Frequency response of initially deflected nanotubes conveying fluid via a nonlinear NSGT model

Farajpour, Ali, Ghayesh, Mergen H. and Farokhi, Hamed (2019) Frequency response of initially deflected nanotubes conveying fluid via a nonlinear NSGT model. Structural Engineering and Mechanics, 72 (1). pp. 71-81. ISSN 1225-4568

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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 Hamiltonś approach, the nonlinear motion equations are derived. Furthermore, Galerkinś 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.

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