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

Nonlinear vibration and instability of embedded doublewalledcarbon nanocones (DWCNCs) conveying viscosefluid are investigated in this article based on Eringen'snonlocal theory and Timoshenko beam (TB) model. Thesmall-size effects on bulk viscosity and slip boundaryconditions of nanoflow through Knudsen number (Kn) areconsidered. The elastic medium is simulated as Pasternakfoundation and the van der Waals (vdW) forces betweenthe inner and the outer layers of DWCNCs are taken intoaccount. Using von Kármán geometric nonlinearity,energy method and Hamilton’s principle, the nonlocalnonlinear motion equations are obtained. The differentialquadrature method (DQM) is applied to discretize themotion equations, which are then solved to obtain thenonlinear frequency and critical fluid velocity of viscousfluid-conveying DWCNCs. The detailed parametric studyis conducted, focusing on the combined effects of thenonlocal parameter and apex angles on the dimensionlessfrequency and critical fluid velocity of DWCNCs. Theresults show that the nonlinear frequency and critical flowvelocity decrease with increasing the nonlocal parameterand cone semi-vertex angle.

کلیدواژه ها:

DWCNC ، Nanoflow ، vibration andinstability ، DQM.