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標題: 英文全書下載 Viscoelastic Materials. Roderic Lakes 2009 《粘彈性材料》 [打印本頁]

作者: 陳小黑    時間: 2015-1-9 22:34
標題: 英文全書下載 Viscoelastic Materials. Roderic Lakes 2009 《粘彈性材料》
本帖最后由 陳小黑 于 2015-1-9 22:37 編輯
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目錄
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: c9 h) z9 z; @0 M2 {Contents6 ^' b& ^2 c; I

0 w7 r  _1 W* xPreface page xvii0 ^% ~2 `) y8 q; }- d6 X7 v2 \
1 Introduction: Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
) Q- G! N: g* c5 t2 O1.1 Viscoelastic Phenomena 1
5 S; N! g/ W7 [+ y' Z1.2 Motivations for Studying Viscoelasticity 3& E* |% g  M5 x$ q) z
1.3 Transient Properties: Creep and Relaxation 3
! v  U( J( H% b: o7 B4 Z# ^. t1.3.1 Viscoelastic Functions J (t), E(t) 3
0 h2 e0 G3 t7 \' ?% g8 p1.3.2 Solids and Liquids 7
' V  n7 i; E$ x: P1 [* n2 R5 j1.4 Dynamic Response to Sinusoidal Load: E∗, tanδ 8- d: S0 C% ]) G& C/ @) o/ T
1.5 Demonstration of Viscoelastic Behavior 10
, {1 b( i$ K: t- s* p7 i1.6 Historical Aspects 10. b, m' C" w2 W" R
1.7 Summary 11
' V, K; H% e; B- L1.8 Examples 11
; K8 M" d: a, \5 V& r7 u1.9 Problems 12/ I2 f9 x3 s. _& [6 k' Y
Bibliography 12& J2 h8 x/ ?; U1 u( ^. `

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* r  l! p! x: x4 p4 e! E* g2 Constitutive Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
% }, S. H( ^. a: r/ @3 K" Z2.1 Introduction 14
; ]  e. |- Y: n2.2 Prediction of the Response of Linearly Viscoelastic Materials 14
# q; l2 i( [& e+ o. b2.2.1 Prediction of Recovery from Relaxation E(t) 148 e0 e/ H5 E7 G' ?& w
2.2.2 Prediction of Response to Arbitrary Strain History 15
+ b  U9 B: x. f: n; b0 x+ Y2.3 Restrictions on the Viscoelastic Functions 176 F9 f: d" W8 v1 Z8 x0 R" ~
2.3.1 Roles of Energy and Passivity 17) B3 i# Q# G- ?: v9 `$ e
2.3.2 Fading Memory 18: i; m3 K6 s4 S/ ?1 R+ {
2.4 Relation between Creep and Relaxation 199 p3 B& w( w. _6 g8 A9 [
2.4.1 Analysis by Laplace Transforms: J (t) ↔ E(t) 197 |% M3 S: @. q( {* ?, x4 l' M% b
2.4.2 Analysis by Direct Construction: J (t) ↔ E(t) 20
6 H# q, S5 x& j8 c2.5 Stress versus Strain for Constant Strain Rate 20& H6 o4 `$ _/ R1 U  _9 \6 |
2.6 Particular Creep and Relaxation Functions 21
  ?' [3 \' F) N7 Z: c2.6.1 Exponentials and Mechanical Models 21+ @! F% Z) t* p5 J& `( n0 f' X: J
2.6.2 Exponentials and Internal Causal Variables 26
  r9 d4 R" t3 d3 G0 P0 C2.6.3 Fractional Derivatives 27
1 Y" C; R+ ~. D7 p2.6.4 Power-Law Behavior 28
5 i$ T6 \) o( A/ h5 {) @" \2.6.5 Stretched Exponential 29
) {4 F7 Y0 S& O6 \. ?- Y2.6.6 Logarithmic Creep; Kuhn Model 29; x# f* m1 }" }4 Y) A1 m
2.6.7 Distinguishing among Viscoelastic Functions 30. a, t8 ^0 H4 w+ ~( A
2.7 Effect of Temperature 30
: Y! V8 F( a  @& y. f2.8 Three-Dimensional Linear Constitutive Equation 33* a- k  V% w" L; w- @7 Y  p
2.9 Aging Materials 35
* m7 y1 h/ H7 n2 T  b2.10 Dielectric and Other Forms of Relaxation 35
- ^5 I: w% W: y$ b( \9 Q  b, |2.11 Adaptive and “Smart” Materials 360 A2 U0 A1 |- R% k& \
2.12 Effect of Nonlinearity 37% @6 N0 L) L! Y# r  ]
2.12.1 Constitutive Equations 37
