Band gap analysis of a three-mass locally resonant structure

Abstract

A mass in a mass locally resonant system has been studied using a numerical and analytical method. This study is performed to compute the band gap and transmission coefficient of a mass–spring locally resonant system. A locally resonant structure is a periodic structure which exhibits negative effective properties in a certain frequency band and reveals band gaps below Bragg’s frequency. In this work, two substructures are attached with main mass so that the system will act as two masses in a mass system. It is found that the presented structure shows two band gaps below 500 Hz with negative effective properties. Addition of a third substructure with the main mass provides an additional band gap at low frequency. The position and width of band gaps can be tuned by changing the values of masses and stiffness.