A Ghorbanpour Arani - Professor, Faculty of Mechanical Engineering, University of Kashan
H Gharbi Afshar - MSc Student; Faculty of Mechanical Engineering, University of Kashan
M Abdollahian - PhD Student; Faculty of Mechanical Engineering, University of Kashan
R Kolahchi - PhD Student; Faculty of Mechanical Engineering, University of Kashan

Nonlinear nonlocal free vibration and instability of viscose fluid-conveying double-walled carbon nanocones surrounded by Pasternak foundation (DWCNCs) are studied using Euler-Bernoulli beam (EB) theory. The governing motion equations are obtained using energy method and Hamilton’s principle. Differential quadrature method (DQM) is applied to solve motion equations numerically. The small-size effects on bulk viscosity and slip boundary conditions of nanoflow through Knudsen number (Kn) is considered. The van der Waals (vdW) forces between the inner and outer nanocones are taken into account. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, apex angles, aspect ratio, Knudsen number, temperature change and the elastic medium coefficient on the dimensionless frequency and critical fluid velocity of DWCNCs. The results show that the smallsize effect on flow field is remarkable on frequency and critical fluid velocity of DWCNC. Also, the nonlinear frequency and critical flow velocity decrease with increasing the nonlocal parameter and cone semi-vertex angle. The results are in good agreement with the previous researches.

Nonlinear vibration, Viscouse fluid flow, DWCNC, DQM, Pasternak foundation