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E-raamat: Dynamics of Pre-Strained Bi-Material Elastic Systems: Linearized Three-Dimensional Approach

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  • Ilmumisaeg: 11-Feb-2015
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319144603
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Dynamics of Pre-Strained Bi-Material Elastic Systems: Linearized Three-Dimensional ApproachSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 11-Feb-2015
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319144603
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This book deals with dynamics of pre-stressed or pre-strained bi-material elastic systems consisting of stack of pre-stressed layers, stack of pre-stressed layers and pre-stressed half space (or half plane), stack of pre-stressed layers as well as absolute rigid foundation, pre-stressed compound solid and hollow cylinders and pre-stressed sandwich hollow cylinders. The problems considered in the book relate to the dynamics of a moving and oscillating moving load, forced vibration caused by linearly located or point located time-harmonic forces acting to the foregoing systems. Moreover, a considerable part of the book relate to the problems regarding the near surface, torsional and axisymmetric longitudinal waves propagation and dispersion in the noted above bi-material elastic systems.
The book carries out the investigations within the framework of the piecewise homogeneous body model with the use of the Three-Dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies.
1 Introduction
1(10)
1.1 A General Background
1(4)
1.2 Text Preview
5(6)
References
7(4)
2 Dynamics of a Moving and Oscillating Moving Load Acting on a Pre-strained Bi-material Layered Systems
11(132)
2.1 Background of Related Investigations
11(4)
2.2 Critical Velocity of a Moving Load Acting on the Pre-stressed Layer Resting on a Pre-stressed Half-Plane
15(13)
2.2.1 Formulation of the Problem
15(4)
2.2.2 Solution Method of the Corresponding Boundary-Contact-Value Problem
19(4)
2.2.3 The Algorithm for Determination of the Critical Velocity
23(1)
2.2.4 Numerical Results and Discussions
24(4)
2.2.5 Conclusions
28(1)
2.3 Dynamical Response of a Pre-stressed System Comprising a Substrate, Bond and Covering Layer to the Moving Load
28(9)
2.3.1 Formulation of the Problem
29(1)
2.3.2 Method of Solution
30(2)
2.3.3 Numerical Results and Discussions
32(4)
2.3.4 Conclusions
36(1)
2.4 Dynamics of a Finite Pre-strained Bi-layered Slab Resting on a Rigid Foundation Under the Action of an Oscillating Moving Load
37(28)
2.4.1 Formulation of the Problem and Some Remarks on the Equations and Relations of the TDLTEWISB
38(10)
2.4.2 Method of Solution
48(3)
2.4.3 General Remarks on the Doppler Effect
51(2)
2.4.4 On the Algorithm Used for Obtaining Numerical Results
53(2)
2.4.5 Numerical Results and Discussions
55(8)
2.4.6 Conclusions
63(2)
2.5 Dynamics of a System Comprising a Pre-stressed Orthotropic Layer and Pre-stressed Orthotropic Half-Plane Under the Action of a Moving Load
65(13)
2.5.1 Formulation of the Problem
65(2)
2.5.2 Method of Solution
67(2)
2.5.3 Numerical Results and Discussions
69(8)
2.5.4 Conclusions
77(1)
2.6 Dynamics of a System Comprising on Orthotropic Layer and Orthotropic Half-Plane Under the Action of an Oscillating Moving Load
78(21)
2.6.1 On the Formulation of the Problem and Solution Method
79(3)
2.6.2 Numerical Results and Discussions
82(14)
2.6.3 Conclusions
96(3)
2.7 Three-Dimensional Problems on the Dynamics of a System Comprising a Pre-stressed Covering Layer and Pre-stressed Half-Space Under the Action of an Oscillating Moving Load
99(27)
2.7.1 Formulation of the Problem
99(3)
2.7.2 Method of Solution
102(5)
2.7.3 Some Notes on the Doppler Effect and the Algorithm for Obtaining the Numerical Results
107(7)
2.7.4 Numerical Results and Discussions
114(11)
2.7.5 Conclusions
125(1)
2.8 Oscillating Moving Load Problems Related to Systems Consisting of Viscoelastic Constituents
126(9)
2.8.1 Formulation of the Problem
126(2)
2.8.2 Method of Solution
128(4)
2.8.3 Numerical Results and Discussions
132(3)
2.9 On One Analogy Between the Moving Load, Near Surface Wave Propagation and Near Surface Stability Loss Problems Related to the Layered Half-Space
135(8)
2.9.1 The Analogy Between the Near-Surface Wave Propagation Problem and the Corresponding Moving Load Problem
136(2)
2.9.2 The Analogy Between the Near-Surface Stability Loss Problem and the Corresponding Moving Load Problem
138(2)
References
140(3)
3 Forced Vibration of Pre-stressed Layered Bodies
143(192)
3.1 Forced Vibration of a System Consisting of a Pre-stressed Covering Layer and a Pre-stressed Half-Plane Under the Action of Arbitrary Linearly-Located Time-Harmonic Forces
143(20)
3.1.1 Formulation of the Problem
143(2)
3.1.2 Method of Solution
145(4)
3.1.3 Some Remarks on the Calculation of the Integrals (3.21)
149(6)
3.1.4 Numerical Results and Discussions
155(6)
3.1.5 Conclusions
161(2)
3.2 The Influence of the Third Order Elastic Constants on the Dynamical Interface Stress Field in a Half-Space Covered with a Pre-stretched Layer
163(21)
3.2.1 Formulation of the Problem
164(8)
3.2.2 Method of Solution
172(3)
3.2.3 Numerical Results and Discussions
175(8)
3.2.4 Conclusions
183(1)
3.3 Axisymmetric Stress Field in a Finite Pre-strained System Comprising a Half-Space and a Covering Layer, and in a Bi-layered Slab Resting on a Rigid Foundation
184(43)
3.3.1 Formulation of the Problem
185(8)
3.3.2 Solution Method
193(5)
3.3.3 Some Remarks on the Calculation of the Integrals in (3.127) and (3.128)
198(2)
3.3.4 Numerical Results and Discussions
200(27)
3.4 Frequency Response of the Axisymmetrically Finite Pre-stretched Slab from Incompressible Functionally Graded Material on a Rigid Foundation
227(10)
3.4.1 Formulation of the Problem
228(2)
3.4.2 General Remarks on the Solution Procedure
230(2)
3.4.3 Numerical Results and Discussions
232(4)
3.4.4 Conclusions
236(1)
3.5 Time-Harmonic Stress Field in a System Comprising a Pre-stressed Orthotropic Layer and Pre-stressed Orthotropic Half-Plane
237(16)
3.5.1 Formulation of the Problem
237(4)
3.5.2 Method of Solution
241(4)
3.5.3 Numerical Results and Discussions
245(7)
3.5.4 Conclusions
252(1)
3.6 Time-Harmonic Lamb's Problem for a System Comprising a Pre-stressed Piezoelectric Layer and Pre-stressed Piezoelectric Half-Plane
253(33)
3.6.1 Formulation of the Problem
253(3)
3.6.2 Method of Solution
256(7)
3.6.3 Some Remarks on the Calculation of Integrals (3.213)
263(3)
3.6.4 Numerical Results and Discussions
266(20)
