Research On Numerical Calculation Methods Of Band Structures Of Elastic Metamaterials And Its Application On Vibration Reduction And Noise Absorption

Low-frequency vibration and noise have become a common noise pollution problem in production and life by virtue of its powerful penetrating ability and tenacious characteristic of difficult attenuation and absorption.Due to the lack of resonance mechanism,the structures that used to reduce low-frequency vibration and absorb noise are designed based on traditional vibration and noise control methods.These structures are generally large and bulky in size.Elastic metamaterials(EMMs)can break through the size and weight limitations and provide a new solution for vibration reduction and noise absorption.However,the current numerical simulation of elastic metamaterials mainly relies on the finite element method,whose geometric modeling is separated from the subsequent response analysis and structural design,leading to the inevitable geometric approximation error and numerical dispersion error problems.Second,most of the existing computational methods of band structures are based on deterministic numerical models,ignoring the uncertainties existing in the design and fabrication processes,which have a great impact on the physical response of metamaterials.In addition,due to the lack of empirical structural shapes and optimization methods,the design of elastic metamaterials often requires the use of complex multiphase material combinations but can only obtain a narrow double-negative bandwidth,which is not applicable to engineering practice.In the application of EMMs,the effective absorption bandwidth of the conventional acoustic structure is relatively narrow,and the frequency of realizing perfect absorption is generally high,which limits its application in industry.This dissertation will start a systematic study on the computational methods,optimization design strategy and application of EMMs.In the first part,efficient and accurate method of computing the metamaterial band structure of solid/solid system and solid/fluid system based on isogeometric analysis is proposed.The hybrid uncertain mass-redistributed finite element method is proposed for elastic metamaterials with uncertainty and fluid-solid interaction,which makes up for the defects of existing deterministic methods.In the second part,a shape optimization strategy for expanding the double-negative parameter bands of EMMs is developed,and the design of EMMs with broad-band double-negative properties is realized.In the application part,a new material structure with hybrid resonance coupling is investigated and manufactured to achieve broadband sound absorption in the low frequency range.The main contents and achievements of this thesis include:(1)The calculation method of the band structure of solid/solid phononic crystals(Pn Cs)based on the isogeometric analysis(IGA)framework is developed,the geometry and displacement fields of the Pn Cs are described by using the unified NURBS function.The boundary collocation points combined with the Lagrange multiplier method are constructed to accurately handle the periodic boundary conditions,and the seamless transition from CAD to CAE process of metamaterials is realized.The application of IGA method is extended to achieve accurate calculation of band curves of Pn Cs for different scatterer shapes,lattice types,and material combinations.It is found that the larger the acoustic impedance matching between the matrix and the scatterer,the more likely to generate in-plane mixed-wave low-order bandgap and out-of-plane transversewave low-order bandgap.(2)A dispersion reduced isogeometric analysis(DR-IGA)method is proposed.The causes of numerical dispersion errors based on Gaussian integration points are revealed,and a new system matrix is constructed to study wave propagation in fluids,realizing the efficient,accurate,and reliable calculation of band structure of fluid-solid Pn Cs.A dispersion error reduction strategy based on the coefficients of the template equation is constructed,and a new type of element matrix in the fluid domain is derived by combining matrix symmetry,energy conservation and static equilibrium constraints.The high-precision calculation of the band curves of different types of fluid-solid coupled Pn Cs is realized,which lays the foundation for the design,analysis,and optimization of fluid-solid coupled phonon crystals/metamaterials.(3)A new hybrid uncertain mass redistribution finite element method(HUMR-FEM)is proposed.It is aimed to construct an accurate numerical analysis model and a reliable uncertainty model for the efficient and accurate quantification of uncertainty that is frequently seen in the design and manufacturing process of metamaterials.The causes of dispersion errors during longitudinal wave simulation in the fluid domain are analyzed,and the mass redistribution strategy is introduced to improve the accuracy of numerical calculations of acoustic-solid coupled Pn Cs.A hybrid uncertainty model is constructed to transform the uncertainty of random response into the deterministic calculation of the extreme value boundary of statistical properties,and the uncertainty of physical response in different types of acoustic-solid coupled Pn Cs is accurately quantified.(4)A new type of single-phase EMMs structure is designed.The reason for the generation of double-negative parameter of EMMs is investigated.A shape optimization strategy based on single-phase chiral metamaterials is formed to realize the design of broadband double-negative parameters of EMMs under different demands.Starting from energy band calculation,dynamic effective parameter extraction,and sensitivity analysis,the physical mechanisms of monopole and dipole resonance of EMMs are revealed,and the shape optimization design strategies of chiral metamaterials with different initial shapes,relative frequencies,and design variables are investigated.Using the optimized structures,three novel physical phenomena related to the property of double negative parameters are demonstrated,including broadband negative refraction,subwavelength imaging with super-resolution of 0.28λ,and stable transverse and longitudinal wave conversion.The application of out-of-plane transverse bandgap using the single-phase chiral metamaterials for vibration reduction is explored,and the inner core rotation angle is found to be the key to open and close the loworder bandgap.(5)The application of elastic metamaterials in noise reduction is expanded.The hybridized resonant EMMs structure of perforated aluminum plate combined with porous materials is proposed and fabricated to achieve broadband sound absorption in the low frequency range.The hybridized resonance coupling between perforated aluminum plate and porous material is studied.The key factors affecting the sound absorption performance are analyzed,and the broadband sound absorption mechanism in the low frequency range is revealed.A composite acoustic metamaterial structure is investigated experimentally,which effectively decreases the frequency that can realize perfect absorption,achieves a broadband effective sound absorption in the low frequency range(≤1000Hz)with a bandwidth nearly 535 Hz.The structure manufactured in this thesis broadens the low-frequency sound absorption performance comparing with traditional sound-absorbing materials.