, s* h* D4 \- y! s- z. d2.12.2 Creep–Relaxation Interrelation: Nonlinear 40$ g' q3 x% D% [; {7 V  B  B
2.13 Summary 43; }2 \, {% y0 B9 D" L. v- P" v! U
2.14 Examples 43! P+ _" i5 n: `/ S
2.15 Problems 51! `4 Y$ r+ Q3 \8 Z! S
Bibliography 52! `- h5 L: i2 n9 z

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3 I; ^' ?6 y: b; S, ]3 Dynamic Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551 \. V, t2 N$ F3 Z7 l
3.1 Introduction and Rationale 55* P8 U  T. P! ]% y) @( F3 f$ x' }; l
3.2 The Linear Dynamic Response Functions E∗, tanδ 56
6 \# N1 J& e: J3.2.1 Response to Sinusoidal Input 57
1 D- H5 ~" w5 z1 D: w/ q7 t  s3.2.2 Dynamic Stress–Strain Relation 59
. z' O$ c# z6 w% l6 w, C3.2.3 Standard Linear Solid 62
( D, ?- j# M$ F4 _  T" H3.3 Kramers–Kronig Relations 63# X! w4 k* ^5 Z5 ]
3.4 Energy Storage and Dissipation 65
8 W/ H- S5 C2 p6 `1 c3 D3.5 Resonance of Structural Members 679 o. N0 N/ Y) d
3.5.1 Resonance, Lumped System 67
/ p* H9 [: I& V9 j3.5.2 Resonance, Distributed System 71# \1 v1 q0 P0 x/ P0 |& B
3.6 Decay of Resonant Vibration 74
& |+ g% x6 T* _% z8 d" U1 t3.7 Wave Propagation and Attenuation 77& f7 U+ R  O6 u2 X
3.8 Measures of Damping 79" ^7 Q8 ?7 x8 M; a# H! E
3.9 Nonlinear Materials 79
+ d/ w. ]$ Q$ x  Y) ~3.10 Summary 816 l7 e. a% @# b3 _* E) v& m
3.11 Examples 81
: d. o& W7 w  }! T9 z3.12 Problems 88
* J' s$ P2 f0 N. H; o3 pBibliography 89
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( ^5 E* T) I% L. s6 m$ @4 Conceptual Structure of Linear Viscoelasticity . . . . . . . . . . . . . . . 91
+ S+ q+ y% O0 A8 a) n9 j( K4.1 Introduction 91
0 D4 f# ^- q  x3 k7 B4.2 Spectra in Linear Viscoelasticity 92
: [. {. D2 F3 N! O5 Q7 F5 u$ ]/ L4.2.1 Definitions H(τ ), L(τ ) and Exact Interrelations 92
5 M9 V8 i; g" N! h# H7 u4.2.2 Particular Spectra 93# s+ D. a9 |6 W  B/ x# I
4.3 Approximate Interrelations of Viscoelastic Functions 95
2 j. z6 }1 i' _8 a& e4 ]4.3.1 Interrelations Involving the Spectra 95  v. s( C/ l7 S; {
4.3.2 Interrelations Involving Measurable Functions 98
6 c7 y( h: ~& U4.3.3 Summary, Approximate Relations 101
9 i( {9 G1 {" G/ L7 M2 s, r$ p  m4.4 Conceptual Organization of the Viscoelastic Functions 101
$ }9 }$ |5 c0 S+ K1 E9 R! R( L4.5 Summary 104
; z7 D7 Y. v: {+ X; x% Q2 G" v4.6 Examples 1049 _! l8 n* F5 y4 L
4.7 Problems 109
0 s" w7 Y2 \/ Y0 ~1 H& g, zBibliography 1093 x- ?7 w0 }8 b

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5 Viscoelastic Stress and Deformation Analysis . . . . . . . . . . . . . . . 111
- k$ }8 i% g2 A4 r% t# b5.1 Introduction 111! u. ^  g2 t3 {- p; B$ r# ]5 ]
5.2 Three-Dimensional Constitutive Equation 111
+ ^! h% h- {' h+ h  u4 o. }5.3 Pure Bending by Direct Construction 112
4 `+ O; R% F/ I/ _' w3 u; z5.4 Correspondence Principle 114" }0 x( d! f+ f# w- m+ c+ c7 ?
5.5 Pure Bending by Correspondence 1167 _5 f$ j3 P( t; w) p
5.6 Correspondence Principle in Three Dimensions 116+ k  t" \" i$ A( K4 o9 ]
5.6.1 Constitutive Equations 116
! P" f3 G# B# I  d  l5.6.2 Rigid Indenter on a Semi-Infinite Solid 1175 j0 o" h& X1 \& {
5.6.3 Viscoelastic Rod Held at Constant Extension 119
. s; F" ]. ?# }% r9 s  k4 x" x5.6.4 Stress Concentration 1196 N. |0 ?: w' \& v/ Z0 ?
