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Topics On The Nonlinear Dynamics And Acoustics Of Ordered Granular Media [Kõva köide]

(Univ Of California, Usa), (Indian Inst Of Science, India), (Univ Of Illinois At Urbana-champaign, Usa), (Technion-israel Inst Of Tech, Israel)
  • Formaat: Hardback, 640 pages
  • Ilmumisaeg: 23-May-2017
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9813221933
  • ISBN-13: 9789813221932
Teised raamatud teemal:
Topics On The Nonlinear Dynamics And Acoustics Of Ordered Granular MediaSuurem pilt
  • Formaat: Hardback, 640 pages
  • Ilmumisaeg: 23-May-2017
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9813221933
  • ISBN-13: 9789813221932
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9789813221932.html
Märksõnad:
This research monograph provides a brief overview of the authors' research in the area of ordered granular media over the last decade. The exposition covers one-dimensional homogeneous and dimer chains in great detail incorporating novel analytical tools and experimental results supporting the analytical and numerical studies. The proposed analytical tools have since been successfully implemented in studying two-dimensional dimers, granular dimers on on-site perturbations, solitary waves in Toda lattices to name a few. The second part of the monograph dwells on weakly coupled homogeneous granular chains from analytical, numerical and experimental perspective exploring the interesting phenomenon of Landau-Zener tunneling in granular media. The final part of the monograph provides a brief introduction to locally resonant acoustic metamaterials incorporating internal rotators and the resulting energy channeling mechanism in unit-cells and in one- and two-dimensional lattices. The monograph provides a comprehensive overview of the research in this interesting domain. However, this exposition is not all exhaustive with regard to equally exciting research by other researchers across the globe, but we provide an exhaustive list of references for the interested readers to further explore in this direction.
Dedication v
Preface vii
Chapter 1 Introduction 1(34)
1.1 Current Research in the Area of Granular Media
12(9)
1.2 Outline of the Monograph
21(3)
References
24(11)
Chapter 2 Acoustics of One-Dimensional Homogeneous Granular Chains 35(24)
2.1 Theoretical Model and Long Wave Approximation for Propagating Solitary Waves
36(6)
2.2 Concept of Compactons
42(2)
2.3 Scattering of the Solitary Waves in the Homogeneous Granular Chains
44(4)
2.4 Homogeneous Chains with Local Defects or Intruders
48(8)
References
56(3)
Chapter 3 Oscillatory Dynamics of One-Dimensional Homogeneous Granular Chains 59(76)
3.1 Nonlinear Normal Modes (NNMs) and Frequency Bands of Homogeneous Granular Chains
60(27)
3.1.1 Introduction
60(1)
3.1.2 Two-Bead Granular System
61(13)
3.1.3 Effect of Pre-compression on the In-phase NNM of the Two-Bead System
74(3)
3.1.4 Three-Bead Granular System
77(6)
3.1.5 Higher Dimensional Granular Systems
83(4)
3.2 Forced Harmonic Responses of Homogeneous Granular Chains
87(23)
3.2.1 Acoustic Filtering in the Frequency-Energy Domain
88(14)
