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标题: 英文全书下载 Viscoelastic Materials. Roderic Lakes 2009 《粘弹性材料》 [打印本页]

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标题: 英文全书下载 Viscoelastic Materials. Roderic Lakes 2009 《粘弹性材料》
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! G% |3 h1 z* A目录  o- `0 g9 b' r  |" x$ k% Z

+ V- P4 U( @% n8 |Contents/ |$ ~( L; N9 n+ T
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Preface page xvii$ H  D" P4 D6 W0 |
1 Introduction: Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 C; {$ u6 K( S7 w% a
1.1 Viscoelastic Phenomena 1
' x  d; D9 B0 a8 K: r1.2 Motivations for Studying Viscoelasticity 3! K# S% m2 H; W% m, c2 N7 Q
1.3 Transient Properties: Creep and Relaxation 3" S$ @- \1 t- ~  k
1.3.1 Viscoelastic Functions J (t), E(t) 33 t1 }6 o/ K1 |" @9 R; O
1.3.2 Solids and Liquids 7% v1 d$ q3 p4 n
1.4 Dynamic Response to Sinusoidal Load: E∗, tanδ 8, E% J9 Z8 O* c0 q/ V
1.5 Demonstration of Viscoelastic Behavior 10) G: `) E" L+ c! Q
1.6 Historical Aspects 10- q6 h) M8 E# p
1.7 Summary 114 ~; {, q$ ?) t3 S) [
1.8 Examples 117 b; B% ^8 H+ V  N7 U
1.9 Problems 123 k$ J4 h) O, k4 i2 K; H+ I4 E* P& m
Bibliography 12+ r0 M' y$ b* f
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/ n6 q- t) U  ]7 h% i' n& c9 y9 A2 Constitutive Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 u7 s* y, O: K1 H0 C5 y7 l/ J0 h
2.1 Introduction 14
4 u4 r6 C. |  L$ ]2.2 Prediction of the Response of Linearly Viscoelastic Materials 147 k3 t: L4 m$ s4 I* r+ A; C& f5 B; ^
2.2.1 Prediction of Recovery from Relaxation E(t) 14- v6 @( x( ^, d0 O1 Y: I0 _9 l
2.2.2 Prediction of Response to Arbitrary Strain History 156 P$ }! @, y. x' |$ {
2.3 Restrictions on the Viscoelastic Functions 17
1 ?) j9 z# P) z: ^% j! S& |: V  b/ h2.3.1 Roles of Energy and Passivity 17/ H! z6 g2 T) c- L4 U# z- u4 S0 ]
2.3.2 Fading Memory 18. k8 H% p, t4 [  f4 p. o
2.4 Relation between Creep and Relaxation 19
! P. K" B% `( g" c9 e- Q2.4.1 Analysis by Laplace Transforms: J (t) ↔ E(t) 19
- Z% [) }3 x6 y0 _" d2.4.2 Analysis by Direct Construction: J (t) ↔ E(t) 20
) r1 ]* L0 v9 Z0 Y2 z2.5 Stress versus Strain for Constant Strain Rate 20
7 }, E  y7 J. ^4 C2.6 Particular Creep and Relaxation Functions 21
8 G" F5 j1 w: {+ ^2.6.1 Exponentials and Mechanical Models 21
; w- C% C1 Q  Y2.6.2 Exponentials and Internal Causal Variables 26& W1 {/ q6 ?4 j' b! Q8 U
2.6.3 Fractional Derivatives 27
2 M8 ^6 O2 a8 s9 h1 N) ]1 {9 L) r2.6.4 Power-Law Behavior 280 ?% ~& Q9 ^+ v4 x1 o) K, q
2.6.5 Stretched Exponential 29
' U3 S  r4 O) Q0 E( ^$ D2.6.6 Logarithmic Creep; Kuhn Model 29
: j+ b4 p3 ]1 A% [/ J9 S% f2.6.7 Distinguishing among Viscoelastic Functions 30
/ h) R) D2 J8 u. W% I2.7 Effect of Temperature 302 \& d, V0 R3 ~# C
2.8 Three-Dimensional Linear Constitutive Equation 33) B5 B8 W3 f. [* L
2.9 Aging Materials 35# v$ }6 X4 ?/ ]  H) W$ r
2.10 Dielectric and Other Forms of Relaxation 35; l  |' R% t( l* B
2.11 Adaptive and “Smart” Materials 36
, ?% P/ X' B) _6 Q4 y2.12 Effect of Nonlinearity 37
4 {: f# C4 _3 a; ~( A* m2.12.1 Constitutive Equations 37
' B- o- n7 a, o  W2.12.2 Creep–Relaxation Interrelation: Nonlinear 40& e- }. p* d2 T( O
2.13 Summary 43
$ }- T& N2 z" P3 d& }9 i" @2.14 Examples 43
! m; X% s1 w- C% H- r2 |2.15 Problems 51
" o" S2 I: _  l% {Bibliography 52
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3 Dynamic Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55% d+ Q  ]/ A% |+ ]* q7 a5 Z) Q
3.1 Introduction and Rationale 55
2 |% ?; _# X; O8 H2 Q/ _3.2 The Linear Dynamic Response Functions E∗, tanδ 56
" j4 a9 A9 ~  U3.2.1 Response to Sinusoidal Input 576 Z# C5 M$ z; f' h3 ?