3.7 Axisymmetric Time-Harmonic Lamb's Problem for a System Comprising a Viscoelastic Covering Layer and Viscoelastic Half-Plane
286(29)
3.7.1 Formulation of the Problem
287(3)
3.7.2 Method of Solution
290(6)
3.7.3 Numerical Results and Discussion
296(17)
3.7.4 Conclusions
313(2)
3.8 Dynamical Response of Two Axially Pre-strained System Comprising a Covering Layer and a Half-Space to Rectangular Time-Harmonic Forces
315(20)
3.8.1 Formulation of the Problem
315(2)
3.8.2 Method of Solution
317(4)
3.8.3 Numerical Results and Discussions
321(11)
References
332(3)
4 Wave Propagation in Pre-strained Layered Systems
335(126)
4.1 Generalized Rayleigh Wave Propagation in a System Consisting of a Pre-stressed Covering Layer and a Pre-stressed Half Plane
335(19)
4.1.1 Formulation of the Problem
336(7)
4.1.2 Solution Procedure
343(2)
4.1.3 Numerical Results and Discussions
345(8)
4.1.4 Conclusions
353(1)
4.2 The Influence of the Imperfect Bonding Between the Pre-stressed Covering Layer and Pre-stressed Half-plane on the Dispersion of the Generalized Rayleigh Wave
354(23)
4.2.1 Formulation of the Shear-Spring Type Imperfect Contact Conditions
354(2)
4.2.2 Dispersion Equation
356(2)
4.2.3 Numerical Results Related to the Influence of the Shear-Spring Type Parameter on the Dispersion Curves and Their Application Fields
358(16)
4.2.4 Conclusions
374(3)
4.3 The Influence of the Normal-Spring + Shear-Spring Type Debonding Between the Covering Layer and Half-Plane with Two-Axial Initial Stresses on the Near-Surface Wave Dispersion
377(12)
4.3.1 Formulation of the Problem
377(3)
4.3.2 On the Solution Method and Dispersion Equation
380(1)
4.3.3 Numerical Results Related to the Influence of the Normal-Spring Type Parameter and Two-Axial Initial Stresses on the Near Surface Wave Propagation Velocity
381(8)
4.3.4 Conclusions
389(1)
4.4 Near-Surface Waves in the System Consisting of a Pre-stressed Piezoelectric Layer and Pre-stressed Metal Elastic Half-Plane
389(24)
4.4.1 Formulation of the Problem
390(3)
4.4.2 Method of Solution
393(7)
4.4.3 Numerical Results and Discussions
400(10)
4.4.4 Conclusions
410(3)
4.5 Lamb Waves in a Pre-strained Sandwich Plate Made of Highly Elastic Compressible Material
413(48)
4.5.1 A Brief Background
414(2)
4.5.2 Formulation of the Problems
416(14)
4.5.3 Method of Solution and Dispersion Equations
430(7)
4.5.4 Numerical Results and Discussions
437(20)
4.5.5 Conclusions
457(1)
References
458(3)
5 Torsional Wave Dispersion in Pre-stressed Compound Cylinders
461(120)
5.1 Torsional Wave Dispersion in Pre-stressed Compound Solid and Hollow Cylinders
461(27)
5.1.1 Formulation of the Problem, the Basic Linearized Field Equations and Relations
461(3)
5.1.2 The Obtaining of the Linearized Field Equations and Relations, from the Non-linear Field Equations Under Small Initial Deformation
464(6)
5.1.3 Solution Procedure and Obtaining the Dispersion Relation
470(4)
5.1.4 Numerical Results and Discussions
474(14)
5.2 The Influence of the Imperfect Bonding Between the Layers on the Torsional Wave Dispersion in Pre-stressed Bi-material Compound Solid and Hollow Cylinders
488(10)
5.2.1 On the Problem Formulation and Solution Method
488(3)
5.2.2 Numerical Results and Discussions
491(7)
5.3 Torsional Wave Dispersion in a Pre-stressed Circular Cylinder Embedded in a Pre-stressed Elastic Medium
498(15)
