The dynamic behaviour of a finite periodic structure comprising either symmetric or asymmetric exponential- and conical-shaped rods

Abstract

Periodic structure research is driven by the aim of incorporating them into modern engineering systems to address specific challenges, such as vibration reduction within defined frequency ranges. This paper explores the dynamic behaviour of a periodic structure comprising rods with varying cross-sectional areas. Two specific cases are considered, one in which the unit cell consists of two rods where the cross-sectional area varies exponentially and one where the cross-sectional areas vary conically. The structures are modelled using receptance matrices of a single cell, which are then transformed into transfer matrices. This facilitates a comparison of the two structures and helps to relate the results between finite and infinite structures. An experimental study to validate the approach and some of the results is also presented. It is shown that the structures composed of rods with exponentially or conically varying cross-section areas have similar behaviour. Reasonably good correspondence between the predictions and the experimental results were found. However, some additional features were found in the measured receptances due to bending vibration that was not considered in the theoretical model. Asymmetric cells are found to perform better and have a wider attenuation band when compared to symmetrical cells.