Wave propagation in infinite periodic structures taking into account energy absorption (original) (raw)

This paper explores the possibility of generalised periodic structure waves (PSW) that include the well-known Bloch-Floquet (BF) waves as a special case. We consider two types of structure waves (SW) in an infinite, uniform, one dimensional structure of equally spaced scatterers that also absorb energy. For the first structure wave type (SW1), forward transmission and backward reflection phase shifts are independent of wave propagation direction. For a second structure wave type (SW2), the phase shifts have opposite signs for opposite directions of propagation. Examples of SW1 are bending waves, such as flexural waves of a plate, and for SW2 longitudinal waves, such as acoustic waves in a fluid. The differences in amplitudes and phases of the forward and backward SW within any “cell” between adjacent scatterers are found to be equivalent to continuous PSW convolved with a periodic structure function. Finding the PSW dispersion relations requires a function that is the solution of a ...