THE EFFECT OF PERIOD ASYMMETRY ON WAVE PROPAGATION IN PERIODIC BEAMS

Abstract The h-p version of the finite element method is used to study flexural wave motion in a periodic beam with identical, but non-symmetric, periods. The convergence behaviour of the h-p method is benchmark validated against an exact analysis provided by the dynamic stiffness method in obtaining solutions for the wave propagation constant as a function of frequency. It is shown that period asymmetry can have a beneficial effect on the dynamic characteristics of the structure from a vibration control viewpoint and could feasibly be exploited as an additional design variable. It is also demonstrated that, in the presence of asymmetry, the pass-band bounding frequencies no longer correspond to the natural frequencies of an isolated bay. A study of the group velocity of wave motion as a function of frequency in an asymmetric system is also included. The ability to compute this information is important because it enables a direct measure of the energy flow, the modal density of the system, and the rate of spatial decay which is caused by an added damping treatment, to be estimated within a given pass-band.