3.2.2 Dynamic Stress–Strain Relation 59
: Y" L1 O, a' ]5 k( Q& A8 ~3.2.3 Standard Linear Solid 622 r8 |: q& m* Z" S
3.3 Kramers–Kronig Relations 63( }/ o) g3 I, x# i
3.4 Energy Storage and Dissipation 65
' g1 g& E6 A. q$ Y' F8 X2 k0 N4 |3.5 Resonance of Structural Members 67
5 J  H5 \. j. }+ t& ]3.5.1 Resonance, Lumped System 671 F; }/ _$ x# U
3.5.2 Resonance, Distributed System 71
2 K) N! z( H( [& Q3.6 Decay of Resonant Vibration 74) n: R; T3 W$ m- }/ H. O7 F* X8 @: X
3.7 Wave Propagation and Attenuation 77# K$ Q. J7 ]" C7 b, `& l! E# o; C! q
3.8 Measures of Damping 795 C0 @4 p9 s7 W
3.9 Nonlinear Materials 79; R8 c& W' A  ?( h
3.10 Summary 81
  ^3 I+ L+ a" x3.11 Examples 811 v* z5 n: D0 |
3.12 Problems 883 [6 s: ^+ H9 m) {
Bibliography 896 D. T: ]! N& l( t5 H* Z
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4 l& o/ F1 r; H6 @4 Conceptual Structure of Linear Viscoelasticity . . . . . . . . . . . . . . . 91
8 U& M+ b! N6 c6 J- ]! l5 l4.1 Introduction 919 |! [- ]+ M. @% ]4 S8 H6 k3 o9 V
4.2 Spectra in Linear Viscoelasticity 92
) H+ X  a% G& h3 V. u2 t7 |+ c4.2.1 Definitions H(τ ), L(τ ) and Exact Interrelations 92# V2 Q% q1 p) `# j9 y$ _. S( T+ Z. r
4.2.2 Particular Spectra 93
' w+ p/ P8 t$ c4 _- e& c4.3 Approximate Interrelations of Viscoelastic Functions 95+ o( j" [. s7 z6 M  z& s' p2 s
4.3.1 Interrelations Involving the Spectra 95
/ @: N/ }9 q; J9 t" x& {# r/ Q% Q4.3.2 Interrelations Involving Measurable Functions 98
' J1 ?6 e0 n) r4.3.3 Summary, Approximate Relations 101
8 @$ E1 L- m& W5 g+ W7 n1 U4.4 Conceptual Organization of the Viscoelastic Functions 101* e/ l& T/ k0 x' m
4.5 Summary 104& p- {* f6 G4 i7 y4 P: s
4.6 Examples 104
4 G9 z# b' x) _9 X/ O4.7 Problems 109( \% s# d6 t4 M% J
Bibliography 109
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. u/ z1 E. t4 b% l! N& ^& w5 Viscoelastic Stress and Deformation Analysis . . . . . . . . . . . . . . . 111
" ~% E  z1 I- n) h' ?' P( T! D) z5.1 Introduction 111" X4 k' U; f6 v0 E. F
5.2 Three-Dimensional Constitutive Equation 111' i4 n: V6 u8 e* r( r
5.3 Pure Bending by Direct Construction 112& j# A$ O7 ^8 M( ?
5.4 Correspondence Principle 114; l6 c7 V. d1 m; m
5.5 Pure Bending by Correspondence 116" B* }% [1 N& J0 t; N' G  Z
5.6 Correspondence Principle in Three Dimensions 116
' Y+ \5 n* \/ b( o4 Y7 X+ L2 G5.6.1 Constitutive Equations 116
' _2 a% Y9 [1 R3 T5.6.2 Rigid Indenter on a Semi-Infinite Solid 117
3 C: J8 @2 X5 y4 x" K5.6.3 Viscoelastic Rod Held at Constant Extension 119
- k4 k0 o$ Q! V0 M9 \5.6.4 Stress Concentration 119, }1 s: X$ h, L' H! s  J8 c; G
5.6.5 Saint Venant’s Principle 120
6 |) Q$ K3 L0 d1 U+ n5.7 Poisson’s Ratio ν(t) 121
+ Q2 w( q5 B0 d7 G; b5.7.1 Relaxation in Tension 1217 d) [7 y) a' T5 [8 G" B" i: k: a
5.7.2 Creep in Tension 1230 |& m6 @- Q8 `$ W
5.8 Dynamic Problems: Effects of Inertia 124
$ Q  v* o- S+ `' l/ I2 K/ `5.8.1 Longitudinal Vibration and Waves in a Rod 124
7 s1 p! M8 i3 R5.8.2 Torsional Waves and Vibration in a Rod 125% B5 M, h% v0 l( M/ Z
5.8.3 Bending Waves and Vibration 128- J$ K& G3 `- D+ n) \9 v
5.8.4 Waves in Three Dimensions 1296 q: m( l0 t9 C0 h+ j, _! P+ O
5.9 Noncorrespondence Problems 131
* l6 Y9 z) N& w  a; |* c. U* `5.9.1 Solution by Direct Construction: Example 131
9 ]9 m. j$ S0 Q" u; V  i5.9.2 A Generalized Correspondence Principle 132
1 P6 a% L4 A# u2 V+ A/ o) h; I5.9.3 Contact Problems 1328 W% p( x2 a2 u, O  H( Q
5.10 Bending in Nonlinear Viscoelasticity 133+ `0 G( F2 L5 ~9 A0 V
5.11 Summary 1343 ~$ J* I% c. ^5 c- {
5.12 Examples 1343 n$ M0 y4 B0 R! A" ]( J. H. `3 T5 Q
5.13 Problems 1428 K5 w& f% @9 h8 G
Bibliography 142
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6 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
( {7 p" _) ]: W/ M8 ?6.1 Introduction and General Requirements 145! T+ S6 ]" P' D  P" H
6.2 Creep 146) ?) F. q9 A2 F# b  X
6.2.1 Creep: Simple Methods to Obtain J (t) 146
" M; ^/ z; r( S' o5 U3 y( n6.2.2 Effect of Risetime in Transient Tests 146- C# T6 d  h3 M+ x8 g5 P
6.2.3 Creep in Anisotropic Media 148
6 d+ L: f" {$ W: c$ J5 b& q6.2.4 Creep in Nonlinear Media 148
- j: j( |; v! |6.3 Inference of Moduli 150/ o$ I( F, l' E) _' B2 K6 w
6.3.1 Use of Analytical Solutions 150! B" p2 G6 ~* c
6.3.2 Compression of a Block 151" H$ {+ s" W) @) K: L0 l' a2 q
6.4 Displacement and Strain Measurement 1523 R0 Z& I- P) A% o+ M
6.5 Force Measurement 156
% K& X) R7 z& ?1 i( E; ]8 X6.6 Load Application 157
8 F# [1 u5 b1 y% Q  q# P" z6.7 Environmental Control 157
/ D: J* l* ?  U; D+ V* ~6.8 Subresonant Dynamic Methods 1585 E" X! M) c, x9 [4 L
6.8.1 Phase Determination 158
  d  ?( N6 K) W% l6 d' E6.8.2 Nonlinear Materials 160
, x! U3 `8 Q8 k$ i- ]6.8.3 Rebound Test 161
7 Q7 _+ W' Q# H) b) E6.9 Resonance Methods 161* ?, ~. ~( S+ z( U
6.9.1 General Principles 161
, j# `. U. s; L' W& ?/ f6.9.2 Particular Resonance Methods 1636 ?2 i: k, a) o% C
6.9.3 Methods for Low-Loss or High-Loss Materials 166; `' \3 Q6 Y. @- R7 Y1 D
6.9.4 Resonant Ultrasound Spectroscopy 168
& h( U, p0 l" F! |& t4 x8 d6.10 Achieving a Wide Range of Time or Frequency 171% O# u8 G5 b& D0 L$ y" S  h
6.10.1 Rationale 171: a  P* f) _0 o3 |
6.10.2 Multiple Instruments and Long Creep 172# C% b7 D9 b+ h# b0 Q2 ]# [* f2 o
6.10.3 Time–Temperature Superposition 1724 n! a1 K( Q+ [3 C
6.11 Test Instruments for Viscoelasticity 173) X1 H' O9 y2 ]& n. c% @
6.11.1 Servohydraulic Test Machines 173
% [5 [  t$ r' G; \, Z6.11.2A Relaxation Instrument 174! c$ v9 l  i% F' P8 G$ w
6.11.3 Driven Torsion Pendulum Devices 174# l  X* L1 C9 D5 W3 w
6.11.4 Commercial Viscoelastic Instrumentation 178
; J, a# n! N! r$ Y6.11.5 Instruments for a Wide Range of Time and Frequency 179, n& R1 |. s  I* o% C; [1 e
6.11.6 Fluctuation–Dissipation Relation 1829 D  a9 q4 G. Q7 E
6.11.7 Mapping Properties by Indentation 183
' s: ?" ^0 H+ {+ ]9 {' Q" R: Q6.12 Wave Methods 184/ }: T/ _  L  ?$ W8 q+ T; D4 D6 ~6 g! S
6.13 Summary 188% {( f) m6 d4 D0 G/ }
6.14 Examples 188
1 m. c7 A  e1 T& P' q( z; V2 ?0 [2 K6.15 Problems 200  g" ?1 ~4 I! ^4 I8 ]$ u. |
Bibliography 201# R% T% {- o) g+ c4 Y
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/ K* U, l" F2 Z! y( c7 Viscoelastic Properties of Materials . . . . . . . . . . . . . . . . . . . . . 207
% m% @: e% E9 U( O+ V( M) P7.1 Introduction 207
; ~9 S# [5 S, b4 P) W' \+ {. J! u7.1.1 Rationale 207
0 g, a$ W3 `7 ~3 `* H# i! K7.1.2 Overview: Some Common Materials 2079 Y. b, z! o8 [
7.2 Polymers 208' _! h) |" S5 E. U6 u
7.2.1 Shear and Extension in Amorphous Polymers 2083 g! {, e- h4 D4 A  u% y4 t
7.2.2 Bulk Relaxation in Amorphous Polymers 212; f* D" u! E( R7 ?  l+ L3 ]2 c+ r
7.2.3 Crystalline Polymers 213
  U' n3 O2 j  N; S1 L7.2.4 Aging and other Relaxations 214" B3 ^0 T: X" m$ L. G
7.2.5 Piezoelectric Polymers 214# X/ e% X2 G. x; w; |& U0 H( ~
7.2.6 Asphalt 214
: s. ~1 `0 J( P# u7.3 Metals 215
/ G1 q& T$ g7 p. c7.3.1 Linear Regime of Metals 2157 U4 k4 `. S7 m" j! A5 ~
7.3.2 Nonlinear Regime of Metals 217* m! ]4 Q+ @* ^4 K* I  H1 O
7.3.3 High-Damping Metals and Alloys 219
; }5 ^& Y  Q2 S0 o# ~8 ?( d% M7.3.4 Creep-Resistant Alloys 224/ U/ u3 U2 k) ?6 @- m& `
7.3.5 Semiconductors and Amorphous Elements 225. Y" g* v3 U* X+ e
7.3.6 Semiconductors and Acoustic Amplification 226
9 M' O5 y1 z7 K4 f8 S/ L8 e8 ]" ^! L* _7.3.7 Nanoscale Properties 2263 W2 }% k) w7 Z' r  D( A- j
7.4 Ceramics 227
  \8 y6 y1 N! M7.4.1 Rocks 227+ O; Y" n& o- p  V2 j
7.4.2 Concrete 229
" H* |) N  W* B- x7.4.3 Inorganic Glassy Materials 231
: w  s7 f# J  W9 I7.4.4 Ice 231
9 a  R# @0 J# X% o8 N7.4.5 Piezoelectric Ceramics 232  `% O/ [& |( z" D; L+ u
7.5 Biological Composite Materials 233
) G( q, k& f; U7 B6 L2 [, p0 O# H9 n7.5.1 Constitutive Equations 234; x) o3 w% W' I
7.5.2 Hard Tissue: Bone 234
) Q+ m: ]$ U: `7.5.3 Collagen, Elastin, Proteoglycans 2365 L/ p3 K2 f: q+ {! Y, c* S
7.5.4 Ligament and Tendon 237; N+ E1 e) t0 B9 C5 }( {
7.5.5 Muscle 2400 V! E5 V, d% G1 U  C( z) R. H
7.5.6 Fat 243& L9 O; o" _) I3 z1 \