5.6.5 Saint Venant’s Principle 120
% X2 m" K  n: U1 N2 H5.7 Poisson’s Ratio ν(t) 121
, m! E: X. H3 H( E  q! e5.7.1 Relaxation in Tension 121
" b$ d9 y# G1 Y8 j7 u5.7.2 Creep in Tension 123
$ @; j. D" Y$ g& |9 h5.8 Dynamic Problems: Effects of Inertia 124
' z# s! \5 v7 [* ^# S5.8.1 Longitudinal Vibration and Waves in a Rod 1241 t( }- {% m: m3 b& y4 T
5.8.2 Torsional Waves and Vibration in a Rod 125/ Y! |% G  a0 i# F
5.8.3 Bending Waves and Vibration 128+ X3 i; k: K; G. Z* g3 s
5.8.4 Waves in Three Dimensions 1290 E- o& L2 c1 y% C! |" C
5.9 Noncorrespondence Problems 131
4 O- v* Q% r% X+ p& s+ e" x) M5.9.1 Solution by Direct Construction: Example 131
! m* ~6 ?, O: z5.9.2 A Generalized Correspondence Principle 132: N6 W0 b: V: ^/ q, j9 l5 o
5.9.3 Contact Problems 132/ c& [' u% b: [0 R" N7 @
5.10 Bending in Nonlinear Viscoelasticity 1336 J' d8 W! O9 X! Q" }" a
5.11 Summary 134
# y# x7 l, R3 |$ z/ F0 M5 h7 A5.12 Examples 1340 g' w1 ~: G: [; e9 X7 s. D& z2 F, |
5.13 Problems 142
! I9 R( M( E  h4 N/ O! v$ zBibliography 142
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1 D7 A' E& k  D- V6 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
, F; w+ |: Q: J7 d8 N$ U. |/ K. q" h6.1 Introduction and General Requirements 145
; n0 _: t8 ]2 l, X2 @6.2 Creep 146
2 x7 F' A( n( N" B4 k; K. {6.2.1 Creep: Simple Methods to Obtain J (t) 146% E8 f: F$ {1 t, d- F8 B0 X
6.2.2 Effect of Risetime in Transient Tests 146. c7 l9 F, Z. ^9 b5 z# a. I, g
6.2.3 Creep in Anisotropic Media 148
" ]1 X: ^  y! }+ }  x6.2.4 Creep in Nonlinear Media 148/ l& a9 J& y7 @" \3 ], K$ R: l2 Z7 A
6.3 Inference of Moduli 150
7 s9 {) V. f- \$ s9 p. M1 G6.3.1 Use of Analytical Solutions 150
$ ]8 h; Q: d& [; g) y6.3.2 Compression of a Block 151
0 g% R1 B: I3 j( L! I1 o6.4 Displacement and Strain Measurement 152
3 D; K) m5 E1 e% s3 R' ?, @6.5 Force Measurement 156( ]& q! j3 k, F
6.6 Load Application 157
& d" Y2 P! \7 R6.7 Environmental Control 157
7 T  o. R; T3 j7 ^6.8 Subresonant Dynamic Methods 158
3 W  h0 M* ]& T4 M# t/ D) e6.8.1 Phase Determination 158
! N$ H. W3 s) o" B0 l4 |% B. w6.8.2 Nonlinear Materials 160
3 w& M4 K  a  G6.8.3 Rebound Test 161
9 t4 N+ q3 z7 g5 o0 V6 I( S6.9 Resonance Methods 1616 e/ W8 b8 k( f8 ^; F# T& T4 {) f
6.9.1 General Principles 161
6 A+ T- \  U4 G$ z% X% N; [5 @/ Q  E5 t6.9.2 Particular Resonance Methods 163
5 T+ m4 N) d2 O" @# S" w0 l" h6.9.3 Methods for Low-Loss or High-Loss Materials 166
! d4 @4 W$ X. W9 K6.9.4 Resonant Ultrasound Spectroscopy 168* @' m2 k& U) A$ P$ {7 C9 h7 ?
6.10 Achieving a Wide Range of Time or Frequency 171/ y1 L8 p' J6 x5 p, t# F3 J3 r
6.10.1 Rationale 171# n6 a8 y1 v$ X: a+ W1 q. g, T
6.10.2 Multiple Instruments and Long Creep 1728 e! S5 \# g. F1 @4 N0 L3 f
6.10.3 Time–Temperature Superposition 172& j  ^( X& U* C  e. A) ]: O3 l
6.11 Test Instruments for Viscoelasticity 173
+ O3 I: ^! q  N; W6 G0 P6 ]6 V6.11.1 Servohydraulic Test Machines 173
  n( u( \* I9 e4 V6.11.2A Relaxation Instrument 174/ B  d/ I! L+ G; X% M
6.11.3 Driven Torsion Pendulum Devices 1743 O6 G% f9 s; U
6.11.4 Commercial Viscoelastic Instrumentation 178
$ {1 D/ O: k0 ?1 y  h/ M) K. f( \6.11.5 Instruments for a Wide Range of Time and Frequency 179
' j0 o9 \* K: @' h0 f6.11.6 Fluctuation–Dissipation Relation 182. |% G0 P; m. T8 C
6.11.7 Mapping Properties by Indentation 183
. P0 U! g$ E5 o# F. a. v6 |( _7 B6.12 Wave Methods 184
/ b0 w& B' ?& d+ w# Y" ^6.13 Summary 188
% y/ {4 l% }1 H+ x/ |6.14 Examples 188
& L7 E7 _9 ~9 j" u6.15 Problems 2002 m" L: r9 }& ?1 B! ~# W" G' b
Bibliography 201
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: K5 B: R9 N$ ?2 I7 Viscoelastic Properties of Materials . . . . . . . . . . . . . . . . . . . . . 207
. R9 _; v" t2 ]- r. }& w' t3 X7.1 Introduction 207
7 ^- b% i8 s6 E  M% `4 h; v7.1.1 Rationale 207: P( I( N1 @( d% H  i
7.1.2 Overview: Some Common Materials 2079 E! T; b" {8 U2 l
7.2 Polymers 208
* u0 G$ [$ w( Y- o7.2.1 Shear and Extension in Amorphous Polymers 208
1 G& O# U- m: w7.2.2 Bulk Relaxation in Amorphous Polymers 212
: K6 \6 Z, H8 o5 v$ f) _9 y7.2.3 Crystalline Polymers 2131 P( f$ j, |. W- O" K, S2 U: C& I: X
7.2.4 Aging and other Relaxations 214# k( n* F# `# D
7.2.5 Piezoelectric Polymers 214
$ x% V7 l- ^" u, u3 X7.2.6 Asphalt 214
; m' T: U+ |7 g4 i& m7.3 Metals 215, Q6 t7 C6 O& B3 A  N8 e
7.3.1 Linear Regime of Metals 215& x4 @8 V9 s/ u& Q. z
7.3.2 Nonlinear Regime of Metals 217
2 h6 U- W/ o( ?& W' n9 |7.3.3 High-Damping Metals and Alloys 219
6 r6 m! u" h% o5 D: _& @$ T! w7.3.4 Creep-Resistant Alloys 224( U, J; \% ~0 U/ x; x7 k: p, }
7.3.5 Semiconductors and Amorphous Elements 225  z+ F) R. D. M7 ], ?
7.3.6 Semiconductors and Acoustic Amplification 226" h& Q4 O6 w2 w- Q! {6 ~! B
7.3.7 Nanoscale Properties 2269 h% t+ ]) H9 l3 C1 b
7.4 Ceramics 227
' V: u; N6 V6 V& z5 w" a- f7.4.1 Rocks 227
1 t+ b. w; Q9 O! _7.4.2 Concrete 229
% m: S& q* l% D2 |7.4.3 Inorganic Glassy Materials 231
7 ~; F3 |4 ?: W4 Q, x6 a* X7 l7.4.4 Ice 2314 A2 q5 P- E* X% X) ]
7.4.5 Piezoelectric Ceramics 232
7 c7 |+ X: n. }7.5 Biological Composite Materials 233
' U& G+ q- W8 E0 g( S0 F3 P7.5.1 Constitutive Equations 234, C2 i$ ^8 Z: f$ F8 K
7.5.2 Hard Tissue: Bone 234
% l1 J8 V+ x! r) U% w3 D% j7.5.3 Collagen, Elastin, Proteoglycans 236
2 p% r- _- y8 [3 E8 Q7.5.4 Ligament and Tendon 237
6 z0 O8 }! D6 d/ C3 D7 x7.5.5 Muscle 2407 m2 h9 C0 k/ ~' ]2 A* B
7.5.6 Fat 243
; u1 J# {, ?; t7.5.7 Brain 243
! v- E; ?9 \" u% v9 f  c7.5.8 Vocal Folds 244
+ i9 a# Y# t+ ], b! \7.5.9 Cartilage and Joints 244* c4 B( p" C' [  Q
7.5.10 Kidney and Liver 2466 S" v; z8 x! n% A
7.5.11 Uterus and Cervix 246
/ H9 s" o6 [9 z. h1 i7.5.12 Arteries 247
9 O/ l2 E& o$ ~; |; L6 ]  K2 D7.5.13 Lung 248+ x7 p2 B. |: P3 H$ Y8 P" v
7.5.14 The Ear 248
/ A3 J1 L: P' T* z7.5.15 The Eye 249
, q2 }0 ]" O8 M. ~7.5.16 Tissue Comparison 251
3 L- @- K" B, _# S- i0 Z1 s1 v7.5.17 Plant Seeds 2522 Q! `! _2 G' Q
7.5.18 Wood 252' Y* ?" N" @# H; ]
7.5.19 Soft Plant Tissue: Apple, Potato 253  P: Z- a' y+ e' V
7.6 Common Aspects 253
; c5 P6 J% h% k# O7.6.1 Temperature Dependence 253! Y4 |5 b  `$ o3 f0 F) i" o9 R# q
7.6.2 High-Temperature Background 254( O. [! {6 I0 O4 ]# O( N% F
7.6.3 Negative Damping and Acoustic Emission 2552 `( F5 W- }4 j
7.7 Summary 255  N& _) E. z! m
7.8 Examples 255
% y# W9 l$ l0 k  k7 m- Y+ R- I7 z7.9 Problems 256
9 ~# b) o( o1 {1 HBibliography 257  Q' v" R) n- v1 C( K) s

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8 Causal Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2711 T% N5 k. J& x
8.1 Introduction 2719 u$ H3 z( u; J( I. l' U
8.1.1 Rationale 271
) T1 g2 j& r: ^# C2 \# H8.1.2 Survey of Viscoelastic Mechanisms 271# O  a3 u  b* i1 x
8.1.3 Coupled Fields 273. C1 {- s: J' {; L% `
8.2 Thermoelastic Relaxation 274
8 @4 k$ v( w: d* A: ^, [8.2.1 Thermoelasticity in One Dimension 274, y: B, L9 k4 \" [
8.2.2 Thermoelasticity in Three Dimensions 275  Z  K+ N- r: B1 O. \# n
8.2.3 Thermoelastic Relaxation Kinetics 2764 {+ ~' \& ?; I
8.2.4 Heterogeneity and Thermoelastic Damping 278% P3 {, E4 N$ R5 t, ?) F- g
8.2.5 Material Properties and Thermoelastic Damping 280
6 }# a. R! `' C$ O8.3 Relaxation by Stress-Induced Fluid Motion 280: z1 }% ]; [( M4 C6 h/ N* |
8.3.1 Fluid Motion in One Dimension 2804 f& A4 Z# Z( x2 |. x) [" X+ ?! X+ a
8.3.2 Biot Theory: Fluid Motion in Three Dimensions 2819 ?) E! L# `: W- z
8.4 Relaxation by Molecular Rearrangement 286& C* S4 r  D1 l- z5 O
8.4.1 Glassy Region 286( k- W  A$ \" `2 h! t
8.4.2 Transition Region 2879 p9 ^. n# ], [+ L& I0 K
8.4.3 Rubbery Behavior 289
- _& z% L; ]1 O2 V- ]4 T$ G5 V2 D8.4.4 Crystalline Polymers 291$ ]+ C) c) r; S! Y' V, |
8.4.5 Biological Macromolecules 2923 M' m7 m) u' }/ i. J4 _
8.4.6 Polymers and Metals 292
, T3 Q$ W( g, l3 V* P8.5 Relaxation by Interface Motion 292
$ Y# F7 `# ~" R2 r+ E. u8.5.1 Grain Boundary Slip in Metals 292' s: L5 [$ h' n( X- |7 _. u6 A1 Y
8.5.2 Interface Motion in Composites 294
. r: N: e, }4 p' ?% ?8.5.3 Structural Interface Motion 294" x3 b( A3 y& h& \; a. h* \
8.6 Relaxation Processes in Crystalline Materials 294
. {( f! s. O4 d+ T1 x* L8.6.1 Snoek Relaxation: Interstitial Atoms 2942 s& _. ?6 v! S) _/ W& j* U
8.6.2 Zener Relaxation in Alloys: Pairs of Atoms 298
( `/ B( p  l/ R% G" V  S9 z# d8.6.3 Gorsky Relaxation 299
" b- d) c- b7 o3 m5 H8.6.4 Granato–L ¨ ucke Relaxation: Dislocations 300- L% c6 D  e3 [7 I' }* M& @, \
8.6.5 Bordoni Relaxation: Dislocation Kinks 303( e6 X* S; ]( T) C5 t# A% f
8.6.6 Relaxation Due to Phase Transformations 305; z) h3 j+ ]: z
8.6.7 High-Temperature Background 314+ S4 L3 v! I0 Q; c
