Vibration Response and Wave Propagation in Periodic Structures

Abstract

The vibration response of periodic, beam-like structures has conventionally been studied either by transfer matrix or normal mode methods. The latter method becomes unwieldy if the damping and modal density are high, whereas the former method does not lend itself readily to giving physical understanding. It is shown in this paper that a special class of flexural wave groups can exist in periodic structures; an understanding of them permits a ready formulation of the response-calculation problem. The formulation can be applied to both infinite and finite structures, and the amount of damping present may have any value. The method is specially well adapted to studying response due to convected pressure fields and loadings and gives great physical insight. Illustrations are given relating to beams resting at regular intervals on flexible supports and to aeronautical rib-skin structures. Some calculated values of vibration response are presented and discussed and optimum structural configurations are considered.