Abstract
The transverse vibration of a single-walled carbon nanotube (SWCNT) with light waviness along its axis is modeled by the nonlocal Euler-Bernoulli and Timoshenko beam theory. Unlike the Euler-Bernoulli beam model (EBM), the effects of transverse shear deformation and rotary inertia are considered within the framework of the Timoshenko beam model (TBM). The surrounding elastic medium is described as both Winkler-type and Pasternak-type foundation models. The governing equations are derived using Hamilton’s principle, and the Galerkin method is applied to solve these equations. According to this study, the results indicate that the frequency calculated by TBM is lower than that obtained by EBM. Detailed results show that the importance of transverse shear deformation and rotary inertia become more significant for stocky SWCNTs with clamped-clamped boundary conditions. Moreover, the influences of the amplitude of waviness, nonlocal parameter, medium constants, boundary conditions and aspect ratio are analyzed and discussed. It is shown that waviness in the curved SWCNT causes an obvious increase in the natural frequency in comparison with the straight SWCNT, especially for a compliant medium, pinned-pinned boundary condition, short SWCNT and large nonlocal coefficient.
Highlights
Seismic loading can induce large damages in industrial facilities and their complex components (Babič and Dolšek 2016; Demartino et al 2017a, b; Nuti et al 2009)
Liquid storage tanks and piping systems are considered as critical components of those industrial facilities (Vathi et al 2017; Bakalis et al 2017)
The maximum seismic design force, i.e. the most unfavorable condition, is obtained in corresponding of the maximum possible liquid fill height in the cylinder, that is when the fluid mass tends to behave like an impulsive mass and sloshing effects become negligible
Summary
Seismic loading can induce large damages in industrial facilities and their complex components (Babič and Dolšek 2016; Demartino et al 2017a, b; Nuti et al 2009). Gases are usually stored under high-pressure, often in liquid form since the volume is largely reduced Within this framework, ground-based horizontal cylindrical tanks resting upon two supports are used mainly for storage of various liquids. As to the first aspect (1), it is worth noting that the seismic analysis of cylindrical storage tanks requires accounting for the fluid–structure interaction This phenomenon, referred to as “liquid sloshing,” is generated by the presence of a free surface allowing for fluid motions and is generally caused by external tank excitation, significantly affecting in many cases the dynamic response (Hamdan 2000; Patkas and Karamanos 2007).
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