Wave Propagation in 1D-Nanostructures: Nanobeams

Abstract

Nanobeams are those which undergo flexural or transverse motion in lateral directions. The cross-sections of such nanostructures could be rectangular or circular. Some of the nano thin films, which find applications in Nano Electro Mechanical Systems (NEMS) is normally idealized as nanobeam with rectangular cross-section, while SWCNT undergoing transverse vibration, are normally idealized as nanobeams with circular cross-section. There are two different theories that describe the motion of beams. The first is the Euler-Bernoulli beam theory, which is also called the elementary beam theory. In this theory, rotation of the cross-section is derived from the transverse motion and the plane sections are assumed plane before and after bending. The second theory is called the Timoshenko beam theory, which is also called the First-order shear deformation Theory (FSDT). In this theory, the rotation of the cross-section is considered as independent motion and not derived from transverse deformation. Due to shear deformation effects, the plane sections do not remain plane after the bending of the section. The main aim of this chapter is to study the effect of nonlocal scale parameter on the transverse wave propagation in nanobeams. As before, we will use spectral analysis, outlined in Chap. 2, to perform this study. Some of the analysis performed in this chapter are the following: