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# X9 ]. L* W- W* V) p% q目录9 X N2 i7 C' S% t
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Contents7 @1 R y5 i, G6 I+ d4 L
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Preface page xvii! ]9 W6 t5 ^2 X1 o
1 Introduction: Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1! z6 F; [. R, U
1.1 Viscoelastic Phenomena 11 X; R2 G9 \! L) \4 u% I
1.2 Motivations for Studying Viscoelasticity 3
/ s; k* P s7 M7 F7 P- T8 ]1.3 Transient Properties: Creep and Relaxation 3
! C0 |" _4 y7 d( e3 {% y) F1.3.1 Viscoelastic Functions J (t), E(t) 3
) Z' |8 }: [# n5 T' f) F; U1.3.2 Solids and Liquids 70 V# Z# e9 y- B) }$ S- M
1.4 Dynamic Response to Sinusoidal Load: E∗, tanδ 8# ^; i+ V0 C* ?; X- Q
1.5 Demonstration of Viscoelastic Behavior 10* T3 | k, K0 I: @& r
1.6 Historical Aspects 10
4 S9 D( w$ D- w9 h# M8 `0 {( C1 \1.7 Summary 11! Q' w3 Y+ J8 q0 o* t7 O9 j- v
1.8 Examples 112 y4 `! N2 x& C. N& w ~3 }( f- q
1.9 Problems 12
- Y' H H7 e0 h5 N7 I# ]Bibliography 12
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2 Constitutive Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
& Z7 S7 {6 d! H% Y/ Q* m0 w2.1 Introduction 14
7 P. {5 G6 G* N, `4 ~% V4 W/ x2.2 Prediction of the Response of Linearly Viscoelastic Materials 14
. d* ] f" U8 ~0 x! C# _& g2.2.1 Prediction of Recovery from Relaxation E(t) 141 |% \0 p8 G7 B
2.2.2 Prediction of Response to Arbitrary Strain History 15/ }) G* | ]( B1 z5 i/ P
2.3 Restrictions on the Viscoelastic Functions 179 C8 {5 I7 F# s8 K" s) Z% N
2.3.1 Roles of Energy and Passivity 17
/ D/ |( h8 w7 v# s6 l2.3.2 Fading Memory 182 C S- |2 \4 @# y: j* D M
2.4 Relation between Creep and Relaxation 198 W, y: k4 \! L f# X( l. x
2.4.1 Analysis by Laplace Transforms: J (t) ↔ E(t) 19
0 \7 b9 g3 u+ ] x" e; W5 S2.4.2 Analysis by Direct Construction: J (t) ↔ E(t) 20/ S+ V8 C- P9 `4 k) @3 W Q
2.5 Stress versus Strain for Constant Strain Rate 209 m; X5 u f3 p
2.6 Particular Creep and Relaxation Functions 21
P6 p- O. ~+ }% Q) B3 h9 g2 ^: p& Z2.6.1 Exponentials and Mechanical Models 21
: e, L/ g3 ~6 U* h2.6.2 Exponentials and Internal Causal Variables 26: R1 f- `" U; c/ s3 ~
2.6.3 Fractional Derivatives 27
" _+ U9 h M$ W. `: b2.6.4 Power-Law Behavior 28( q W* ^& d6 T$ Y9 C
2.6.5 Stretched Exponential 299 s4 v5 E1 ?; ]3 c+ Y
2.6.6 Logarithmic Creep; Kuhn Model 29
: J# n, O. }" O# @2.6.7 Distinguishing among Viscoelastic Functions 30
) f- p- |/ E8 F8 S/ q+ r, i2.7 Effect of Temperature 30
- R: s0 ^8 R1 o" Y2.8 Three-Dimensional Linear Constitutive Equation 33, K( L* |0 k! H( Q( [
2.9 Aging Materials 35
" P2 d* R( U" x! f! X0 ?( L2.10 Dielectric and Other Forms of Relaxation 354 k0 @' }2 t2 [9 w9 s' R
2.11 Adaptive and “Smart” Materials 36
' `+ W, n/ W1 ~5 U& R% D0 q2.12 Effect of Nonlinearity 37
/ @" ^/ ^9 H5 }2.12.1 Constitutive Equations 37 V) D. c6 b1 p! ~0 n! e2 b# l
2.12.2 Creep–Relaxation Interrelation: Nonlinear 40, U3 p/ ?" y: ^1 e7 ]# k
2.13 Summary 43' x f( q- V% o
2.14 Examples 43
, ?$ M3 x: l1 n$ d& V' E! L! q, N2.15 Problems 51
* D- t5 W/ ?; Z5 T* ? r+ @: x, VBibliography 524 s9 Z7 o9 | z' [7 O* b: x
