Propagation Characteristics Of Acoustic Waves In One Dimensional Nonlinear Periodic Structures And Metamaterials

In nature,most of the substances exhibit certain nonlinear effects under certain conditions.The mathematical description of nonlinearity will make the model much more difficult.So in order to simplify the calculation,we usually remove the nonlinear terms which do not have a significant impact.However,with the development of science and technology,especially the progress of electronic technology and computer technology and the development of new materials,people have to pay more attention to the nonlinear term and make use of it.In recent years,the research on acoustic rectification effect and acoustic artificial materials has received much attention.Inspired by electron diodes and thermal rectification,Chinese researchers achieved sound rectification through specially designed acoustic materials for the first time.Phononic crystals and nonlinear acoustics play a very important role in the study of acoustic rectification.The characteristics of acoustic waves in one dimensional nonlinear periodic structures and metamaterials are studied in this paper.In the first chapter,the introduction reviews the progress of the research on the periodic structure of linear acoustics,the nonlinear acoustic periodic structure and the acoustic artificial materials,as well as some research progress on the nonlinear acoustics.In the second chapter,several common methods for calculating the band structure of phononic crystals are introduced,including the transfer matrix derivation and the calculation of the band structure with the transfer matrix.The principle and characteristics of the finite difference time domain method are also introduced.The third and fourth sections introduce the processing of phononic crystals by plane wave expansion and concentrated mass method respectively.In the third chapter,we study the nonlinear properties of periodic structures with the same mass and different spring stiffness.According to the linear dispersion curve of this periodic structure,we predicted the nonlinear characteristics of the structure,that is,the nonlinear spring can make the acoustic branch cut-off frequency shift when the optical branch cut-off frequency is constant,and the prediction is confirmed by the simulation of the transmission coefficient curve.This conclusion shows that our structure can control the band gap more flexibly and achieve better filtering results.Based on this linear and nonlinear periodic structure,we have designed a non reciprocal structure.Since the structure breaks the reciprocity principle,so the elastic wave can realize asymmetric transmission in it.The simulation results show that if the input signal is the same,the amplitude ratio output from different directions of propagation can be up to an order of magnitude.This can be regarded as an acoustic diode(AD)without circuit elements and frequency movement.Our research on nonlinear mass spring systems has expanded the potential applications of periodic structures.In the fourth chapter,we carry out linear and nonlinear simulation of mass-in-mass acoustic metamaterials.The results show that the band gap corresponding to the transmission coefficient curve conforms to the theory.Finally,in the fifth chapter,the main contents and prospects for future work are given.The innovative points of this work are as follows:1.A one-dimensional periodic structure with same mass and different spring stiffness is designed,and the expression of its dispersion curve is different from that of the general diatomic chain.2.We predict its nonlinear characteristics based on the dispersion curve of the periodic structure,which has been verified by simulation.3.Based on the nonlinear periodic structure and the linear periodic structure,we have designed a kind of acoustic non reciprocal material.The working principle of the material is discussed and the rectification effect is proved by the simulation.Compared with the structure previously designed by researchers,the structure has certain characteristics.4.We studied the dispersion curves of mass-in-mass acoustic metamaterials and simulated the transmission coefficients.The simulation results are in good agreement with the theory.