Tractable Models of Solid Mechanics
Formulation, Analysis and Interpretation
1st Edition
Published on 4. January 2011
XIV, 302 pages
978-3-642-15372-3 (ISBN)
Description
This book describes significant tractable models used in solid mechanics - classical models used in modern mechanics as well as new ones. The models are selected to illustrate the main ideas which allow scientists to describe complicated effects in a simple manner and to clarify basic notations of solid mechanics. A model is considered to be tractable if it is based on clear physical assumptions which allow the selection of significant effects and relatively simple mathematical formulations.
The first part of the book briefly reviews classical tractable models for a simple description of complex effects developed from the 18th to the 20th century and widely used in modern mechanics. The second part describes systematically the new tractable models used today for the treatment of increasingly complex mechanical objects - from systems with two degrees of freedom to three-dimensional continuous objects.
Reviews / Votes
From the reviews:
"This book by L. I. Manevitch and O. V. Gendelman is focused on a series of so-called 'tractable models'. . This book presents new original ideas in analysis of models from very different topics of nonlinear mechanics. The proposed approaches allow the authors to simplify complicated nonlinear problems and describe some important solutions. This book may be useful for specialists dealing with nonlinear mechanics, for theoretical physicists, and also for use in academic courses. The book is recommended for libraries." (Yuri V. Mikhlin, Mathematical Reviews, Issue 2012 a)
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Oleg V. Gendelman | Leonid I. Manevitch
Tractable Models of Solid Mechanics
Formulation, Analysis and Interpretation
Book
01/2011
Springer
€160.49
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Content
1 - Preface [Seite 4]
2 - Abbreviations [Seite 7]
3 - Contents [Seite 8]
4 - 1 Introduction: Historical Development of Tractable Models [Seite 11]
4.1 - References [Seite 21]
5 - 2 Discrete Finite Systems [Seite 22]
5.1 - 2.1 Linear Oscillators [Seite 22]
5.1.1 - 2.1.1 Linear Conservative Oscillator [Seite 23]
5.1.2 - 2.1.2 Linear Oscillator with Viscous Damping [Seite 24]
5.1.2.1 - 2.1.2.1 Strong Energy Dissipation (e >> 1) [Seite 25]
5.1.2.2 - 2.1.2.2 Weak Energy Dissipation (e<<1) [Seite 28]
5.1.2.3 - 2.1.2.3 Exercise [Seite 30]
5.1.3 - 2.1.3 Linear Oscillator with Viscous Damping and Periodic (Harmonic) Forcing [Seite 30]
5.1.3.1 - 2.1.3.1 Exercise [Seite 32]
5.1.4 - 2.1.4 Two Coupled Oscillators [Seite 33]
5.1.4.1 - 2.1.4.1 Weakly Coupled Oscillators with Strongly Different Frequencies [Seite 33]
5.1.4.2 - 2.1.4.2 Exercise [Seite 36]
5.1.4.3 - 2.1.4.3 Weakly Coupled Oscillators with Close Frequencies [Seite 36]
5.1.4.4 - 2.1.4.4 Exercise [Seite 40]
5.1.4.5 - 2.1.4.5 Strongly Coupled Oscillators with Essentially Different Frequencies [Seite 40]
5.1.4.6 - 2.1.4.6 Exercise [Seite 42]
5.1.4.7 - 2.1.4.7 Strongly Coupled Oscillators with Close Frequencies [Seite 43]
5.1.4.8 - 2.1.4.8 Exercise [Seite 43]
5.2 - 2.2 Single-DOF Nonlinear Oscillator [Seite 43]
5.2.1 - 2.2.1 Quasilinear Oscillator [Seite 45]
5.2.2 - 2.2.2 Strongly Nonlinear Oscillator and Vibro-Impact Approximation [Seite 48]
5.2.2.1 - 2.2.2.1 Special Solutions for Vibro-Impact Motions [Seite 48]
5.2.2.2 - 2.2.2.2 Vibro-Impact Systems Treatable by Analytic Functions [Seite 51]
5.2.3 - 2.2.3 Oscillator with Multiple Equilibriums [Seite 55]
5.3 - 2.3 Forced Nonlinear Oscillator [Seite 56]
5.3.1 - 2.3.1 General Remarks [Seite 56]
5.3.2 - 2.3.2 Governing Equations [Seite 57]
5.3.3 - 2.3.3 The Dynamics of the Oscillator without Dissipation and the LPT [Seite 59]
5.3.4 - 2.3.4 The Transient Dynamics of a Weakly Damped Oscillator [Seite 62]
5.3.4.1 - 2.3.4.1 Non-smooth Temporal Transformations [Seite 63]
5.3.4.2 - 2.3.4.2 The Construction of a Generating Solution [Seite 64]
5.3.4.3 - 2.3.4.3 Calculation of A0(t0) and .0(t0) [Seite 67]
5.3.5 - 2.3.5 Quasi-Linear Oscillations [Seite 70]
5.4 - 2.4 Entrainment, Synchronization and Resonance Capture [Seite 73]
5.4.1 - 2.4.1 Pendulum with Constant External Torque [Seite 74]
5.4.2 - 2.4.2 Entrainment of the Van der Pol Oscillator by External Harmonic Force [Seite 77]
5.4.3 - 2.4.3 Synchronization of Oscillators and Related Models [Seite 84]
5.4.4 - 2.4.4 Resonance Capture [Seite 86]
5.4.4.1 - 2.4.4.1 Exercises [Seite 89]
5.4.5 - 2.4.5 Forced Oscillator with Multiple States of Equilibrium [Seite 90]
5.5 - 2.5 Symmetric Systems of Coupled Nonlinear Oscillators Beating Phenomena [Seite 93]
5.5.1 - 2.5.1 Exercise [Seite 102]
5.6 - 2.6 2DOF Systems of Nonlinear Oscillators with Essential Asymmetry Targeted Energy Transfer (TET) [Seite 103]
5.6.1 - 2.6.1 Targeted Energy Transfer in an Unforced 2DOF System [Seite 103]
5.6.2 - 2.6.2 Targeted Energy Transfer in Forced 2DOF System [Seite 114]
5.7 - 2.7 Coupled Nonlinear Oscillators with Time Delays [Seite 142]
5.7.1 - 2.7.1 Analytic Model [Seite 142]
5.7.2 - 2.7.2 Numeric Verification -- Straight Modes [Seite 150]
5.7.3 - 2.7.3 Numeric Verification -- "Oval"-- Modes and Phase -- Locked Solutions [Seite 153]
5.8 - 2.8 Low-DOF Discrete Nonlinear Systems [Seite 156]
5.9 - 2.9 Concluding Remarks [Seite 169]
5.10 - References [Seite 170]
6 - 3 Infinite Discrete Systems [Seite 175]
6.1 - 3.1 Dynamics of Infinite Nonlinear Chains [Seite 175]
6.1.1 - 3.1.1 Long-Wavelength Approximation. Equation of Supersonic Extension Solitons in an Infinite FPU Chain [Seite 175]