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3 Dynamic Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3 k9 y$ [; k2 ?( B. P% W3.1 Introduction and Rationale 55( A. N- \4 Q' ], A, |5 u/ c7 H
3.2 The Linear Dynamic Response Functions E∗, tanδ 56
8 X4 | F: r: N3.2.1 Response to Sinusoidal Input 57
* X8 o6 s) y+ w" p4 O7 [* `+ R3.2.2 Dynamic Stress–Strain Relation 59; B$ C9 n5 L2 k$ j* K2 M) t
3.2.3 Standard Linear Solid 62
1 M: {8 _7 {& m2 ]. f3.3 Kramers–Kronig Relations 63
( ^) Q. v s0 s. u8 R3.4 Energy Storage and Dissipation 65
" ?9 [9 Q2 X6 P R f+ A$ z3.5 Resonance of Structural Members 673 O: n& p4 O, s% m0 P7 v0 O0 D) w
3.5.1 Resonance, Lumped System 67. z3 n% B7 \ R i y5 B
3.5.2 Resonance, Distributed System 715 U7 V9 c# K+ c7 n
3.6 Decay of Resonant Vibration 74
. p* a3 [# j8 y9 U( r! E) r/ O& \3.7 Wave Propagation and Attenuation 77" P2 _: n5 ]1 C# X, c# U5 H* F5 T9 e
3.8 Measures of Damping 791 }% S% P, K$ T- ?( j- F
3.9 Nonlinear Materials 79
* y% F: J S+ [; N- M3.10 Summary 81$ e, X, d {0 K1 h
3.11 Examples 81/ f4 v; ]6 W! ]2 G4 F' T
3.12 Problems 88" Y& z2 J& G" C) n
Bibliography 89
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. S9 s! Z0 ^! ~4 D' L4 V4 Conceptual Structure of Linear Viscoelasticity . . . . . . . . . . . . . . . 91
8 i5 u0 N7 _) `9 i- k4.1 Introduction 91
* W+ K( Y1 {$ A7 l6 P4.2 Spectra in Linear Viscoelasticity 92
6 ?3 y# U& b2 g8 d0 M! @6 o4.2.1 Definitions H(τ ), L(τ ) and Exact Interrelations 92& E* N9 k; V; s
4.2.2 Particular Spectra 93
' E" N* d6 L+ A+ p. ]$ t4.3 Approximate Interrelations of Viscoelastic Functions 95
5 ^) E- `( u# k; ]+ x& j) ^$ x4.3.1 Interrelations Involving the Spectra 95
1 _& o* x2 Y$ |" B! Z* q4.3.2 Interrelations Involving Measurable Functions 98( c4 m( y$ R5 ]
4.3.3 Summary, Approximate Relations 101
% i3 ~; P* T7 Q4.4 Conceptual Organization of the Viscoelastic Functions 101
, Z. o' D' Y; ]& n* T4.5 Summary 104- p( {5 K* A! q( U! {
4.6 Examples 104
, x) j; g( b) n! T: Z2 t4.7 Problems 1090 n2 _+ O# E( _* N
Bibliography 109$ H- N! Y3 ~3 M' |/ N
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5 Viscoelastic Stress and Deformation Analysis . . . . . . . . . . . . . . . 111
1 o9 a9 C6 P- ^# E5.1 Introduction 111
0 Q: [* w% _& b% b |4 L& X5.2 Three-Dimensional Constitutive Equation 111! N* N0 {5 o& c: V( R; k! J
5.3 Pure Bending by Direct Construction 112
, l. K' }: F# x( b6 J) c$ D5.4 Correspondence Principle 114
; N0 x9 R. v [/ I# N* H3 N" O# m5.5 Pure Bending by Correspondence 116+ L/ g2 y: \, ]2 F) A2 H2 Q) O5 l
5.6 Correspondence Principle in Three Dimensions 116
7 ? C: c/ S/ o' D3 n5.6.1 Constitutive Equations 116
% f/ K m; `: B5.6.2 Rigid Indenter on a Semi-Infinite Solid 117' @ B. J* F( \$ C' c
5.6.3 Viscoelastic Rod Held at Constant Extension 119! j! @* c* s+ c0 o- `% j
5.6.4 Stress Concentration 119
2 R$ t# u, R+ B$ w3 h0 v* y5.6.5 Saint Venant’s Principle 120 O. c' y* D. M' {: g9 Q. G$ I) l
5.7 Poisson’s Ratio ν(t) 121
5 k! q% {9 D2 `7 M. Y: Z% q5.7.1 Relaxation in Tension 121* ~) G( \. @, {0 j+ n6 h. U# `
5.7.2 Creep in Tension 1239 R$ @6 O* c7 Z& q
5.8 Dynamic Problems: Effects of Inertia 124
y) U3 ^/ j3 T$ w! r. C# x7 l1 C) ~5 B, W5.8.1 Longitudinal Vibration and Waves in a Rod 124# o/ w7 t; J* r4 x# o3 x( i
5.8.2 Torsional Waves and Vibration in a Rod 125