7.5.7 Brain 243
. T& {- Q2 j8 a7 L. D7.5.8 Vocal Folds 244
  o9 n  c) C5 |  f7 J7.5.9 Cartilage and Joints 244
7 l. S3 c. A: m' q' D7.5.10 Kidney and Liver 246
& J# y; Q9 @' U1 w7 ~7.5.11 Uterus and Cervix 246* I" M$ K  ]" R4 K) Q# O
7.5.12 Arteries 247
; W! \8 o" V5 p- h  o% O7.5.13 Lung 2483 o  \4 O0 p6 @3 Z8 ~( q- }# Z
7.5.14 The Ear 248- @7 j) Z8 ]# `4 |
7.5.15 The Eye 249& X* |$ y$ w, ?6 ^3 `7 n
7.5.16 Tissue Comparison 251* u: V# g7 Y2 h9 j; M
7.5.17 Plant Seeds 252" e) e' R) ]# @, R7 j% N
7.5.18 Wood 252* k8 [5 D. W9 x$ e, h  g& D, X
7.5.19 Soft Plant Tissue: Apple, Potato 253
" p# I) y; R1 G* p$ _9 _2 f8 W5 R7.6 Common Aspects 253* W" b4 M8 `7 O0 Q; q* P
7.6.1 Temperature Dependence 253) ?: ^6 h4 ^* ~* k$ b+ D) X; R4 F
7.6.2 High-Temperature Background 2541 h% |" W3 z7 n
7.6.3 Negative Damping and Acoustic Emission 255+ D) c& h3 Y+ T) T
7.7 Summary 255
# Q3 @; a6 k  ?7.8 Examples 255/ ~. [  Q1 C4 t& D& a$ \+ _; x) ~
7.9 Problems 256
- h  ]% b- X6 H' i- b+ JBibliography 257
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8 Causal Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
9 c' B3 M( P5 U8.1 Introduction 271: t% N8 Q8 X! v) I% J. r! I( A
8.1.1 Rationale 271
* ]; }: F* x, L& c8 }" D8.1.2 Survey of Viscoelastic Mechanisms 2712 s/ U6 R, W0 m% d( v  B
8.1.3 Coupled Fields 273
( j% _5 n; A8 e1 X8.2 Thermoelastic Relaxation 274
0 j6 Q% p6 x9 g' z* v2 f8.2.1 Thermoelasticity in One Dimension 2743 n" s* _* c  O! j6 T7 c
8.2.2 Thermoelasticity in Three Dimensions 275
  t4 f6 e6 @. U8 f1 R8 v( d7 _# z  O8.2.3 Thermoelastic Relaxation Kinetics 276( g: T/ N2 G2 |
8.2.4 Heterogeneity and Thermoelastic Damping 278
) H0 o5 o6 b0 o1 C* x  q8.2.5 Material Properties and Thermoelastic Damping 280
" [2 ]! @+ N5 w/ |' j/ P" ^8.3 Relaxation by Stress-Induced Fluid Motion 280$ M2 J- L8 S' a7 k+ w
8.3.1 Fluid Motion in One Dimension 280& q- X6 T+ _' i. o* g- D
8.3.2 Biot Theory: Fluid Motion in Three Dimensions 281
6 t& X1 T2 |5 T, B; g; {8.4 Relaxation by Molecular Rearrangement 2861 m2 X5 m/ e/ d( a  b, ^4 q
8.4.1 Glassy Region 286
% s, y) d& @' Q1 X  M8 ]8.4.2 Transition Region 287) z/ e- a$ E1 |
8.4.3 Rubbery Behavior 2898 t& |4 E% H" u1 y( y$ Y
8.4.4 Crystalline Polymers 291
1 L0 p; ~8 v) [' u; X7 U8.4.5 Biological Macromolecules 292
' ?* O' v) E; r* |2 Z4 ~5 F8.4.6 Polymers and Metals 292
3 [# ^. _# u- h2 d- k/ x* i+ o  L$ I8.5 Relaxation by Interface Motion 292- t! ^8 X6 z" p$ D
8.5.1 Grain Boundary Slip in Metals 292
6 K! I$ ]* K! x( r4 ?+ F0 t8.5.2 Interface Motion in Composites 294
+ q( ~# D& A) N) z8.5.3 Structural Interface Motion 294
! O' H7 j7 F* ?  z* O# c8.6 Relaxation Processes in Crystalline Materials 294$ u, G- ^1 y! U$ {( u# `1 s" ^/ x
8.6.1 Snoek Relaxation: Interstitial Atoms 294) e0 u& }2 B) O% k8 s9 W
8.6.2 Zener Relaxation in Alloys: Pairs of Atoms 298( b  f+ M0 T* m! [. y1 Q
8.6.3 Gorsky Relaxation 299
4 a) {. T6 \, F8 `6 o: t6 k% R8.6.4 Granato–L ¨ ucke Relaxation: Dislocations 300' n- }# F% L: q: B0 H6 }/ V
8.6.5 Bordoni Relaxation: Dislocation Kinks 303
+ h. m9 x1 A: l: a5 K0 @9 b8.6.6 Relaxation Due to Phase Transformations 305( U" e' Y. c3 y2 o* f
8.6.7 High-Temperature Background 314! M1 }, L# r, g" e& \& M
8.6.8 Nonremovable Relaxations 3158 b/ M& v" k# |7 f
8.6.9 Damping Due to Wave Scattering 316- W' C" v" Q1 [- B; a" R8 b
8.7 Magnetic and Piezoelectric Materials 316
3 r: J1 D( w9 \) T5 m1 j8.7.1 Relaxation in Magnetic Media 3167 p. ~3 Z' S. ]* `# S6 B  Y
8.7.2 Relaxation in Piezoelectric Materials 318  K5 }* U' i+ {8 @( C: p
8.8 Nonexponential Relaxation 3220 P# u, G; X( \- D8 t! G
8.9 Concepts for Material Design 3239 r. u$ w1 R& O; I: C! m; v
8.9.1 Multiple Causes: Deformation Mechanism Maps 323
# L( e3 u/ Q6 h0 I8.9.2 Damping Mechanisms in High-Loss Alloys 326* I1 k. z' I0 \! v4 R1 f2 F. ]* O7 U' q
8.9.3 Creep Mechanisms in Creep-Resistant Alloys 326
' Q8 o4 U) f2 V# `+ j8.10 Relaxation at Very Long Times 3275 T% }9 y5 Z5 p& d& A
8.11 Summary 327
* M1 m: z- @" K% ?( i1 C1 t0 Z# R$ u8.12 Examples 3287 R, [3 L) s" B. n* L! \
8.13 Problems and Questions 332) J  C; v: h1 W+ `/ h3 D
Bibliography 332
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- z; I; h2 ~/ _& @, C9 Viscoelastic Composite Materials . . . . . . . . . . . . . . . . . . . . . . . 341
$ [4 Z& u- R6 W5 c' E- M+ z6 m+ S9.1 Introduction 341- i& o  v2 _7 u7 {8 t3 a; {3 s
9.2 Composite Structures and Properties 341. B& C+ P- y0 m' J3 K
9.2.1 Ideal Structures 341
1 e+ f4 l3 V. b" d7 ~9.2.2 Anisotropy due to Structure 342& Q- v" @- Z" d0 k6 p, A2 l  e
9.3 Prediction of Elastic and Viscoelastic Properties 344
! d, x; f( W0 T% i9.3.1 Basic Structures: Correspondence Solutions 344$ M/ w8 M  s) f9 W- T7 s5 H
9.3.2 Voigt Composite 345, w4 e. a. ]5 J2 s. m8 n
9.3.3 Reuss Composite 345/ b4 F+ s( [$ v  m( _0 e$ e
9.3.4 Hashin–Shtrikman Composite 346. k4 M+ `% W' f- n
9.3.5 Spherical Particulate Inclusions 347
  E0 H3 ]5 S) R2 D9.3.6 Fiber Inclusions 349, b# S0 B- y) [
9.3.7 Platelet Inclusions 349
" }3 o/ b9 X5 L- u" g# w: `9.3.8 Stiffness-Loss Maps 350
, {! ]0 T6 a. ?9.4 Bounds on the Viscoelastic Properties 3530 }5 k2 {9 c$ W' n; c0 I  D. A" o
9.5 Extremal Composites 354' z1 n: M. _7 r+ `* V- k
9.6 Biological Composite Materials 3560 D% j. I/ L# i! G5 y0 w
9.7 Poisson’s Ratio of Viscoelastic Composites 3574 n) ^1 j; t4 s9 f  K" w
9.8 Particulate and Fibrous Composite Materials 358
$ @* h4 R) ]8 f- ]3 G* e9.8.1 Structure 3581 }  v. `9 q' y$ q! o$ S8 m
9.8.2 Particulate Polymer Matrix Composites 3596 ~2 P6 F) Z4 O0 C0 x) `
9.8.3 Fibrous Polymer Matrix Composites 3614 F2 e! z" Z% c6 `
9.8.4 Metal–Matrix Composites 362
* p" \: p4 B6 j2 [" k2 E/ m& g# U9.9 Cellular Solids 363% |2 C5 c1 c" m! d' E4 P
9.10 Piezoelectric Composites 366% ~, u9 l* ?- I: Z
9.11 Dispersion of Waves in Composites 3664 o8 a, a  o5 N+ `
9.12 Summary 3673 h# v* K& n7 M; |: ^
9.13 Examples 367
. T( W# N& l' ?% j8 K# D9.14 Problems 370, X- Y. E; L: [3 b
Bibliography 370
, F, G% A0 P3 x$ y: c) ]/ p8 X4 g+ M2 G; G& b* Y8 \: p

