Disturbance wave propagation on a semi-infinite one-dimensional lattice containing a mass defect

Abstract

We use a simple techique to study the influence of a “weak” mass defect on the propagation of a general disturbance on a semi-infinite one-dimensional monoatomic lattice. The location of the deffective mass is assumed arbitrary. Result are expressed as combinations of Bessel functions and integrals of Bessel functions. A numerical example demonstrates that the influence of the defect appears to modulate the response of the otherwise perfect chain. This modulation vanishes in the limit as t → ∈.