8.6.8 Nonremovable Relaxations 315
* G# G$ w2 [9 R8.6.9 Damping Due to Wave Scattering 316
2 {6 D, c, {( E, u$ j5 S1 r& B* d8.7 Magnetic and Piezoelectric Materials 3167 [# \, p+ o$ R% ~4 d: }3 K1 x" `' [
8.7.1 Relaxation in Magnetic Media 316( `+ S0 w) B$ k
8.7.2 Relaxation in Piezoelectric Materials 318
, L( ~' `$ w  n; {9 \( U! l8.8 Nonexponential Relaxation 3229 f+ U& ?( x) }( `/ C, n
8.9 Concepts for Material Design 323
3 S# I4 n9 o6 v  f8.9.1 Multiple Causes: Deformation Mechanism Maps 323# W' s$ @6 W2 [4 a6 b6 s& K
8.9.2 Damping Mechanisms in High-Loss Alloys 3269 r* L# G/ w4 M
8.9.3 Creep Mechanisms in Creep-Resistant Alloys 326
# @& o, q8 M' m7 t% D8.10 Relaxation at Very Long Times 327
8 E* e+ B& e+ h# P4 C8.11 Summary 327
, j! ^9 A+ c5 ?8.12 Examples 328
, p5 }, J4 P& b# x+ m& x5 l: B8.13 Problems and Questions 332
. O) U: ?* @( \' h) OBibliography 3327 |+ ^" o) j3 G) U3 S' y3 S
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9 Viscoelastic Composite Materials . . . . . . . . . . . . . . . . . . . . . . . 3414 |5 H1 ?! P3 k. k0 g4 _, b5 o
9.1 Introduction 341
" P1 i- t7 K; R, M2 W5 Q9.2 Composite Structures and Properties 341# B, E2 b, V4 N8 w8 g. ^
9.2.1 Ideal Structures 341# Q, u; f  `1 R1 |6 p
9.2.2 Anisotropy due to Structure 3423 e' e0 U; ^  p9 m% ?/ ^/ w
9.3 Prediction of Elastic and Viscoelastic Properties 344
; y/ M1 U# V/ O9.3.1 Basic Structures: Correspondence Solutions 344
8 E9 }  t  ~8 T+ s& F9.3.2 Voigt Composite 345- i$ O% b+ s4 T7 ?
9.3.3 Reuss Composite 3454 z1 x: t/ n9 x5 i* Y+ _
9.3.4 Hashin–Shtrikman Composite 346) m" b+ x( x4 p  T
9.3.5 Spherical Particulate Inclusions 347
2 A% U1 g2 p! c1 R9.3.6 Fiber Inclusions 349
/ @" a) D$ ]% @1 S/ {- b7 ~5 x9.3.7 Platelet Inclusions 3499 p& U* Q1 p# E0 G
9.3.8 Stiffness-Loss Maps 3504 f- j( D- ^; Q* D2 q0 k! u+ `9 H/ N
9.4 Bounds on the Viscoelastic Properties 353
* d1 G) J. R" C0 |, z9.5 Extremal Composites 354
; A' j, ^4 `' {2 d- X) N+ @4 w9.6 Biological Composite Materials 356! z- {: A* E3 L3 R% s
9.7 Poisson’s Ratio of Viscoelastic Composites 357
& J$ q0 h* A, F9.8 Particulate and Fibrous Composite Materials 3580 T2 A0 e: X! ~, a7 @
9.8.1 Structure 3583 d3 |0 ^& E  H; ~& [' c" g+ @
9.8.2 Particulate Polymer Matrix Composites 359) a: s2 S" {) D5 d3 N  I9 W
9.8.3 Fibrous Polymer Matrix Composites 361- b0 \5 t+ ^1 o
9.8.4 Metal–Matrix Composites 362% c! G6 r, B5 S# S: o- x/ c8 O
9.9 Cellular Solids 363
. M9 G' L( ?" w  X9.10 Piezoelectric Composites 366. c0 ]7 G- O9 ?6 C* M- l
9.11 Dispersion of Waves in Composites 366# h3 j5 T" V* K/ M( U3 t) A
9.12 Summary 367$ j9 s+ g$ c" A4 O
9.13 Examples 367
/ ^0 P4 J; g# K7 B1 Z8 A& K" q4 N9.14 Problems 3704 e. d$ q) x, m% A
Bibliography 370* s6 w" h; N4 o* y% Y

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10 Applications and Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . 377
8 @$ B# l6 g- V8 r& n2 y# `# M0 V( U10.1 Introduction 3772 P) D! p( U$ x' S- |( Q" w
10.2 A Viscoelastic Earplug: Use of Recovery 377
