechanical Engineering, University of Adelaide, South Australia 5005, Australia 2Department of Mechanical and Construction Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, UK | ||