# R$ }+ m0 f4 m5 i0 t+ N0 }7 {; W5.8.3 Bending Waves and Vibration 128
/ k3 L# s: y# C$ h" M) g. [5.8.4 Waves in Three Dimensions 129
; r, S& s) r) ~5.9 Noncorrespondence Problems 131' _5 `0 _4 T8 R0 N; ]
5.9.1 Solution by Direct Construction: Example 1318 _0 s" P4 l/ U6 |
5.9.2 A Generalized Correspondence Principle 132
) w7 @) W% U& o; x2 I/ Z G) [; l5.9.3 Contact Problems 1322 D% Q/ ?5 r$ b8 }; W \1 i
5.10 Bending in Nonlinear Viscoelasticity 133
, i# q( s( u/ h5.11 Summary 134
4 B' s8 |& r2 ^. ^5.12 Examples 1342 u" T. N! e, x7 U( d# {
5.13 Problems 142
( ?3 U% k& W' i+ g' t, p" F0 {9 e( E* yBibliography 142+ t. }! f1 k& B
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. T3 [8 e5 z' _' x- k) |6 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1458 j. \) h6 }: G& |4 U5 f
6.1 Introduction and General Requirements 145
( P& k' H8 I* Y( o1 e; }: D+ T5 c( \6.2 Creep 146
- ] u0 j) F6 p6.2.1 Creep: Simple Methods to Obtain J (t) 146
; C( S6 t8 o5 [$ Z. p3 D6.2.2 Effect of Risetime in Transient Tests 146
0 L* u7 X* M* J6.2.3 Creep in Anisotropic Media 1489 g" p& L- M6 N x4 L5 f- E
6.2.4 Creep in Nonlinear Media 148
. x/ G* E. u1 A- y7 f( G6.3 Inference of Moduli 150) f) a6 k/ s _4 ~: E
6.3.1 Use of Analytical Solutions 1507 S) A2 L- o8 |! q
6.3.2 Compression of a Block 151
2 J+ s2 w. v; i6.4 Displacement and Strain Measurement 152 a/ ^4 H) Q$ A8 A% _
6.5 Force Measurement 156) }: X! s* ^# V r
6.6 Load Application 1577 J0 y0 R: _$ b$ T# @( Y
6.7 Environmental Control 157" k0 B' Q& \$ p9 C; F% n6 }
6.8 Subresonant Dynamic Methods 158
) D8 a. [4 }+ @* \0 l( v) h7 l6.8.1 Phase Determination 158
1 G1 S1 R' F3 q' T' k6.8.2 Nonlinear Materials 160% V9 C" }8 w3 S* A. x$ E! ^
6.8.3 Rebound Test 161
4 w3 `! N" K6 J; v0 K& T) j6.9 Resonance Methods 161- }' x9 ~5 G- B+ D6 I' h! l. C
6.9.1 General Principles 1618 I5 i/ K! d i$ L2 V
6.9.2 Particular Resonance Methods 163
$ p0 d5 m, F; H [/ s6.9.3 Methods for Low-Loss or High-Loss Materials 166! `' S( c: [) A# V9 w; r
6.9.4 Resonant Ultrasound Spectroscopy 168
/ S2 z+ [3 H" K6.10 Achieving a Wide Range of Time or Frequency 171( P7 ~( V, @! N( a: X" ?
6.10.1 Rationale 171
) ~% ?+ v; \9 l7 U3 X, f8 r/ x6.10.2 Multiple Instruments and Long Creep 172
% Q) ~8 n1 P- C) a: H6.10.3 Time–Temperature Superposition 172; J* P1 O- p$ K3 @
6.11 Test Instruments for Viscoelasticity 173/ t2 R, [0 [! R8 S
6.11.1 Servohydraulic Test Machines 173
) R3 `# w+ K4 ]/ N$ t6.11.2A Relaxation Instrument 174
6 }/ _: k7 ]- x: m6.11.3 Driven Torsion Pendulum Devices 1743 P: h8 r7 B# s C" _. T0 K
6.11.4 Commercial Viscoelastic Instrumentation 178
. {- r' R. I; V( f- q6.11.5 Instruments for a Wide Range of Time and Frequency 179. ?. j* k: G8 H: j" s- S
6.11.6 Fluctuation–Dissipation Relation 182' O. X- r7 `0 H
6.11.7 Mapping Properties by Indentation 183
3 c' {% m2 s4 M/ A( ~: l4 R6.12 Wave Methods 184
# j. X" ~' W& ]- R. R9 P0 g1 J% m6.13 Summary 188
) x; q; J; i: X$ o# O1 u6.14 Examples 188: h1 u6 a4 q4 |+ q5 P
6.15 Problems 200
9 ?2 e4 x" U3 bBibliography 201; E0 y+ l1 i3 ^: }9 r
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) E* O/ q1 r" p1 ?' a" l7 Viscoelastic Properties of Materials . . . . . . . . . . . . . . . . . . . . . 207
* f4 N* [5 N6 @7.1 Introduction 2071 E+ v% u# k5 m4 i
7.1.1 Rationale 207
) }, J( t' X; i7 H1 X7.1.2 Overview: Some Common Materials 207" _" n; W- |7 u
7.2 Polymers 2081 A# Q y6 g; v5 P) ?
7.2.1 Shear and Extension in Amorphous Polymers 2083 }3 Z- l4 V" {! V E9 ]
7.2.2 Bulk Relaxation in Amorphous Polymers 2120 b) N9 O$ `. k% m# S
7.2.3 Crystalline Polymers 213
. i" P4 {5 j; o0 A. ^7.2.4 Aging and other Relaxations 214. g6 V+ i! O' l# w: }1 Z7 u
7.2.5 Piezoelectric Polymers 214
p1 }/ z; q) |3 d2 u7.2.6 Asphalt 214
) n- H8 j- r, g* _' z* ~2 a7.3 Metals 2159 T) a+ J* W* v( q3 s
7.3.1 Linear Regime of Metals 215
" b( ^% Q1 v) v9 l. j7.3.2 Nonlinear Regime of Metals 2175 l* O/ o: q2 R$ O
7.3.3 High-Damping Metals and Alloys 219
, V& ~) C3 t5 U, s4 Q7.3.4 Creep-Resistant Alloys 2248 e8 Y+ R9 c5 x5 J" i
7.3.5 Semiconductors and Amorphous Elements 2253 Q/ g$ a! V- \) ~; F4 n ^3 M( b3 g2 e
7.3.6 Semiconductors and Acoustic Amplification 226
/ X6 q' H& K6 H! _4 M" @7.3.7 Nanoscale Properties 226* w2 P' N0 d- C0 d1 Q3 }3 X9 e: K6 k
7.4 Ceramics 227
$ R* Z, w7 J5 l2 @/ p, _7.4.1 Rocks 227% F5 h, o1 n7 s
7.4.2 Concrete 229; K- A# ]* o: I3 T
7.4.3 Inorganic Glassy Materials 231, n, `: d' t; k/ c* p" Z) R/ O2 _
7.4.4 Ice 231
6 H# g+ @ {, B8 [* C7.4.5 Piezoelectric Ceramics 232' P& n( B' \! w7 E! H
7.5 Biological Composite Materials 233! R. H8 y" ]' a% M$ {
7.5.1 Constitutive Equations 2340 Z5 I+ l$ t0 _, G3 ]% ]
7.5.2 Hard Tissue: Bone 234
% o0 ^9 j) W8 u1 K1 Z8 S4 b( u; H7.5.3 Collagen, Elastin, Proteoglycans 236
( {# V+ J) g/ ~& m+ i5 [7.5.4 Ligament and Tendon 2378 i" _8 @; ^: C- L. @3 l" R& N
7.5.5 Muscle 2406 f$ X* r/ [( T) F* G* ^% T: E2 ?1 R
7.5.6 Fat 2435 o$ c7 x# t, V. B/ U# F, G) \
7.5.7 Brain 243
+ d, m4 R0 G( i0 h, g( A" ?7.5.8 Vocal Folds 244
% c; f1 m0 H. G7.5.9 Cartilage and Joints 244
) [5 e9 a3 {6 w8 d- e @) t5 X5 ?7.5.10 Kidney and Liver 2466 w* Q; ~, c1 u @
7.5.11 Uterus and Cervix 246
% u/ V, W/ I" y" O- H/ ~: E7.5.12 Arteries 247
2 B$ H/ f8 v5 y# @7.5.13 Lung 248; r# v1 u7 Z( Y! f/ x5 h1 Y
7.5.14 The Ear 248
- B$ j: q* h) O. o/ i5 t7.5.15 The Eye 249) W& n% V8 z( \# H7 Z( x7 S
7.5.16 Tissue Comparison 2511 ]! W5 p0 H; { Y6 K1 c. d2 \
7.5.17 Plant Seeds 252
8 A: f# p) H) G) J; g5 t7.5.18 Wood 252% w" o- i$ m K/ M! u2 _) k
7.5.19 Soft Plant Tissue: Apple, Potato 253
. h$ {, Y$ i) [" W/ {7.6 Common Aspects 253# ^8 A! N3 Z' x) f0 ]$ v
7.6.1 Temperature Dependence 253
( C9 R! y; k2 o+ J! O4 f" T. n, D7.6.2 High-Temperature Background 254
7 |" u/ Z* O, C7.6.3 Negative Damping and Acoustic Emission 255
+ x4 @# c: t0 S7.7 Summary 2552 k$ s: z h4 b, | k+ w
7.8 Examples 2555 h4 C5 R4 L) }
7.9 Problems 256
7 [3 [/ X9 [- k9 C$ ^Bibliography 257/ q. i, i# Z$ J5 j0 a$ S
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7 i" @7 I: U# }9 ]8 Causal Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
6 W- j' W+ T5 r, _% _0 r. q8.1 Introduction 271
, B; ^$ x* O& r8.1.1 Rationale 271; ?; x, d+ f8 b, r. K' @" i
8.1.2 Survey of Viscoelastic Mechanisms 271: M7 h0 S! C2 j+ G
8.1.3 Coupled Fields 273, T5 l1 `. v* `6 l) Q* @
8.2 Thermoelastic Relaxation 274
" H6 C% T0 R8 @; Q2 b+ C5 I8.2.1 Thermoelasticity in One Dimension 274
% G# @6 @/ x( o8.2.2 Thermoelasticity in Three Dimensions 2751 ?2 w' h9 B/ H2 E
8.2.3 Thermoelastic Relaxation Kinetics 2766 Q7 Y" r6 w1 O
8.2.4 Heterogeneity and Thermoelastic Damping 278: C, h$ N% u7 x6 H- [' v- |
8.2.5 Material Properties and Thermoelastic Damping 280/ Y Y6 _/ V! E$ z$ m' G- Z) Q4 X* t
8.3 Relaxation by Stress-Induced Fluid Motion 2807 \. S% D# v, e7 e E, `+ }
8.3.1 Fluid Motion in One Dimension 280; V5 W% V! b* z0 B: ^
8.3.2 Biot Theory: Fluid Motion in Three Dimensions 281" R/ L4 C6 x8 d' S I% q* f
8.4 Relaxation by Molecular Rearrangement 2866 P6 [2 j) N; G
8.4.1 Glassy Region 286
; r, C: c$ x% M% R0 x- f8.4.2 Transition Region 287
7 {# v: D) a3 \6 n4 }9 e) c, Z- |% R& y8.4.3 Rubbery Behavior 2891 j2 @9 ]0 o1 I) n) e" j
8.4.4 Crystalline Polymers 2913 d" }: T3 @5 X z
8.4.5 Biological Macromolecules 292
$ P1 z! r/ ?. r& ^# F9 c8 Q# K8.4.6 Polymers and Metals 2925 m" ^5 v6 A; r5 q9 j
8.5 Relaxation by Interface Motion 2925 s9 m8 Y8 W2 G* @) A
8.5.1 Grain Boundary Slip in Metals 2929 t) i2 y4 v' }! A5 h( P8 V
8.5.2 Interface Motion in Composites 294
; D, y9 T7 k4 r; D# L0 X8.5.3 Structural Interface Motion 2942 R* z% ~. S8 { j5 A5 x: ?3 O
8.6 Relaxation Processes in Crystalline Materials 294
- q% L" s& ~1 A% E8.6.1 Snoek Relaxation: Interstitial Atoms 294
/ k! Z, Z7 d) I) t# J* J8.6.2 Zener Relaxation in Alloys: Pairs of Atoms 298
2 i, r2 i/ i5 X! j8.6.3 Gorsky Relaxation 299/ r4 N( Q/ z, z) o
8.6.4 Granato–L ¨ ucke Relaxation: Dislocations 300
6 _# F% f5 ~, Z; p; r; J8.6.5 Bordoni Relaxation: Dislocation Kinks 303 S+ }9 G: y! `7 s5 e
8.6.6 Relaxation Due to Phase Transformations 305
! g1 w- k4 o$ e8.6.7 High-Temperature Background 3144 ^( o' ^- C! B& P( n, n
8.6.8 Nonremovable Relaxations 315
8 j- ]5 H) c' z8.6.9 Damping Due to Wave Scattering 316: y9 m' u# E" i: x Y- j
8.7 Magnetic and Piezoelectric Materials 316! f7 l, S! t' G* G' C' \: T- M0 ~' h W
8.7.1 Relaxation in Magnetic Media 316; N: r6 E% X, u; [
8.7.2 Relaxation in Piezoelectric Materials 318
+ V" m0 t9 p) K, f( S8.8 Nonexponential Relaxation 322' q/ V3 w, f7 A) o3 z( n
8.9 Concepts for Material Design 323
; ?* `5 F4 e' ~8.9.1 Multiple Causes: Deformation Mechanism Maps 323% J: x$ }. z9 |, E4 I3 c
8.9.2 Damping Mechanisms in High-Loss Alloys 326# N/ r8 X9 S" o( E; d( g9 h m
8.9.3 Creep Mechanisms in Creep-Resistant Alloys 326! M* u) R& ]8 t3 \" V+ N; I
8.10 Relaxation at Very Long Times 327. i5 k$ M1 E. z
8.11 Summary 327
9 J+ z9 z' T0 P8 ^6 W4 H8.12 Examples 328* ~# Q. e5 f9 Y
8.13 Problems and Questions 332
T; Y# i9 j* [3 J& R \- p* }9 pBibliography 332: F! m4 @, o( k% r. c G
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; N0 l% {, U1 _: c1 h) I9 Viscoelastic Composite Materials . . . . . . . . . . . . . . . . . . . . . . . 341
2 Y1 b& q+ m; r7 r4 u9.1 Introduction 341
1 s8 U5 D4 H% ]9.2 Composite Structures and Properties 341
3 P8 [" u& D! r; `9.2.1 Ideal Structures 3417 d" I) j$ G! \- r: Z; w
9.2.2 Anisotropy due to Structure 3424 ]7 J7 W+ S# d' U' O3 Q1 q% M" }
9.3 Prediction of Elastic and Viscoelastic Properties 344* S3 X0 t- r W3 S. `9 M r
9.3.1 Basic Structures: Correspondence Solutions 3447 b' S+ r) {( N2 ?
9.3.2 Voigt Composite 3450 H2 _% J1 t+ C6 w0 b4 d3 P
9.3.3 Reuss Composite 345
. E9 G X5 o v! r9.3.4 Hashin–Shtrikman Composite 346$ }) B) V: ^+ d7 U( z" Y
9.3.5 Spherical Particulate Inclusions 347" q& ]! [8 \8 E) Q; r
9.3.6 Fiber Inclusions 3492 v: U& c! F: z+ ?/ M
9.3.7 Platelet Inclusions 349! C9 {. a; M% @$ J+ W2 R
9.3.8 Stiffness-Loss Maps 350( T& ~ c$ e* }4 _
9.4 Bounds on the Viscoelastic Properties 3538 @1 }2 J# {" ^7 Z
9.5 Extremal Composites 354& W& I& w; \# x3 ?6 x9 K$ P/ o# R
9.6 Biological Composite Materials 356
. h) U& m1 |; i1 o4 a: E9.7 Poisson’s Ratio of Viscoelastic Composites 357# q0 A, r, b' K* |8 E
9.8 Particulate and Fibrous Composite Materials 358( H) j9 q! j/ ?5 J
9.8.1 Structure 3589 y+ f; W- s& D. \2 J6 W
9.8.2 Particulate Polymer Matrix Composites 3596 Q: [/ M. x# P1 ~, x2 i; ^
9.8.3 Fibrous Polymer Matrix Composites 361+ t* L2 ]% Q/ W# Y8 r. O
9.8.4 Metal–Matrix Composites 362: j7 q5 k: i6 Q7 t0 O- `
9.9 Cellular Solids 363* l3 F( I9 O& }9 |9 O
9.10 Piezoelectric Composites 366" v8 c0 T; C2 I( q$ b3 u$ n; @/ J
9.11 Dispersion of Waves in Composites 366
7 q" s7 t* }9 I* G: ^8 Y0 y `0 f9.12 Summary 367
( u" u0 P" _. ]9.13 Examples 367% \; F" C4 K [& _! q
9.14 Problems 3707 O" Y4 d8 i3 r0 l$ l
Bibliography 370& Y; I7 ^& ?# o- @* o! z
" z6 O' ]$ m4 V/ y, B- j
: M0 i0 b! r( e( O
" v) c T' m$ c10 Applications and Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . 377/ k7 e0 b- Q7 E& k9 O7 t
10.1 Introduction 377
0 b) H* J. K4 [0 N. @; w10.2 A Viscoelastic Earplug: Use of Recovery 3771 v2 `, C. x4 s2 ?
