ABSTRACT
After studying wave propagation in large or macro-structural systems, in this chapter, we will study the nature of wave propagation and its characteristics in nanostructures and nanocomposite structures. These structures are part of a material system that is of nanometer scale and the effect they have on the propagation characteristics of these systems are quite different compared to the macro-scale structures. While analyzing such structures at the nanometer scale using continuum models, one would wonder if such models are valid at that atomistic scale, although a significant amount of literature has shown that such models indeed predict the wave parameters to some reasonable accuracy in certain cases. Such continuum models use a local theory of elasticity to derive the governing equations. There is a second school of thought that questions very much the use of continuum models for such atomistic simulations, arguing that scale effects significantly affect the wave behavior at the nanometer scale and hence advocates molecular dynamics or some ab initio modeling principle, which is computationally prohibitive. The via media between these two approaches is the non-local gradient elasticity theory, which incorporates the scale effects in the continuum models. This was briefly introduced in Chapter 2. In this chapter, we will present wave propagation analysis in nano waveguides using both these modeling theories, namely the local and non-local elasticity theories. Before doing this, we will first introduce fundamentals of nanostructures, their types, and some of their properties.