6.1.2 - 3.1.2 Zigzag Chain and Long-Wave Solitons [Seite 177]
6.1.3 - 3.1.3 Envelope Solitons [Seite 179]
6.1.4 - 3.1.4 Optical Breathers in a Zigzag Chain [Seite 184]
6.1.5 - 3.1.5 Torsional Solitons [Seite 194]
6.1.6 - 3.1.6 Approximation of Immobile Neighbour Chains [Seite 196]
6.2 - 3.2 Dynamics of Essentially Nonlinear and Vibro-Impact Chains [Seite 200]
6.2.1 - 3.2.1 Oscillatory Chain with Rigid Barriers [Seite 201]
6.2.2 - 3.2.2 Discrete Breathers in a Vibro-Impact Chain [Seite 206]
6.2.2.1 - 3.2.2.1 System of Klein-Gordon (KG) Type [Seite 207]
6.2.2.2 - 3.2.2.2 System of Fermi-Pasta-Ulam (FPU) Type [Seite 211]
6.3 - 3.3 The Problem of Heat Conduction in Dielectrics [Seite 215]
6.4 - 3.4 Solitons in Energetically Nondegenerate Quasi-One-Dimensional Models [Seite 225]
6.4.1 - 3.4.1 Quasi-One-Dimensional Model of a Molecular Crystal: Soliton Modes of Motion in a Bistable Nonlinear System [Seite 227]
6.5 - 3.5 Dynamics of Ensembles of Interacting Nonlinear Chains [Seite 233]
6.6 - 3.6 Concluding Remarks [Seite 241]
6.7 - References [Seite 241]
7 - 4 Continuous Systems [Seite 245]
7.1 - 4.1 One-Dimensional Models [Seite 245]
7.1.1 - 4.1.1 Bolotin Model [Seite 245]
7.1.1.1 - 4.1.1.1 Exercises [Seite 249]
7.1.2 - 4.1.2 Simplification of the Timoshenko Beam [Seite 249]
7.2 - 4.2 The Planar Dynamical Problem and Tractable One-Dimensional Models of an Elastic Solid [Seite 256]
7.2.1 - 4.2.1 Exercises [Seite 261]
7.3 - 4.3 The Two-Dimensional Orthotropic Model and Its Application to a Complex Contact Problem [Seite 261]
7.3.1 - 4.3.1 Basic Asymptotic Decomposition of the Orthotropic Plate Problem [Seite 261]
7.3.2 - 4.3.2 The Contact Problem for a Planar Orthotropic Strip [Seite 267]
7.4 - 4.4 Models of Elastic Foundation [Seite 272]
7.4.1 - 4.4.1 General Equations and Asymptotic Analysis [Seite 272]
7.4.2 - 4.4.2 Example -- Dynamical Problem [Seite 276]
7.4.3 - 4.4.3 Example -- An Axisymmetric Stamp [Seite 278]
7.5 - 4.5 On the Concept of Solids [Seite 289]
7.6 - 4.6 Models of Non-Fourier Heat Conduction [Seite 292]
7.7 - 4.7 Concluding Remarks [Seite 299]
7.8 - References [Seite 299]
8 - Afterword [Seite 302]
9 - Index [Seite 304]
2 - Abbreviations [Seite 7]
3 - Contents [Seite 8]
4 - 1 Introduction: Historical Development of Tractable Models [Seite 11]
4.1 - References [Seite 21]
5 - 2 Discrete Finite Systems [Seite 22]
5.1 - 2.1 Linear Oscillators [Seite 22]
5.1.1 - 2.1.1 Linear Conservative Oscillator [Seite 23]
5.1.2 - 2.1.2 Linear Oscillator with Viscous Damping [Seite 24]
5.1.2.1 - 2.1.2.1 Strong Energy Dissipation (e >> 1) [Seite 25]
5.1.2.2 - 2.1.2.2 Weak Energy Dissipation (e<<1) [Seite 28]
5.1.2.3 - 2.1.2.3 Exercise [Seite 30]
5.1.3 - 2.1.3 Linear Oscillator with Viscous Damping and Periodic (Harmonic) Forcing [Seite 30]
5.1.3.1 - 2.1.3.1 Exercise [Seite 32]