  G" q& ^0 F/ }! [. |3 c10.3 Creep and Relaxation of Materials and Structures 378+ x; ?  j# g/ _/ x
10.3.1 Concrete 378. y8 Z( k  N( x' H
10.3.2 Wood 378
4 h7 l/ ~' I5 R' B6 q10.3.3 Power Lines 379
5 l. A* p# [3 T/ N: h10.3.4 Glass Sag: Flowing Window Panes 380+ S, B6 w( P+ Z0 x/ f5 `- S$ @
10.3.5 Indentation: Road Rutting 3807 k( [+ z) U" X9 ~. C% }
10.3.6 Leather 3813 S7 l7 q' x- }8 [6 {5 b( Q
10.3.7 Creep-Resistant Alloys and Turbine Blades 381! k' z% N2 j) M  l
10.3.8 Loosening of Bolts and Screws 382
/ K" u1 f* K2 |10.3.9 Computer Disk Drive: Case Study of Relaxation 384
: r. p8 D4 G$ k( W10.3.10 Earth, Rock, and Ice 385
% X6 r& \) {3 E2 x10.3.11 Solder 386
! w# }9 V3 S* r3 C/ l10.3.12 Filamentsi nL ight Bulbs and Other Devices 387( T. B2 n% b# J2 e4 s5 t, \
10.3.13Tires: Flat-Spotting and Swelling 388
- I" X( D2 U( D; O2 G, F" y10.3.14Cushionsfor Seats and Wheelchairs 3882 I" h6 v' Y5 r) k
10.3.15 Artificial Joints 389
" e# X$ K& k, q( ]  F' D0 a2 H8 w10.3.16 Dental Fillings 389
1 j, V1 Z7 D2 `; Z! p( l( @, e10.3.17 Food Products 389/ g* c2 D9 u$ u
10.3.18 Seals and Gaskets 390
& \# _' \' `4 `10.3.19 Relaxationi nM usical Instrument Strings 390. u( n" J/ B8 ^" r
10.3.20 Winding of Tape 391
, s) U" O+ }$ k3 w% c% Y1 b10.4 Creep and Recovery in Human Tissue 391
, X" D8 Y' H! W7 D- P10.4.1 Spinal Discs: Height Change 391
! _$ W  ~4 x$ F+ S9 _10.4.2 The Nose 392
3 ~$ n" n4 k* f+ V1 _& S7 Q& k- \10.4.3 Skin 392$ C; z4 w; j+ d. l6 Q/ v- a
10.4.4 The Head 3937 c. \/ z/ B! d9 S8 ~
10.5 Creep Damage and Creep Rupture 394
2 Q# m3 F- V; t10.5.1 Vajont Slide 394
/ ~9 g2 I( r! M1 ?10.5.2 Collapse of a Tunnel Segment 3945 b- }5 `: }  n$ G1 V$ ]$ G) b4 P
10.6 Vibration Control and Waves 394
9 f' i: h9 {4 V  D8 Z; r$ {10.6.1 Analysis of Vibration Transmission 394
7 o1 i) `0 a- X2 D) M10.6.2 Resonant (Tuned) Damping 397
$ y' P+ E( u$ ]  U9 F10.6.3 Rotating Equipment Vibration 397
, _# |- n. @$ g) S10.6.4 Large Structure Vibration: Bridges and Buildings 398! v5 R7 C) @- n- ]# D
10.6.5 Damping Layers for Plate and Beam Vibration 399
4 ], m' i: @* n1 k$ Z2 e10.6.6 Structural Damping Materials 400
* c: g7 ~5 O& `! |10.6.7 Piezoelectric Transducers 402
. n0 q0 d5 t% m& G10.6.8 Aircraft Noise and Vibration 4027 y; f( V9 ]! i( X" f5 l
10.6.9 Solid Fuel Rocket Vibration 404
5 m/ N0 _: ]6 H9 C. G10.6.10 Sports Equipment Vibration 404
: T* L( v" f/ J) v$ {1 g6 G10.6.11 Seat Cushions and Automobiles: Protection of People 404
3 M" Z; i2 _" Z4 ^  Q0 |  ]10.6.12 Vibrationi n ScientificI nstruments 406. Y$ s, _7 u/ x
10.6.13 Waves 406
3 z# M# i; y+ C& F0 n5 `! g10.7 “Smart” Materials and Structures 407% {/ S) f- \; m
10.7.1 “Smart” Materials 407; c. b6 U: r9 T) F0 q3 R; ~: d, O
10.7.2 Shape Memory Materials 408
0 C/ [3 r! L1 Q# r6 o10.7.3 Self-Healing Materials 409$ d. J+ E5 f6 {$ Z& \" s8 ?, g
10.7.4 Piezoelectric Solid Damping 409
* I' @; p" ?0 Y9 X. O1 ]  s  d10.7.5 Active Vibration Control: “Smart” Structures 409
" v+ A/ C+ ^7 y! P+ }( [4 G! A4 z7 U1 [10.8 Rolling Friction 409
