An Alternative approach to design periodic rods

Abstract

The reduction of structural vibration has been an important topic for many engineering applications. In traditional projects different passive control techniques involving viscoelastic materials and dynamic absorbers and, more recently, active control methodologies including actuators and sensors have been successfully employed. Different researches have demonstrated that vibration reduction can be obtained using the concept of periodicity. The periodic structures involve identical elements or parts connected repeatedly. The design of periodic structures can be employed to get frequency band without elastic waves propagation, i.e., stop bands, introducing an effect similar to the filter. In this context, the present work introduces an alternative approach for designing periodic rods. This alternative involves the modeling of an infinite hybrid type periodic rod in which a finite periodic structure is connected between two semi-infinite rods. It is used a methodology that relates state vector and wave amplitudes. The main proposal of this work is to develop a relation between the transmitted and incident longitudinal waves amplitudes in terms of physical and geometrical properties of a generic candidate structure to simplify the process of designing. Based on this approach is shown that a periodic rod can be designed to satisfy requirements of a vibration suppression. A hypothetical problem is proposed and numerical and experimental results show the stop bands obtained to solve the problem. It shows that this approach is an important tool for designing this type of structures.