This book derives physical models from basic principles, studies the effect of equivalent models on the dynamic characteristics of phononic crystals and acoustic metamaterials, and analyzes the physical mechanisms behind vibration and noise reduction. It first summarizes the research status of vibration and noise reduction, and research progress in phononic crystals and acoustic metamaterials. Based on this, one-dimensional periodic beam, two-dimensional thin plate with circular hole, and corresponding gradient structures are introduced, and their dynamic characteristics are discussed in detail. Therefore, different equivalent methods for different models are proposed through theoretical analysis, modal analysis and transmission rate analysis. Finally, a Helmholtz-type acoustic metamaterial, i.e. a multi-layer slotted tube acoustic metamaterial, is studied. Aiming at the low-frequency band gap of this model, a theoretical model for solving the inverse problem of acousto-electric analogue equivalent is proposed, and the effect of structural parameters on the low-frequency band gap is studied using this equivalent model.
This book closely revolves around how to conduct equivalent research on artificially fabricated periodic structures. The methods and conclusions presented in this book provide a new theoretical basis for the application of artificial woven periodic structures in the field of low-frequency vibration reduction and noise reduction and are also an innovation in the discipline of vibration and noise control. This book is suitable for undergraduate students, graduate students and teachers in vibration and noise majors in universities, and can also provide references for engineering and technical personnel in related fields.
Author(s): Nansha Gao, Jie Deng
Publisher: Springer
Year: 2022
Language: English
Pages: 184
City: Singapore
Preface
Research and Application on Dynamic Equivalent Inverse Problem of Acoustic Metamaterials
Contents
1 Introduction
1.1 Research Background and Significance
1.1.1 The Harmful Effects of Vibrations and Noise
1.1.2 Vibration and Noise Control Methods
1.2 Review of Phononic Crystals and Acoustic Metamaterials
1.2.1 The History of Development of Phononic Crystals and Acoustic Metamaterials
1.2.2 Equivalence Theory of Phononic Crystals and Acoustic Metamaterials
1.2.3 Recent Development Trend of Phononic Crystals and Acoustic Metamaterials
1.3 A Brief Introduction into the Research Done in this Work
1.3.1 Research Contents
1.3.2 Book Structure Organization
References
2 Basic Theories of Acoustic Metamaterials for Solving the Dynamic Equivalent Inverse Problem
2.1 Introduction
2.2 Basic Theories of Acoustic Metamaterials
2.2.1 Wave Equations in Elastic Media
2.2.2 Lattice Theory of Photonic Crystals
2.2.3 Bloch's Theorem and Brillouin Zones
2.3 A Theory of Dynamic Equivalence for Solving the Inverse Problems of Acoustic Metamaterials
2.3.1 Methods of Calculating the Dispersion Relation and Energy Band Relation of Acoustic Metamaterials
2.3.2 Theoretical Model of Dynamic Equivalence for Solving the Inverse Problems of Acoustic Metamaterials
2.3.3 Theoretical Model for Solving the Inverse Problems of Acoustic-Electric Analogical Equivalence
2.4 Chapter Summary
References
3 Theoretical Model for Solving the Inverse-Problem of Dynamic Equivalent Media of Periodic Rod-Beam Structures
3.1 Introduction
3.2 Periodic Rod-Beam Structures
3.2.1 Calculation Model of Periodic Rod-Beam Structure
3.2.2 Dispersion Relation and Energy Band Relation of the Periodic Rod-Beam Structure
3.2.3 Vibration Mode Analysis for the Periodic Rod-Beam Structure
3.3 Theoretical Model for Solving the Inverse Problems of Dynamic Equivalent Media of Periodic Rod-Beam Structures
3.3.1 Wave Equations of Beam Structures
3.3.2 Calculation of Dynamic Equivalent Material Parameters of Periodic Beam Structures
3.3.3 Verification of Dynamic Equivalent Material Parameters of the Periodic Beam Structure
3.4 Theoretical Model for Solving the Inverse Problems of Dynamic Equivalent Media of Periodic Rods
3.4.1 The Wave Equation of a Rod
3.4.2 Calculation of Dynamic Equivalent Material Parameters of Periodic Rods
3.4.3 Verification by Dynamic Equivalent Material Parameters of Periodic Rod Structures
3.5 Chapter Summary
References
4 Theoretical Model for Solving the Inverse Problems of Dynamic Equivalent Media of Periodic Plate Structures
4.1 Introduction
4.2 Periodic Plate Structure with Circular Holes
4.2.1 A Model of Periodic Plate Structure with Circular Holes
4.2.2 Dispersion Relation and Energy Band Relation of Periodic Plate Structures with Circular Holes
4.3 Theoretical Model for Solving the Inverse Problems of Dynamic Equivalent Media of Periodic Plate Structures with Circular Holes
4.3.1 The Wave Equation of a Plate Structure
4.3.2 Calculation of Dynamic Equivalent Material Parameters of Periodic Plate Structures with Circular Holes
4.3.3 Verification of Dynamic Equivalent Material Parameters of the Periodic Plate Structure with Circular Holes
4.4 Chapter Summary
References
5 Study on the Vibration Characteristics of a Gradient Rod Based on the Theoretical Model for Solving the Inverse Problem of the Dynamic Equivalent Medium
5.1 Introduction
5.2 Gradient Rod Structure
5.2.1 Dispersion Relation and Energy Band Relation of a Cell Structure of the Gradient Rod Structure
5.2.2 Dynamic Equivalent Material Parameters of a Cell Structure of the Gradient Rod
5.2.3 Equivalent Model of Gradient Rod
5.3 Propagation Characteristics of the Gradient Rod Structure
5.3.1 Theoretical Analysis of Vibration Propagation Characteristics of the Gradient Rod Structure
5.3.2 Finite Element Analysis of Vibration Transmission Characteristics of the Gradient Rod Structure
5.4 Chapter Summary
Reference
6 Study on the Low-Frequency Bandgap Mechanism of a Multilayer Slit-Tube Structure Based on the Acoustic-Electric Analogical Equivalent Model
6.1 Introduction
6.2 Multilayer Slit-Tube Acoustic Metamaterials
6.2.1 Dispersion Relation Calculation of Multilayer Slit-Tube Acoustic Metamaterials
6.2.2 Dispersion Relation Analysis of Multilayer Slit-Tube Acoustic Metamaterials
6.2.3 Vibration Mode Analysis of Multilayer Slit-Tube Acoustic Metamaterials
6.3 Acoustic-Electric Analogical Equivalent Model for Multilayer Slit-Tube Acoustic Metamaterials
6.3.1 Acoustic-Electric Analogical Equivalent Model Under Resonant Modes
6.3.2 Influencing Factor Analysis of Resonant Modes Based on the Acoustic-Electric Analogical Equivalent Model
6.4 Study on the Acoustic Transmission Characteristics of Finite Rows of Multilayer Slit-Tube Structures
6.5 Inverse Design of a Multi-Layer Slit-Tube Structure Based on the Acoustic-Electric Analogical Equivalent Model
6.6 Experimental Test and Data Analysis
6.6.1 Design and Preparation of Samples
6.6.2 Test Principles of Standing Wave Tubes
6.6.3 Experimental Test Scheme
6.6.4 Experimental Results and Discussion
6.7 Chapter Summary
References
