Forced vibration and wave propagation in mono-coupled periodic structures

This paper describes the wave propagation and vibration characteristics of mono-coupled structures which are of spatially periodic nature. The receptance approach to periodic structure theory is applied to study undamped periodic systems with composite structural elements; particular emphasis is laid on investigating resonant periodic point loading and its pronounced effect on the propagation of longitudinal waves. General mono-coupled periodic systems are first assumed to be infinite in extent; thereafter reflections caused by arbitrary end terminations of finite structures are considered and a general `closed form' solution is found for the forced harmonic response at element junctions. This `junction-receptance' is used to determine-discrete junction mode shapes of a finite system. Finally, the forced response of a finite structure with an internal obstruction is derived as a natural extension of the determination of the junction-receptance. The influence of such a disorder is illustrated by a simple example