Keywords: Free transverse vibration Vibration mode shapes Double-walled carbon nanotubes (DWCNTs) Nonlocal Rayleigh beam theory Reproducing kernel particle method (RKPM) a b s t r a c t The true understanding of free vibration of double-walled carbon nanotubes (DWCNTs) plays a vital role in optimal design and dynamic control of such nanostructures. This paper is aimed to examine free flexural v...

The nanostructures under rotation have high promising future to be used in nano-machines, nano-motors and nano-turbines. They are also one of the topics of interests and it is new in designing of rotating nano-systems. In this paper, the scale-dependent vibration analysis of a nanoplate with consideration of the axial force due to the rotation has been investigated. The governing equation and b...

In this paper, the effect of the temperature change on the vibration frequency of mono-layer graphene sheet embedded in an elastic medium is studied. Using the nonlocal elasticity theory, the governing equations are derived for single-layered graphene sheets. Using Levy and Navier solutions, analytical frequency equations for single-layered graphene sheets are obtained. Using Levy solution, the...

This paper is concerned with the surface and small scale effects on transverse vibration of a viscoelastic single-layered graphene sheet (SLGS) subjected to an in-plane magnetic field. The SLGS is surrounded by an elastic medium which is simulated as Visco-Pasternak foundation. In order to investigate the small scale effects, the nonlocal elasticity theory is employed due to its simplicity and ...

A method used recently to obtain a discrete formalism for classical fields with nonlocal actions preserving chiral symmetry and uniqueness of fermion fields yields a discrete version of Huygens’ principle with free discrete propagators that recover their continuum forms in certain limit.

In this paper, Eringen’s nonlocal elasticity and Timoshenko beam theories are implemented to analyze the bending vibration for non-uniform nano-beams.  The governing equations and the boundary conditions are derived using Hamilton’s principle. A Generalized Differential Quadrature Method (GDQM) is utilized for solving the governing equations of non-uniform Timoshenko nano-beam for pinned-pinned...

In this paper, the wave propagation method is combined with nonlocal elasticity theory to analyze the buckling and free vibration of rectangular Reddy nanoplate. Wave propagation is one of the powerful methods for analyzing the vibration and buckling of structures. It is assumed that the plate has two opposite edges simply supported while the other two edges may be simply supported or clamped. ...

In this study, the small scale effect on the linear free-field vibration of a nano-circular plate has been investigated using nonlocal elasticity theory. The formulation is based on the classical theory and the linear strain in cylindrical coordinates. To take into account the small scale and the linear geometric effects, the governing differential equation based on the nonlocal elasticity theo...

A size-dependent Euler–Bernoulli beam model, which accounts for nonlocal stress field, strain gradient field and higher order inertia force field, is derived based on the nonlocal strain gradient theory considering velocity gradient effect. The governing equations and boundary conditions are derived both in dimensional and dimensionless form by employed the Hamilton principle. The analytical so...

In this paper, buckling and free vibration analysis of a circular tapered nanoplate subjected to in-plane forces were studied. The linear variation of the plate thickness was considered in radial direction. Nonlocal elasticity theory was employed to capture size-dependent effects. The Raleigh-Ritz method and differential transform method were utilized to obtain the frequency equations for simpl...