7 G( H* w0 i- t. p- @10.8.1 Rolling Analysis 410& L' U5 E! p9 P6 V1 |
10.8.2 Rolling of Tires 411
7 ^- a0 q1 |/ f) K10.9 Uses of Low-Loss Materials 4126 @+ k- _7 a7 n* Y
10.9.1 Timepieces 4121 C! H0 J5 Y  u' q1 v
10.9.2 Frequency Stabilization and Control 413
# t8 M  ~) {8 M3 L5 T: r8 e10.9.3 Gravitational Measurements 413: K# x0 v* E2 W# |0 U
10.9.4 Nanoscale Resonators 414( D1 h2 f1 v* u1 p0 y
10.10 Impulses, Rebound, and Impact Absorption 414; [6 K& L3 x5 X; K* N0 k3 Q- \" E
10.10.1 Rationale 414
$ g; r! D4 ^3 ~3 v4 h7 h  i1 Y. v10.10.2 Analysis 415
) @) Q* \  A! c- q10.10.3 Bumpers and Pads 418
- ]. S/ w* f, _1 i% N0 }, u10.10.4 Shoe Insoles, Athletic Tracks, and Glove Liners 4198 `0 L- c& @# ^7 V% b# d! _6 B
10.10.5 Toughness of Materials 419
" ]  \; ^, y5 T3 L+ |" {10.10.6 Tissue Viscoelasticity in Medical Diagnosis 4202 v; U0 W9 ~4 H6 [
10.11Rebound of a Ball 421/ A  Q; j7 g) B: w8 T; z) \" H4 B# I
10.11.1 Analysis 421
* q0 h- U) `2 u& Y% Q$ J10.11.2 Applications in Sports 422* u9 d/ C3 ~9 G! d8 I
10.12 Applications of Soft Materials 424
+ }/ Q) o1 c$ h6 H10.12.1 Viscoelastic Gels in Surgery 424& @7 H$ v; D6 s8 f: |& z
10.12.2 Hand Strength Exerciser 4241 s! c* m& H1 ~( {/ r" C! y
10.12.3 Viscoelastic Toys 424
/ G4 a8 r- {& K9 |/ Y6 J10.12.4 No-Slip Flooring, Mats, and Shoe Soles 425
, Z# e" h( I6 R: }  B% g3 b10.13 Applications Involving Thermoviscoelasticity 425
! r8 E9 F5 t' T- d2 N* c& O10.14 Satellite Dynamics and Stability 4261 b$ r9 J) c9 d, z1 ^5 l
10.15 Summary 4284 @' C7 K2 H4 B4 `& d* u
10.16 Examples 429
" g) i7 b; }1 `* W$ y1 v) o10.17 Problems 4317 W1 f8 |0 j0 j9 T1 `4 V: `
Bibliography 431: j; F6 S* z3 \9 y% y$ c

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A: Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441! a& M, X# B  c9 \
A.1 Mathematical Preliminaries 441
5 @1 d- }# b/ w. F; W2 `7 B; UA.1.1 Introduction 4413 w0 u3 X9 ?0 m  ^) W
A.1.2 Functionals and Distributions 441
, w' r$ ?: L  R6 N. a9 mA.1.3 Heaviside Unit Step Function 4426 O3 F% G' Z: d8 r: v  H/ h! n
A.1.4 Dirac Delta 4421 N  e- c0 D+ B" l
A.1.5 Doublet 443* m: m2 L  i/ q- K* Z9 _
A.1.6 Gamma Function 445
: i# g2 B  f& ?+ sA.1.7 Liebnitz Rule 445
% E( W" K9 x! Q5 H4 _  ]' b* H: ^A.2 Transforms 445
  v: {$ J: y. ?4 g6 ~, i6 dA.2.1 Laplace Transform 446" r0 B2 E+ R6 {9 G" |
A.2.2 Fourier Transform 446
4 c2 s/ j, h" I, W9 E5 t3 lA.2.3 Hartley Transform 447
4 c9 C6 d! B6 J! `9 oA.2.4 Hilbert Transform 447
- a$ q! B2 a! }A.3 Laplace Transform Properties 448& i4 p. {* \$ N) u* S2 v  @
A.4 Convolutions 449
5 Q& X( |* V+ W, C- QA.5 Interrelations in Elasticity Theory 451. S# A5 O& s) H5 E3 T; K
A.6 Other Works on Viscoelasticity 451; f8 h! n. J; b7 B
Bibliography 452' t" @) I# _* n9 w2 ~
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0 X% V% [3 J+ _  c4 kB: Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455! ]0 {5 O; I/ x6 Y. G
B.1 Principal Symbols 455
/ I$ u& |2 Y, [- ^  ^. d( R! i) @4 bIndex 457
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