Traveling wave analytical solutions of vibration band gaps of composite periodic beams

This paper is concerned with elastic wave propagation and vibration band gaps in periodic beams formed by alternating combinations of various materials with the same geometric parameters. Such composite periodic systems have the similar feature of filtering characteristics of periodic beams. The study is performed by using an exact analytical approach based on a combination of the traveling wave analysis method and periodic structure theory. Based on the wave theory, a general mathematical model of composite periodic beam with uniform cross-section is established, the band gaps mechanism and vibration characteristics of this model are discussed, and the analytical solutions of the dynamic model and the explicit expression of band gaps are derived. Based on these equations, an explicit expression is provided for the calculation of intermediate frequency boundary frequency, all the band gaps information can be obtained in an exact and simple manner, and several illustrative examples are also provided.