3.2.1.1 Experimental Setup and the Numerical Model
93(1)
3.2.1.2 Numerical Results
94(6)
3.2.1.3 Experimental Results
100(2)
3.2.2 Analytical Study of the Dynamics in the Attenuation Zone
102(8)
3.3 Classification of the NNMs in Finite Homogeneous Granular Chains
110(22)
3.3.1 Introduction
111(3)
3.3.2 Auxiliary and Vibro-Impact Models Based on the Concept of Effective Particles
114(6)
3.3.3 Classification of NNMs
120(7)
3.3.4 Theoretical Modeling of the Dynamics of Effective Particles
127(5)
References
132(3)
Chapter 4 Acoustics of Periodic Diatomic (Dimer) Chains without Pre-Compression 135(182)
4.1 Acoustics of 1:1 Dimers
136(108)
4.1.1 Introduction
136(3)
4.1.2 Anti-Resonances and Solitary Waves
139(31)
4.1.2.1 Numerical Evidence of Solitary Waves in the Dimer
139(15)
4.1.2.2 Analytical Study of the Anti-Resonances (Solitary Waves) in the Dimers
154(14)
4.1.2.3 Conclusions
168(2)
4.1.3 Resonances leading to Pulse Attenuation in the Dimers
170(29)
4.1.3.1 Numerical Evidence of Pulse Attenuation and Resonances in the Dimers
171(16)
4.1.3.2 Beating Wave-Packets following the 1:1 Resonance
187(4)
4.1.3.3 Analytical Study of the Nonlinear Resonances in the 1:1 Dimer
191(4)
4.1.3.4 Binary Collision Approximation for the 1:1 Resonance
195(3)
4.1.3.5 Conclusions
198(1)
4.1.4 Effect of Pre-Compression on the Resonances and the Anti-Resonances
199(4)
4.1.5 Periodic Traveling Waves and Bifurcations
203(24)
4.1.5.1 Excitation of Families of Traveling Waves in Semi-Infinite Dimer Chains
204(4)
4.1.5.2 Periodic Traveling Waves in Dimer Chains
208(14)
4.1.5.3 Correlation of the Stability of the Traveling Waves with the Dynamics of the Finite Dimer Chains
222(4)
4.1.5.4 Conclusions
226(1)
4.1.6 Experimental Verification of the Resonances and the Anti-Resonances in the 1:1 Dimers
227(17)
4.1.6.1 Experimental Fixture
228(3)
4.1.6.2 Theoretical Modeling
231(4)
4.1.6.3 Experimental Results
235(8)
4.1.6.4 Conclusions
243(1)
4.2 Acoustics of 1:N Dimers
244(68)
4.2.1 Introduction
244(1)
4.2.2 General Asymptotic Formulation for Primary Pulse Propagation in 1:N Dimer Chains
245(6)
4.2.3 Anti-Resonances and the Solitary Waves in 1:2 Dimer Chains
251(24)
4.2.3.1 Pulse Transmission in Finite 1:2 Dimer Chains
270(3)
4.2.3.2 Conclusions
273(2)
4.2.4 Resonances in 1:2 Dimer Chains
275(16)
4.2.4.1 Conclusions
289(2)
4.2.5 Resonances and Anti-Resonances in General 1:N (N>2) Dimer Chains
291(10)
4.2.6 Dynamics of 1:N Dimer Chains with Large Stiffness Ratios
301(6)
4.2.7 Validity of the Asymptotic Approach for General 1:N Dimer Chains
307(5)
References
312(5)
Chapter 5 Acoustics of Weakly Coupled Granular Chains 317(170)
5.1 Nonlinear Energy Exchanges, Waves and Breathers
317(27)
5.1.1 Spatially Periodic Traveling Waves
328(1)
5.1.2 Standing Waves and Discrete Breathers
328(4)
5.1.3 Traveling (Moving) Breathers
332(6)
5.1.4 Numerical Simulations
338(6)
5.2 Passive Wave Redirection under Impulsive Excitation
344(24)
5.2.1 Analysis
350(12)
5.2.2 Numerical Simulations
362(6)
5.3 Passive Wave Redirection under Periodic Excitation
368(30)
5.3.1 Forced Discrete Breathers and Recurrent Energy Transfers
372(7)
5.3.2 Passive Wave Redirection and Resonance Captures
379(19)
