Nonlinear free vibration of double walled carbon nanotubes by using describing function method with multiple trial functions

2012-09-01
In this paper, nonlinear free vibration of double walled carbon nanotubes (DWCNTs) embedded in an elastic medium with geometric nonlinearity and interlayer van der Waals force nonlinearity are studied. The motion of the DWCNT is represented by multiple eigenfunctions of the linear system which are referred as trial functions. Describing function method (DFM) is employed in order to represent the nonlinear forces as a multiplication of a nonlinear stiffness matrix and a displacement vector, which made it possible to identify when it is necessary to consider multiple trial functions. The results revealed that it is important to consider multiple trial functions, especially in case of out-of-phase vibrations of DWCNTs with interlayer van der Waals force nonlinearity. The effects of number of trial functions and medium stiffness on the free vibration of DWCNTs are investigated. It is observed that utilizing multiple trial functions made it possible to detect different vibration modes occurring at a single vibration frequency.
PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES

Suggestions

Nonlinear free vibrations of curved double walled carbon nanotubes using differential quadrature method
Ciğeroğlu, Ender (Elsevier BV, 2014-11-01)
Nonlinear free vibration analysis of curved double-walled carbon nanotubes (DWNTs) embedded in an elastic medium is studied in this study. Nonlinearities considered are due to large deflection of carbon nanotubes (geometric nonlinearity) and nonlinear interlayer van der Waals forces between inner and outer tubes. The differential quadrature method (DQM) is utilized to discretize the partial differential equations of motion in spatial domain, which resulted in a nonlinear set of algebraic equations of motion...
Nonlinear vibrations of curved single and doublewalled carbon nanotubes /
Samandari, Hamed; Ciğeroğlu, Ender; Department of Mechanical Engineering (2014)
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 eigenfunc...
Magnetic properties of multiband U=infinity Hubbard model on anisotropic triangular and rectangular lattice strips
CHERANOVSKII, VO; Esentürk, Okan; PAMUK, HO (1998-11-01)
We study the dependence of the ground state spin of a multiband Hubbard model with infinite electron repulsion on anisotropic triangular and rectangular lattice strips on the model parameters. Considering the results of numerical calculations for the exact spectra of finite triangular lattice strips at different values of hopping integrals, we show the existence of a type of magnetic transitions with the jump of the ground state spin between minimal and maximal values. This transition is found only for spec...
Hamiltonian for a particle in a magnetic field on a curved surface in orthogonal curvilinear coordinates
Shikakhwa, M. S.; Chair, N. (2016-08-19)
The Schrodinger Hamiltonian of a spin-less particle as well as the Pauli Hamiltonian with spin-orbit coupling included of a spin one-half particle in electromagnetic fields that are confined to a curved surface embedded in a three-dimensional space spanned by a general Orthogonal Curvilinear Coordinate are constructed. A new approach, based on the physical argument that upon squeezing the particle to the surface by a potential, then it is the physical gauge-covariant kinematical momentum operator (velocity ...
Free vibration characteristics of a 3d mixed formulation beam element with force-based consistent mass matrix
Soydas, Ozan; Sarıtaş, Afşin (2017-09-01)
In this analytical study, free vibration analyses of a 3d mixed formulation beam element are performed by adopting force-based consistent mass matrix that incorporates shear and rotary inertia effects. The force-based approach takes into account the actual distribution of mass of an element in the derivation of the mass matrix. Moreover, the force-based approach enables accurate determination of free vibration frequencies of members with varying geometry and material distribution without any need for specif...
Citation Formats
E. Ciğeroğlu, “Nonlinear free vibration of double walled carbon nanotubes by using describing function method with multiple trial functions,” PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES, pp. 160–173, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46569.