Frequency analysis of a double-nanobeam-system

Abstract

In this paper, a problem of transverse free vibration of a double-nanobeam--system is considered. The nanobeams of the system are coupled by an arbitrary number of translational springs. The solution of the problem by using the Green's functions properties is obtained. A numerical example is presented.

Steady states of elastically-coupled extensible double-beam systems

“…• According to §4, nonsymmetric unimodal solutions pop up, as well as unimodal solutions for which the elastic energy is not evenly distributed. This feature is illustrated in the forthcoming pictures 6 . Moreover, not only a double series of bifurcations of the trivial solution occurs, but even buckled unimodal solutions suffer from a further bifurcation (see Lemma 4.1 and Fig.…”

“…Their interest, which is relevant in structural mechanics, has been recently extended even to nanostructures (see e.g. [6] and references therein).…”

Frequency analysis of a double-walled nanotubes system

“…The derivation of the Green's functions has been presented in paper [6]. The equations (10)- (11) are satisfied for all values of independent variables 2 2 2 1 1 2 2 2 3 1 2 2 2 2 1 2 1 2 2 2 2 2 1 2 1…”

Free vibration to a system of cantilever nanobeams

“…The equations of motion for the transverse vibration of two simply-supported nanobeams that are coupled by n-discrete transitional springs were presented in paper [9]. Considering the free vibrations to a system of cantilever nanobeams we assume the transverse displacement in the form: ( ) ( )…”

“…n in equations (8)- (9) and in equations which express the second order derivatives of the functions 1 1 ( ) ξ W and 2 2 ( ) ξ W , a system of equations is obtained. This equation system can be written in the following matrix form: The non-trivial solutions of equation (10) exist for these values of the Ω for which the determinant of the matrix Y is equal to zero.…”