Simulation On Low-frequency Bandgap Characteristics Of A Two-dimensional Tapered Scatterer Phononic Crystal Slab

The control of low-frequency vibration and noise is one of the difficult problems that need to be solved urgently in the current engineering field.This paper focuses on the two core issues of reducing the bandgap frequency and widening the bandgap range,aiming to obtain phononic crystals with characteristics of low-frequency wide bandgap and good vibration damping performance.Phononic crystal is an artificial periodic composite material with elastic wave bandgap,which can be used to control the propagation of elastic wave and acoustic wave,and has a broad application prospect in the fields of vibration reduction and noise reduction.In this work,we first introduce the research status of phononic crystals in the past 20 years,summarize the excellent research results of many scholars at home and abroad,and point out some problems existing in the research of phononic crystals and the direction of research.In addition,some basic concepts,basic theories and bandgap calculation methods of phononic crystals are explained.Then,according to the bandgap characteristics of phononic crystals and combined with the research results of existing literatures,two different structure types of phononic crystal models are designed respectively,and their bandgap characteristics are studied in detail by finite element method.The main conclusions are obtained as follows:An embedded two-dimensional tapered scatterer phononic crystal plate model is designed,which consists of four epoxy resin short connecting plates embedded with tapered scatterers coated with silicone rubber coating.The finite element method is used to simulate the bandgap characteristics of the phononic crystal plate.The results show that the newly designed phononic crystal plate can obtain a very wide full bandgap in the low frequency range.Compared with the bonded square connection plate model structure,the newly designed phononic crystal plate has a lower starting frequency of the first full bandgap and a bandwidth increase of nearly 15 times.In addition,the effects of geometric parameters,symmetry of phononic crystal plate model and the depth of scatterers embedded in silicone rubber on energy band structure are also studied in detail.In order to obtain a wider local resonance bandgap,an attached two-dimensional tapered scatterer phononic crystal plate model is designed.The model is composed of tapered lead scatterers periodically arrayed on both sides of a two-dimensional two-component base plate,wherein the base plate is composed of silicon rubber filler and four epoxy resin short plates connected.The band structure,transmission loss and displacement vector field of the phononic crystal plate are simulated and calculated by finite element method.The generation mechanism of the local resonance bandgap is analyzed,and the influence of the scatterer material,lattice constant of the phononic crystal plate and geometric parameters of silicone rubber filling layer on the bandgap is further studied.It is found that the phononic crystal model can generate multiple local resonant bandgaps in the frequency range of 0-2750 Hz,with the total bandgap bandwidth accounting for 91.2%.The bandgap can be controlled to a certain extent by changing the density of scatterers,the lattice constant of phononic crystal plates and geometric parameters of silicone rubber filling layer.The work done in this dissertation has certain reference value for bandgap adjustment control and structure optimization of phononic crystals.Two new two-dimensional tapered scatterer phononic crystal plate models designed have good low-frequency bandgap characteristics,which provide reliable theoretical basis for the application of phononic crystals in the field of low-frequency vibration reduction and noise reduction.