5.4 Acoustic Filtering Properties
398(33)
5.4.1 Low-Frequency Pass Bands
403(9)
5.4.2 Breathers at Intermediate Frequency Ranges
412(13)
5.4.3 High-Frequency Stop Bands
425(6)
5.5 Energy Equi-partition
431(24)
5.5.1 Theoretical Study
431(8)
5.5.2 Experimental Study
439(16)
5.6 The Effects of Non-Smooth Boundary Conditions
455(24)
5.6.1 Nonlinear Acoustic Filtering
462(8)
5.6.2 Propagating Pulses and Moving Breathers
470(4)
5.6.3 Near-Field Oscillations and Passive Wave Arrest
474(5)
References
479(8)
Chapter 6 Wave Propagation in Two-Dimensional Granular Crystals 487(86)
6.1 Introduction to Wave Propagation in Two-Dimensional Granular Crystals
487(1)
6.2 Evolution of Nesterenko Solitary Waves in Granular Scalar Models
488(56)
6.2.1 Interaction of Nesterenko Solitary Waves in Weakly Perturbed Granular Scalar Media
491(52)
6.2.1.1 General Model and Motivation
491(2)
6.2.1.2 Modulation of Nesterenko Solitary Waves- Generalized Analytical Approximation
493(16)
6.2.1.3 Applications of the Analytical Procedure
509(37)
6.2.1.3.1 Unperturbed Scalar Models
509(13)
6.2.1.3.2 Effect of the Elastic Foundation and Dissipation
522(11)
6.2.1.3.3 Effect of the Active Media and Formation of Stable Attractors
533(9)
6.2.1.3.4 Limitations of the Analytical Procedure
542(1)
6.2.2 Conclusions
543(1)
6.3 Primary Wave Transmission in Two-Dimensional Granular Setups
544(25)
6.3.1 Primary Wave Transmission in Hexagonally Packed, Damped Granular Crystal with a Spatially Varying Cross Section
546(5)
6.3.1.1 Fundamental Model
546(1)
6.3.1.2 Main Assumptions and Restrictions
547(1)
6.3.1.3 Normalization of the Equations of Motion
548(3)
6.3.2 Numerical Evidence for the Formation of a Primary Front
551(2)
6.3.3 Analytical Approximation of the Evolution of the Primary Pulse
553(10)
6.3.3.1 Construction of the Reduced Order Model
554(2)
6.3.3.2 Description of the Evolution of a Primary pulse using the Nonlinear Map Procedure
556(3)
6.3.3.3 Long Wave Approximation
559(4)
6.3.4 Numerical Verification
563(5)
6.3.4.1 Time Domain
563(2)
6.3.4.2 Space-Time Diagrams
565(3)
6.3.5 Conclusions
568(1)
References
569(4)
Chapter 7 Acoustic Metamaterials with Locally Resonant Structure 573(50)
7.1 Introduction to Locally Resonant Acoustic Metamaterials
573(2)
7.2 Two-Dimensional Energy Channeling in Inertially Coupled Metamaterials
575(41)
7.2.1 Basic Concept of Nonlinear Energy Channeling: Unit Cell Model
575(14)
7.2.1.1 Numerical Evidence of Uni-Directional Energy Transport from Axial to Lateral Vibrations
578(2)
7.2.1.2 Multi-Scale Analysis
580(4)
7.2.1.3 Slow Dissipative Flow (mu not equal to 0)
584(2)
7.2.1.4 Uni-Directional Energy Channeling
586(3)
7.2.2 Two-Dimensional Nonlinear Wave Channeling in the Quasi One-Dimensional Locally Resonant Chain
589(27)
7.2.2.1 Theoretical Study of Resonant Wave Channeling Mechanisms
591(25)
7.2.2.1.1 Multi-Scale Analysis
592(4)
7.2.2.1.2 Analytical Prediction of Wave Channeling Mechanism
596(1)
7.2.2.1.3 Conservative Case: Bi-Directional Wave Channeling
597(6)
7.2.2.1.4 Dissipative Case: Uni-Directional Wave Channeling
603(3)
7.2.2.1.5 Numerical Verification
606(10)
7.3 Conclusions
616(1)
References
617(6)
Index 623