Nonlinear vibrations of curved single and doublewalled carbon nanotubes /

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.


Nonlinear fiber modeling of steel-concrete partially composite beams with channel shear connectors
Öztürk, Alper; Baran, Eray; Department of Civil Engineering (2017)
The purpose of this study is to develop a nonlinear fiber-based finite element model of steel-concrete composite beams. The model was developed in OpenSees utilizing the available finite element formulations and the readily available uniaxial material constitutive relations. The model employed beam elements for the steel beam and the concrete slab, while zero-length connector elements were used for the steel-concrete interface. The channel shear connector response used in numerical models was based on the p...
Analysis of RC walls with a mixed formulation frame finite element
Sarıtaş, Afşin (2013-10-01)
This paper presents a mixed formulation frame element with the assumptions of the Timoshenko shear beam theory for displacement field and that accounts for interaction between shear and normal stress at material level. Nonlinear response of the element is obtained by integration of section response, which in turn is obtained by integration of material response. Satisfaction of transverse equilibrium equations at section includes the interaction between concrete and transverse reinforcing steel. A 3d plastic...
Structural, electronic and magnetic properties of various nanosystems : molecular dynamics simulations and density functional theory calculations
Sholejh, Alaei; Erkoç, Şakir; Jalili, Seifollah; Department of Physics (2014)
In this study, we aim to investigate the structural, magnetic and electronic properties of various nanosystems using molecular dynamics simulation technique and density functional theory calculations. In the first part, iron oxide nanostructures (nanorods, clusters and nanoparticles) were considered. We applied strain, at different temperatures, on nanorods in order to study stability of iron oxide nanorods using molecular dynamics simulation. Furthermore, radial distribution functions of iron oxide nanopar...
Modeling of the nonlinear behavior of steel framed structures with semi rigid connections
Sarıtaş, Afşin; Özel, Halil Fırat (null; 2015-07-21)
A mixed formulation frame finite element with internal semi-rigid connections is presented for the nonlinear analysis of steel structures. Proposed element provides accurate responses for spread of inelasticity along element length by monitoring the nonlinear responses of several crosssections, where spread of inelasticity over each section is captured with fiber discretization. Each material point on the section considers inelastic coupling between normal stress and shear stress. The formulation of the ele...
Nonlinear Vibrations of a Functionally Graded Material Microbeam with Geometric Nonlinearity
Uz, Canan; Ciğeroğlu, Ender (2017-02-02)
In this paper, nonlinear vibration analysis of micro scale functionally graded material (FGM) beams with geometric nonlinearity due to large deflection is studied using modified couple stress theory (MCST). MCST is a nonlocal elasticity theory which includes a material length scale parameter since the size of an atomic microstructure becomes comparable to the length of the microbeam. Equations of motion of the micro scale FGM beam are obtained by using Hamilton's principle. Nonlinear free vibrations of the ...
Citation Formats
H. Samandari, “Nonlinear vibrations of curved single and doublewalled carbon nanotubes /,” Ph.D. - Doctoral Program, Middle East Technical University, 2014.