Nonlinear vibration and instability of embedded DWCNC conveying nanoflow based on nonlocal Timoshenko beam theory

چکیده مقاله

Nonlinear vibration and instability of embedded double- walled carbon nanocones (DWCNCs) conveying viscose fluid are investigated in this article based on Eringen's nonlocal theory and Timoshenko beam (TB) model. The small-size effects on bulk viscosity and slip boundary conditions of nanoflow through Knudsen number (Kn) are considered. The elastic medium is simulated as Pasternak foundation and the van der Waals (vdW) forces between the inner and the outer layers of DWCNCs are taken into account. Using von Kármán geometric nonlinearity, energy method and Hamilton’s principle, the nonlocal nonlinear motion equations are obtained. The differential quadrature method (DQM) is applied to discretize the motion equations, which are then solved to obtain the nonlinear frequency and critical fluid velocity of viscous- fluid-conveying DWCNCs. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter and apex angles on the dimensionless frequency and critical fluid velocity of DWCNCs. The results show that the nonlinear frequency and critical flow velocity decrease with increasing the nonlocal parameter and cone semi-vertex angle.