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In this paper, the vibration and instability of double-walled carbon nanotube (DWCNT) conveying fluid were investigated by using the modified strain gradient theory. The Donnell's shell theory was used by taking into consideration the three size effects and simply-supported boundary conditions. The effect of van der Waals force between the two intended walls and the surroundings of the DWCNT was modelled as visco-Pasternak foundation. The governing equations of the problem and boundary conditions were derived from Hamilton’s principle. Also, Navier procedure was used to solve the vibration problem. To verify the results, a comparison was drawn between the results of this study and those of the references. According to the findings, the effects of fluid velocity, stiffness and damping of visco-Pasternak foundation, length of DWCNT and size effect are more considerable in the modified strain gradient theory than in the modified couple stress theory and classical theory.
Keywords: Modified strain gradient theory, Donnell’s shell theory, DWCNT, size effect, shell vibration.
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