1 Q1 W* c1 }$ e! m! ~# b4 ~/ n; J! ?8 d  E8 y4 H" R- Y4 b8 `
10 Applications and Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . 377
4 |+ h) B1 E! O4 R* v1 w4 c( j10.1 Introduction 377; q$ Z' ^! ]% v5 G( p
10.2 A Viscoelastic Earplug: Use of Recovery 377* C# C8 d3 `* b; _) i
10.3 Creep and Relaxation of Materials and Structures 378
/ X- X3 h  P4 x1 R/ G* r2 z/ p( n10.3.1 Concrete 378) g: ^2 Y! v$ V  @
10.3.2 Wood 378: X' ]1 z( h, R2 Z
10.3.3 Power Lines 379
4 N9 A3 k! c8 o9 E( b+ s10.3.4 Glass Sag: Flowing Window Panes 3809 O; E+ I, e4 ?
10.3.5 Indentation: Road Rutting 380# h4 z" ^  O! m7 z7 E5 k% D
10.3.6 Leather 3811 @& k+ r5 ?# c9 L% N; }
10.3.7 Creep-Resistant Alloys and Turbine Blades 381# x( B3 A- C  e8 _# s! E8 ~0 b% D. p
10.3.8 Loosening of Bolts and Screws 3823 |. y, {( i, n3 ~" Y- ]
10.3.9 Computer Disk Drive: Case Study of Relaxation 384
) X* ^( i* J2 M. A5 l- a10.3.10 Earth, Rock, and Ice 385  k5 \5 v% a1 J& `$ ]
10.3.11 Solder 386/ ?6 Y$ Q) |2 W0 y  @7 n
10.3.12 Filamentsi nL ight Bulbs and Other Devices 3872 X! O4 F4 ^3 S) ]8 X  g% ?
10.3.13Tires: Flat-Spotting and Swelling 388/ F! T$ G/ Y. U: A; |( x$ h
10.3.14Cushionsfor Seats and Wheelchairs 388/ B% x( C# k6 S6 T4 r
10.3.15 Artificial Joints 389
0 Z* K+ U# n$ C8 |* J7 A* V10.3.16 Dental Fillings 3899 S9 |! W* M& C: G; {
10.3.17 Food Products 389
: p6 k2 P( V; u) n2 Q% P10.3.18 Seals and Gaskets 390
/ n% I) w/ m3 F6 k1 d5 T7 N0 f* Z10.3.19 Relaxationi nM usical Instrument Strings 390
: ]# `' e! v1 E$ A10.3.20 Winding of Tape 391
4 p# N& v7 n# Q10.4 Creep and Recovery in Human Tissue 391
/ R7 W* d' z, U) U% a: y$ ~- _10.4.1 Spinal Discs: Height Change 391- K9 \$ l8 r; p& s
10.4.2 The Nose 392
. }5 i. w. l0 C& W10.4.3 Skin 392
0 F5 w% U( V4 f- T4 k- n10.4.4 The Head 393
2 B+ g3 U$ ?3 L' {' {" d3 q) X10.5 Creep Damage and Creep Rupture 394
) L6 Z% f) y+ I% i10.5.1 Vajont Slide 394
0 \& }0 N2 f; e2 T" v; B10.5.2 Collapse of a Tunnel Segment 394
: G3 Q: j" g. X8 a. ?10.6 Vibration Control and Waves 394
/ I" _, o9 Q4 M! i0 R. U% ]. }10.6.1 Analysis of Vibration Transmission 394
8 R" [( h& G) |, f* H# |' _" ^10.6.2 Resonant (Tuned) Damping 397* U5 L0 D( s/ B8 A$ s
10.6.3 Rotating Equipment Vibration 397
( p/ ?0 p# z1 J& E  ?3 n10.6.4 Large Structure Vibration: Bridges and Buildings 398$ X9 a5 G. }4 s2 j
10.6.5 Damping Layers for Plate and Beam Vibration 399
9 H5 O# a$ K0 i2 L10.6.6 Structural Damping Materials 400
+ m, K4 ?1 _; \7 K, [( M7 x3 N5 T10.6.7 Piezoelectric Transducers 402
, P) x, d/ l8 i5 K, A10.6.8 Aircraft Noise and Vibration 402
+ `1 v, }; J  D% u* H- o3 \10.6.9 Solid Fuel Rocket Vibration 404
6 x- F& h1 c* N+ l4 U10.6.10 Sports Equipment Vibration 404
% O1 Z0 a6 F7 g3 v4 }; l0 k8 k10.6.11 Seat Cushions and Automobiles: Protection of People 4044 Q, r  s8 _% ~- O0 v
10.6.12 Vibrationi n ScientificI nstruments 406
! P: O* T; X, z; a3 I- y8 D  D  L, C& W10.6.13 Waves 406
, d( ?9 x7 o2 `2 M) E0 N+ g10.7 “Smart” Materials and Structures 4074 R$ }7 k/ }& d
10.7.1 “Smart” Materials 407+ `$ A8 R. B7 n4 M
10.7.2 Shape Memory Materials 408& E! S. T( @, N+ ?* ?' I
10.7.3 Self-Healing Materials 409  k$ e# B5 c: }  b! I7 d4 Y
10.7.4 Piezoelectric Solid Damping 409+ |" E+ t) F* q8 R1 d
