Analysis and design of periodic beams for vibration attenuation

This paper presents a new finite-element-based design procedure for geometrically periodic beam structures to target a specific desired attenuation frequency band. Using the "forward approach," the effects of the cell geometric parameters on the location of the stop bands are first studied. Then using the "reverse approach," explicit expressions for the start and end frequencies of all stop bands are derived as functions of the cell geometric parameters using a symbolic solver. These expressions are used in the design procedure to determine the cell geometric parameters that will result in vibration attenuation in the desired attenuation band. The design procedure has been validated by comparison with the results of the forward approach in different problems targeting the first or second stop bands. It was found that, depending on the frequency range of the desired attenuation band, and the stop band selected to target the desired attenuation band in the design, one, two or no solution set for the cell geometric parameters can be obtained. For the case of two available solutions, the designer will have two design options that satisfy the design requirements to choose from.