Bandgap properties in simplified model of composite locally resonant phononic crystal plate

Abstract

This paper extends the traditional plane wave expansion (PWE) method to calculate the band structure of the proposed simplified model of composite locally resonant phononic crystal (LRPC) plate. Explicit matrix formulations are developed for the calculation of band structure. In order to illustrate the accuracy of the results, the band structure calculated by PWE method is compared to that calculated by finite element (FE) method. In addition, in order to reveal the bandgap properties, band structures of the “spring–mass” simplified model of stubbed-on LRPC plate, “spring–torsional spring–mass” simplified model of stubbed-on LRPC plate and “spring–torsional spring–mass” simplified model of composite LRPC plate with and without the viscidity considered are presented and investigated in detail.