Nonlinear vibrations of curved single and doublewalled carbon nanotubes /

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2014
Samandari, Hamed
In this thesis, effects of Geometric, initial curvature, and van der Waals (vdW) interlayer force nonlinearities on the variation of nonlinear natural frequency of Carbon Nanotubes (CNTs) are investigated in detail throughout several case studies. Galerkin method with a single trial function, which is the eigenfunction of the linear system, is widely used in literature in studying nonlinear vibrations of CNTs. However, eigenfunctions of the nonlinear systems can be significantly different than the eigenfunctions of the linear system. Therefore, depending on the nonlinearity, it may not be possible to capture the nonlinear characteristics by using a single trial function. Consequently, for the first time in this thesis, multiple trial functions are used to investigate the nonlinear free vibrations of CNTs. Moreover, a new solution approach– describing function method– is proposed which has the advantage of expressing the nonlinear force as a nonlinear complex stiffness matrix multiplied by displacement vector, where the off-diagonal terms of the nonlinear stiffness matrix can provide a comprehensive knowledge about the coupling between the trial functions. Depending on the boundary conditions considered, it is hard to find suitable trial functions that satisfies all the boundary conditions; hence, in order to overcome this difficulty, iterative path following method (IPFM) based on differential quadrature method (DQM) is developed which does not require trial functions. It is concluded that DQM based nonlinear solution method is very promising in solving nonlinear continuous systems, since it requires less number of gird points which results in less number of nonlinear equations compared to finite element methods.

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Citation Formats
H. Samandari, “Nonlinear vibrations of curved single and doublewalled carbon nanotubes /,” Ph.D. - Doctoral Program, Middle East Technical University, 2014.