5.3.1 Formulation of the Problem, on the Solution Method and Dispersion Equations
499(6)
5.3.2 Numerical Results and Discussions
505(8)
5.4 Torsional Wave Dispersion in a Finitely Pre-strained Hollow Sandwich Circular Cylinder
513(30)
5.4.1 Formulation of the Problem
513(9)
5.4.2 Solution Procedure and Obtaining the Dispersion Equation
522(5)
5.4.3 Numerical Results and Discussions
527(15)
5.4.4 Conclusions
542(1)
5.5 Torsional Wave Dispersion in a Hollow Sandwich Circular Cylinder Made from Viscoelastic Materials
543(38)
5.5.1 A Brief Background
544(2)
5.5.2 Formulation of the Problem
546(1)
5.5.3 Method of Solution and Obtaining the Dispersion Equation
547(8)
5.5.4 Numerical Results and Discussions
555(21)
5.5.5 Conclusions
576(2)
References
578(3)
6 Axisymmetric Longitudinal and Flexural Wave Propagation in Pre-strained Bi-material Compound Circular Cylinders
581(224)
6.1 Axisymmetric Longitudinal Wave Propagation in a Finite Pre-stretched Compound Cylinder Made of Highly Elastic Incompressible Materials
582(26)
6.1.1 Formulation of the Problem
582(8)
6.1.2 Solution Procedure and Obtaining the Dispersion Equation
590(6)
6.1.3 Numerical Results and Discussions
596(10)
6.1.4 Conclusions
606(2)
6.2 Axisymmetric Longitudinal Wave Propagation in a Finite Pre-strained Cylinder Made from Highly Elastic Compressible Materials
608(28)
6.2.1 Formulation of the Problem and Obtaining Some Basic Linearized Equations and Relations
608(7)
6.2.2 Solution Procedure and Obtaining the Dispersion Equations
615(6)
6.2.3 Numerical Results and Discussions
621(14)
6.2.4 Conclusions
635(1)
6.3 The Influence of the Imperfect Bonding Between the Cylinders on the Dispersion Curves Related to the Axisymmetric Waves in the Solid Compound Cylinder
636(17)
6.3.1 On the Problem Formulation and the Solution Method
636(1)
6.3.2 Numerical Results and Discussions
637(15)
6.3.3 Conclusions
652(1)
6.4 Dispersion of Axisymmetric Longitudinal Waves in a Pre-strained Perfectly and Imperfectly Bonded Bi-layered Hollow Cylinder
653(27)
6.4.1 On Problem Formulation and Solution Method
653(9)
6.4.2 Numerical Results and Discussions
662(18)
6.5 The Influence of the Third Order Elastic Constants on Axisymmetric Wave Propagation in the Pre-stressed Bi-material Compound Solid and Hollow Cylinders
680(36)
6.5.1 Formulation of the Problems
681(9)
6.5.2 Solution Procedure and Obtaining the Dispersion Equations
690(15)
6.5.3 Numerical Results and Discussions
705(11)
6.6 Dispersion Relations of Axisymmetric Wave Propagation in an Initially Twisted Bi-material Solid Compound Cylinder
716(32)
6.6.1 Formulation of the Problem
717(4)
6.6.2 Method of Solution
721(9)
6.6.3 Numerical Results and Discussions
730(16)
6.6.4 Conclusions
746(2)
6.7 Flexural Wave Dispersion in Finitely Pre-strained Solid and Hollow Circular Cylinders Made of Compressible Materials
748(27)
6.7.1 A Brief Background
748(2)
6.7.2 Formulation of the Problem and Governing Field Equations
750(6)
6.7.3 Solution Procedure and Obtaining the Dispersion Equation
756(5)
6.7.4 Numerical Results and Discussions
761(13)
6.7.5 Conclusions
774(1)
6.8 Flexural Wave Dispersion in Bi-material Solid and Hollow Compound Cylinders Under Perfect and ImPerfect Contact Conditions
775(30)
6.8.1 Formulation of the Problem
775(2)
6.8.2 Solution Method
777(3)
6.8.3 Numerical Results and Discussions
780(20)
