Vibrations in Lattices

Abstract

We shall examine the nature of the vibrations which can arise in a lattice structure, that is to say a system of point masses which in their state of rest have a periodic spatial distribution, under a variety of different hypotheses. These will include uni-dimensional and three-dimensional lattices, and interactions which may be closely or remotely coupled, and linear or non-linear. In the case of non-linear interactions between the elements of an uni-dimensional lattice, analysis of the process of propagation leads, on the basis of an approximation of long-wave type, to a standard partial differential equation, known as the Korteweg-de Vries equation, which will form the subject of detailed study in Chapter 12.