High frequency, periodic disturbances in dissipative systems - I. Small amplitude, finite rate theory

TLDR: In this article, a theory is developed describing finite amplitude, high frequency, periodic disturbances in dissipative systems, where the transmitting medium is taken to be a viscoelastic string and the results are applicable to nonlinear transmission lines and nonlinear dielectrics.

Abstract: A theory is developed describing finite amplitude, high frequency, periodic disturbances in dissipative systems. Although, for definiteness, the transmitting medium is taken to be a viscoelastic string, the results are applicable to nonlinear transmission lines and nonlinear dielectrics, as well as relaxing and reacting gas mixtures. Part I of the paper describes small amplitude but finite rate processes: part II will describe disturbances of unrestricted amplitude. It is shown that by interpreting high frequency waves as modulated simple waves with slowly changing Riemann invariants, the parameter expansion techniques of geometrical optics can be modified to include finite amplitude waves. The roles of the linear models of viscoelasticity and elasticity as well as that of nonlinear elasticity as approximations to the nonlinear viscoelastic model are elucidated.