Wave attenuation in periodic three-layered beams: analytical and FEM study

We study infinite composite beams with periodic simple supports and analyze their vibration attenuation characteristics. In the literature single spans of such beams have been studied for determining their loss factors. Such loss factor information is insufficient for determining attenuation in the periodic or multi-span case. Here, we directly derive propagation constants as a function of frequency. Two distinct cases are investigated in detail. The first is a three-layered periodic beam with a continuous central visco-elastic layer. The second is a periodic beam with visco-elastic inserts of finite extent. The former is analytically tractable and yields insight, while the latter has better structural properties for practical applications. The continuous layer case is studied using several different beam theories. The case with inserts is studied for several different configurations using FEM. Dependence of attenuation characteristics on size, location, and number of inserts is presented. This study provides insights that will be useful for designing visco-elastic inserts for vibration attenuation in periodic structures.