6.8.4 Conclusions
800(1)
References
801(4)
7 Some Stability Loss and Wave Propagation Problems Regarding the Double-Walled Carbon Nanotube (DWCNT)
805(50)
7.1 Microbuckling of a DWCNT Embedded in an Elastic Matrix
805(27)
7.1.1 A Brief Background
806(2)
7.1.2 Formulation of the Problem
808(3)
7.1.3 Method of Solution
811(11)
7.1.4 Numerical Results and Discussions
822(8)
7.1.5 Conclusions
830(2)
7.2 Axisymmetric Longitudinal Wave Propagation in Double-Walled Carbon Nanotube
832(23)
7.2.1 A Brief Background
833(3)
7.2.2 Formulation of the Problem
836(2)
7.2.3 Method of Solution
838(7)
7.2.4 Numerical Results and Discussions
845(7)
7.2.5 Conclusions
852(1)
References
853(2)
8 On One Application of the Approach Developed in
Chapter 3 on the Dynamics of Pre-strained Hydro-elastic Systems
855(46)
8.1 Forced Vibrations of a System Consisting of a Pre-strained Highly Elastic Plate Under Compressible Viscous Fluid
855(26)
8.1.1 A Brief Background
856(1)
8.1.2 Formulation of the Problem and Governing Field Equations
857(6)
8.1.3 Method of Solution
863(6)
8.1.4 Numerical Results and Discussions
869(10)
8.1.5 Conclusions
879(2)
8.2 Frequency Response of a Viscoelastic Plate Under Compressible Viscous Fluid Loading
881(20)
8.2.1 The Problem Formulation and Governing Field Equations
881(1)
8.2.2 Solution Method
882(5)
8.2.3 Numerical Results and Discussions
887(12)
References
899(2)
9 Some Problems on the Sandwich Plate-Strip with Piezoelectric Face and Elastic Core Layers Containing Interface Cracks
901(38)
9.1 Buckling Delamination of a Sandwich Plate-Strip with Piezoelectric Face and Elastic Core Layers
901(15)
9.1.1 A Brief Background
902(1)
9.1.2 Formulation of the Problem
902(4)
9.1.3 Method of Solution
906(4)
9.1.4 Numerical Results and Discussions
910(6)
9.1.5 Conclusions
916(1)
9.2 The Total Electro-mechanical Potential Energy and Energy Release Rate at the Interface Crack Tips in an Initially Stressed Sandwich Plate-Strip with Piezoelectric Face and Elastic Core Layers
916(23)
9.2.1 A Brief Background
917(2)
9.2.2 Formulation of the Problem
919(4)
9.2.3 Method of Solution
923(2)
9.2.4 Numerical Results and Discussions
925(10)
9.2.5 Conclusions
935(1)
References
936(3)
10 Forced Vibration of the Initially Stressed Rectangular Plates with Holes and Inclusions
939(60)
10.1 Forced Vibration of an Initially Stressed Rectangular Thick Plate Made from Orthotropic Material with Cylindrical Hole
939(12)
10.1.1 A Brief Background
940(1)
10.1.2 Formulation of the Problem and on the Solution Method
940(4)
10.1.3 FEM Modeling
944(2)
10.1.4 Numerical Results and Discussions
946(4)
10.1.5 Conclusions
950(1)
10.2 3D Analysis of the Forced Vibration of a Pre-stressed Rectangular Composite Plate with Two Neighboring Cylindrical Cavities
951(14)
10.2.1 Formulation of the Problem and on the Solution Method
951(4)
10.2.2 FEM Modeling
955(2)
10.2.3 Numerical Results and Discussions
957(8)
10.2.4 Conclusions
965(1)
10.3 Forced Vibration Analysis of Pre-stretched Plate-Strip with Twin Circular Inclusions
965(34)
10.3.1 A Brief Background
966(2)
10.3.2 Formulation of the Problem and Computational Procedure
968(4)
10.3.3 Finite Element Model
972(4)
10.3.4 Numerical Results and Discussions
976(19)
10.3.5 Conclusions
995(1)
References
996(3)
Index 999
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