10.3 Creep and Relaxation of Materials and Structures 3788 C( T) o) c- P2 ~3 V1 ~! ~5 u
10.3.1 Concrete 378: Z+ W; n! m/ J
10.3.2 Wood 3787 e1 Z" ^. y* Y B
10.3.3 Power Lines 379
' q* X: s& w P10.3.4 Glass Sag: Flowing Window Panes 380
1 u# E" M! [ }- s u6 f, O. t0 ~10.3.5 Indentation: Road Rutting 380
1 U4 v* n0 x: B; g# L* T10.3.6 Leather 381+ o: G; }; Z" W' @- v, p& \
10.3.7 Creep-Resistant Alloys and Turbine Blades 381- a) V/ S1 ^/ |- \; J4 B
10.3.8 Loosening of Bolts and Screws 382
* c+ W0 _' F* q2 \+ [2 }$ b; n: H- C10.3.9 Computer Disk Drive: Case Study of Relaxation 384
$ \+ I. d0 F. r$ q" O# [5 ~10.3.10 Earth, Rock, and Ice 385
. M: H* f+ \( ^( t/ F+ p10.3.11 Solder 386
& d7 h, ~- a4 Y! _, \. l10.3.12 Filamentsi nL ight Bulbs and Other Devices 387
5 Q/ B- T8 b# X( W" d10.3.13Tires: Flat-Spotting and Swelling 388) l# u0 j; h J1 O; o
10.3.14Cushionsfor Seats and Wheelchairs 388
& \2 N) d( ?( i Q4 R/ n, I* u10.3.15 Artificial Joints 389
2 k. F0 b* y& F J" M+ D, G10.3.16 Dental Fillings 389
! r; O- ? F' k3 }3 }/ Q10.3.17 Food Products 389
B0 e* Q& W/ g! k10.3.18 Seals and Gaskets 390( K/ n5 z3 h& X- A3 S8 h
10.3.19 Relaxationi nM usical Instrument Strings 3906 _& _! \ B# j d7 f6 d6 I3 C9 s
10.3.20 Winding of Tape 391
1 [ B7 }1 [- X) p# ]10.4 Creep and Recovery in Human Tissue 391
/ o0 t5 [7 Q8 m& P% Z2 c0 \10.4.1 Spinal Discs: Height Change 3916 d. q8 F7 V% H9 W/ @
10.4.2 The Nose 3920 O4 ~* _* L4 S( G# f
10.4.3 Skin 392
" ]) f, G! [# }( o/ W' V10.4.4 The Head 393
; T; J: x+ ]% y# m5 I10.5 Creep Damage and Creep Rupture 394
5 n6 a3 O0 X% p! q S$ U10.5.1 Vajont Slide 394 m. ^1 _# d) x! w# R" q+ i- E" s
10.5.2 Collapse of a Tunnel Segment 394' M; h! C6 K* ]% u' M' K- X
10.6 Vibration Control and Waves 394
: q' r- }' N9 n, Q$ ~) M6 [10.6.1 Analysis of Vibration Transmission 3945 B6 C% q( d& z6 A
10.6.2 Resonant (Tuned) Damping 397
( d/ M7 [1 e& A% ~0 O6 ?10.6.3 Rotating Equipment Vibration 397' Z" o; R% q' V1 b* k+ Z
10.6.4 Large Structure Vibration: Bridges and Buildings 398
/ u0 ~0 g; {% O0 _10.6.5 Damping Layers for Plate and Beam Vibration 399
- l' ]1 r3 F. w/ h2 [( b! d10.6.6 Structural Damping Materials 400, V( R. [3 T8 ]) A7 r, q! ]
10.6.7 Piezoelectric Transducers 402
& H, ~" S# H$ b# } d6 d) u10.6.8 Aircraft Noise and Vibration 402+ g. Q7 l3 K- g0 ]/ w; c
10.6.9 Solid Fuel Rocket Vibration 404" Y5 G; r- x4 b$ {5 `2 [; L
10.6.10 Sports Equipment Vibration 404
1 n3 s! h1 `" v3 P* M, U6 K10.6.11 Seat Cushions and Automobiles: Protection of People 404
' A) H5 N, a, y# I9 f7 L" G; x10.6.12 Vibrationi n ScientificI nstruments 4061 [- ]5 I- K4 U. X6 m5 B. v
10.6.13 Waves 4061 ]4 G& C2 \- J$ G) m
10.7 “Smart” Materials and Structures 407$ J! P& e# k" q: w. l" D
10.7.1 “Smart” Materials 407
* d( o" \# X. U8 ?10.7.2 Shape Memory Materials 4080 H0 L& \* X# [$ J; V8 P1 }
10.7.3 Self-Healing Materials 409 W* i. @; ^" ^/ f
10.7.4 Piezoelectric Solid Damping 409
+ E4 [3 ]& Z2 L1 B7 \( L8 V10.7.5 Active Vibration Control: “Smart” Structures 409
, q/ U2 K" ~; _) c' r3 @+ @10.8 Rolling Friction 409
- c; }9 [) H' _ s10.8.1 Rolling Analysis 410 X0 K+ _- @6 a* Q/ z
10.8.2 Rolling of Tires 4112 ]$ y6 [2 r& R# W: @ {
10.9 Uses of Low-Loss Materials 412' @1 @8 t- i; D2 K8 g3 ]
10.9.1 Timepieces 412
9 X- W+ g, l- e10.9.2 Frequency Stabilization and Control 413
9 `7 c) j) D g# c10.9.3 Gravitational Measurements 4138 Y1 D9 f( M, v& u, u \6 ?