10.7.5 Active Vibration Control: “Smart” Structures 409
" e; N+ N* h9 m8 V10.8 Rolling Friction 4092 \+ Y4 i- o6 y& r5 T0 Y0 K
10.8.1 Rolling Analysis 410
8 l, p9 u/ c/ ^9 S. L: N* A7 x10.8.2 Rolling of Tires 411
7 ^+ @; P: R% z7 z* ]5 r10.9 Uses of Low-Loss Materials 412
2 n$ c( H6 A2 \7 E- T10.9.1 Timepieces 4121 z8 O6 Z4 D/ K- K# S1 {1 W1 G
10.9.2 Frequency Stabilization and Control 413
" z8 |9 N1 W! [  |% v/ w" g10.9.3 Gravitational Measurements 413
" |, x1 E1 g9 m+ g5 Q9 e10.9.4 Nanoscale Resonators 414
% P5 E/ Y7 ]$ s  R) ?3 Q10.10 Impulses, Rebound, and Impact Absorption 4143 F$ J' Q9 C+ |6 h
10.10.1 Rationale 4145 l4 a6 Y7 q' j( _1 G
10.10.2 Analysis 415( i, U" }% D$ |$ i( U7 |
10.10.3 Bumpers and Pads 418
# Q: V- ~& y! Z! S10.10.4 Shoe Insoles, Athletic Tracks, and Glove Liners 419' |3 n% i/ u+ I" T3 Q
10.10.5 Toughness of Materials 419
- W0 ?+ K& G- z' e! B6 O% _10.10.6 Tissue Viscoelasticity in Medical Diagnosis 420
! J) ~4 o$ J$ @  z+ T$ \4 Q- o' ^+ U8 r10.11Rebound of a Ball 4217 f, _- V, F7 b6 c3 N
10.11.1 Analysis 421' ?9 `# R8 P  O3 Q, n: A) g) K; b
10.11.2 Applications in Sports 422! f1 l1 N" u" x, g- n3 F7 |
10.12 Applications of Soft Materials 424
  g; w' N; E, b8 L5 P2 E10.12.1 Viscoelastic Gels in Surgery 424+ I. N8 H  h( }1 c) `: \& p
10.12.2 Hand Strength Exerciser 424
, N% `1 r1 f% }9 C8 [10.12.3 Viscoelastic Toys 424
$ {8 k2 W) U0 ], l) l+ P+ U5 P10.12.4 No-Slip Flooring, Mats, and Shoe Soles 425
5 y2 }" F. j) r; f& `* M10.13 Applications Involving Thermoviscoelasticity 425+ s& X! j+ h0 ?
10.14 Satellite Dynamics and Stability 426$ x9 z1 X& |/ l, q' m
10.15 Summary 428
' Z) O, v) M& _$ p$ y$ S10.16 Examples 429# {  j. {  B' k3 ^' l' V, F- j
10.17 Problems 431! M  d3 Z- ]+ N6 U5 N
Bibliography 431
$ [- o) [: b0 j0 F7 X* a  Z9 m
% C% L# j- J) F$ Y( @: c) e7 \1 m$ T5 q- f
4 U/ A( I$ V: Y/ K, K
A: Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441* L% v) n) g/ {7 |$ b2 R
A.1 Mathematical Preliminaries 4417 V: P' `/ K. p% E9 x
A.1.1 Introduction 441$ W$ ~: w+ p, N# B7 O
A.1.2 Functionals and Distributions 441
; g5 s. q! L. K' j/ F, lA.1.3 Heaviside Unit Step Function 442
7 J; E2 G1 z. c+ f- U+ R) gA.1.4 Dirac Delta 442
9 ~8 R: l2 }6 O2 f! `  H5 c) U9 iA.1.5 Doublet 443
, M$ M6 w5 @7 }& Y/ `A.1.6 Gamma Function 445( w7 U0 L# _. |
A.1.7 Liebnitz Rule 4450 O1 l0 {3 p" H- E" {' u4 A. I# C
A.2 Transforms 445/ V& p8 ?* N/ ~) s
A.2.1 Laplace Transform 446
+ e/ g! P  M: TA.2.2 Fourier Transform 446
5 O9 c# _& U1 mA.2.3 Hartley Transform 4473 }" v/ O5 n: i9 X; M. o
A.2.4 Hilbert Transform 447
" \' {! x8 i% K9 n! W2 ?* LA.3 Laplace Transform Properties 448
9 H: ]' n0 b2 N8 |A.4 Convolutions 449
; v: R* ~* H1 O, H' m) xA.5 Interrelations in Elasticity Theory 451
" s# R$ y6 L! @7 O% U* n% xA.6 Other Works on Viscoelasticity 451
& N! i: ?- h9 q/ C% b! f! k3 x1 EBibliography 4521 W& \. x1 z: U0 N+ c2 {7 k. y
/ _* @1 R) u8 U) t! Y' `' e) L

# H$ n5 `5 ]1 Y7 ^+ Z7 {B: Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455+ a+ S" o. @* w  M
B.1 Principal Symbols 4553 h/ m0 K6 I: D
Index 457& ]$ H$ `& ~* [; w5 Q* _) C, J  W

$ i6 \. E4 [4 ], |, }1 z
$ l( j5 s' e1 J




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