10.9.4 Nanoscale Resonators 414
4 ~- ^7 U' L* S" R6 f10.10 Impulses, Rebound, and Impact Absorption 4145 F- r) F: H+ _) m$ n9 n8 _
10.10.1 Rationale 414
) e, }) [. j! u; w10.10.2 Analysis 4153 d% S& G" ~( q! A1 w
10.10.3 Bumpers and Pads 418
% X% H9 _1 \6 C0 U7 i; W- z10.10.4 Shoe Insoles, Athletic Tracks, and Glove Liners 419
0 e) `* L# w2 q) K10.10.5 Toughness of Materials 4198 D c# R; Y2 B# `0 G6 b
10.10.6 Tissue Viscoelasticity in Medical Diagnosis 420# L8 o% ?4 M3 f4 J3 c
10.11Rebound of a Ball 421" X* A" V5 G2 ~& S7 C2 l
10.11.1 Analysis 4210 R9 G+ Q( [ Q6 t2 y
10.11.2 Applications in Sports 422
6 V% c& u$ G$ k" t+ A2 d4 A10.12 Applications of Soft Materials 424! l8 v2 l) e& ~
10.12.1 Viscoelastic Gels in Surgery 424& b7 g8 y3 `5 F" `
10.12.2 Hand Strength Exerciser 424+ @+ G3 C- b/ A& r5 ^8 }
10.12.3 Viscoelastic Toys 424 k% L; [& _4 R" G# G% @
10.12.4 No-Slip Flooring, Mats, and Shoe Soles 425
6 I6 E1 i7 R& w9 ^" M3 F6 z( M9 Y* u4 I9 R10.13 Applications Involving Thermoviscoelasticity 425
5 {* Q: g {2 p10.14 Satellite Dynamics and Stability 426
- ~( A+ e' N; O5 O10.15 Summary 428
# n5 f% I) R$ _9 R10.16 Examples 4292 c/ e3 E' c, Z0 F, `& l6 x
10.17 Problems 431% A' H4 J$ R! C9 U
Bibliography 431
: ~/ I' A& `, t% f. l. q5 M3 r3 J% j
/ W2 H8 a" l4 o* ]+ W
& S6 ~* k1 h5 } VA: Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4411 D4 I1 E* Z* [+ V
A.1 Mathematical Preliminaries 441' \$ m5 [* g, S1 }6 E, `+ O
A.1.1 Introduction 441
+ G! U4 v0 v# [2 o8 q, PA.1.2 Functionals and Distributions 441
! F4 ^1 G+ @& \0 n) m0 ~8 dA.1.3 Heaviside Unit Step Function 442
7 N+ l# {: ]! I, q) m' _& h* fA.1.4 Dirac Delta 442$ T% K+ O( \) r
A.1.5 Doublet 443
! _3 L+ L6 X( c7 u: `/ w/ F5 rA.1.6 Gamma Function 445
\: A4 g5 I% K9 M2 Z9 KA.1.7 Liebnitz Rule 4453 y) m n: F' s0 [, O' J
A.2 Transforms 445
`2 ~! \% E2 w* i% G) RA.2.1 Laplace Transform 446
7 i% W0 L' `4 _& pA.2.2 Fourier Transform 446" d- @) \5 t4 @& E
A.2.3 Hartley Transform 447- o& c4 P2 x6 W$ E0 b/ C
A.2.4 Hilbert Transform 447
5 D+ v* x+ p% [* B1 yA.3 Laplace Transform Properties 448
3 S" J5 A2 R3 z2 h! y- i5 DA.4 Convolutions 4497 M, E# j4 Q+ Q( e1 o/ Z! U
A.5 Interrelations in Elasticity Theory 451
9 {& W" H- r5 }; y J1 AA.6 Other Works on Viscoelasticity 451
& w. x" L8 A7 ]* d: _5 t0 |! F/ vBibliography 4524 f! ~, h4 z) k5 y/ U9 ^3 e
$ {7 J) Y3 @" w& b U1 a
9 S' U- \+ k& W# M* d: [& B; jB: Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455
2 j; a$ {/ C$ L$ s/ q* k. z7 WB.1 Principal Symbols 455
# C Y# w1 B8 O: O N$ Q, D( d, rIndex 457
5 E. V& O; ?& A; F' P6 A8 m5 y" V- N# ^2 P8 D. d2 ?( X+ o
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发表于 2015-1-9 22:34:06