5.1.4 - 2.1.4 Two Coupled Oscillators [Seite 33]
5.1.4.1 - 2.1.4.1 Weakly Coupled Oscillators with Strongly Different Frequencies [Seite 33]
5.1.4.2 - 2.1.4.2 Exercise [Seite 36]
5.1.4.3 - 2.1.4.3 Weakly Coupled Oscillators with Close Frequencies [Seite 36]
5.1.4.4 - 2.1.4.4 Exercise [Seite 40]
5.1.4.5 - 2.1.4.5 Strongly Coupled Oscillators with Essentially Different Frequencies [Seite 40]
5.1.4.6 - 2.1.4.6 Exercise [Seite 42]
5.1.4.7 - 2.1.4.7 Strongly Coupled Oscillators with Close Frequencies [Seite 43]
5.1.4.8 - 2.1.4.8 Exercise [Seite 43]
5.2 - 2.2 Single-DOF Nonlinear Oscillator [Seite 43]
5.2.1 - 2.2.1 Quasilinear Oscillator [Seite 45]
5.2.2 - 2.2.2 Strongly Nonlinear Oscillator and Vibro-Impact Approximation [Seite 48]
5.2.2.1 - 2.2.2.1 Special Solutions for Vibro-Impact Motions [Seite 48]
5.2.2.2 - 2.2.2.2 Vibro-Impact Systems Treatable by Analytic Functions [Seite 51]
5.2.3 - 2.2.3 Oscillator with Multiple Equilibriums [Seite 55]
5.3 - 2.3 Forced Nonlinear Oscillator [Seite 56]
5.3.1 - 2.3.1 General Remarks [Seite 56]
5.3.2 - 2.3.2 Governing Equations [Seite 57]
5.3.3 - 2.3.3 The Dynamics of the Oscillator without Dissipation and the LPT [Seite 59]
5.3.4 - 2.3.4 The Transient Dynamics of a Weakly Damped Oscillator [Seite 62]
5.3.4.1 - 2.3.4.1 Non-smooth Temporal Transformations [Seite 63]
5.3.4.2 - 2.3.4.2 The Construction of a Generating Solution [Seite 64]
5.3.4.3 - 2.3.4.3 Calculation of A0(t0) and .0(t0) [Seite 67]
5.3.5 - 2.3.5 Quasi-Linear Oscillations [Seite 70]
5.4 - 2.4 Entrainment, Synchronization and Resonance Capture [Seite 73]
5.4.1 - 2.4.1 Pendulum with Constant External Torque [Seite 74]
5.4.2 - 2.4.2 Entrainment of the Van der Pol Oscillator by External Harmonic Force [Seite 77]
5.4.3 - 2.4.3 Synchronization of Oscillators and Related Models [Seite 84]
5.4.4 - 2.4.4 Resonance Capture [Seite 86]
5.4.4.1 - 2.4.4.1 Exercises [Seite 89]
5.4.5 - 2.4.5 Forced Oscillator with Multiple States of Equilibrium [Seite 90]
5.5 - 2.5 Symmetric Systems of Coupled Nonlinear Oscillators Beating Phenomena [Seite 93]
5.5.1 - 2.5.1 Exercise [Seite 102]
5.6 - 2.6 2DOF Systems of Nonlinear Oscillators with Essential Asymmetry Targeted Energy Transfer (TET) [Seite 103]
5.6.1 - 2.6.1 Targeted Energy Transfer in an Unforced 2DOF System [Seite 103]
5.6.2 - 2.6.2 Targeted Energy Transfer in Forced 2DOF System [Seite 114]
5.7 - 2.7 Coupled Nonlinear Oscillators with Time Delays [Seite 142]
5.7.1 - 2.7.1 Analytic Model [Seite 142]
5.7.2 - 2.7.2 Numeric Verification -- Straight Modes [Seite 150]
5.7.3 - 2.7.3 Numeric Verification -- "Oval"-- Modes and Phase -- Locked Solutions [Seite 153]
5.8 - 2.8 Low-DOF Discrete Nonlinear Systems [Seite 156]
5.9 - 2.9 Concluding Remarks [Seite 169]
5.10 - References [Seite 170]
6 - 3 Infinite Discrete Systems [Seite 175]
6.1 - 3.1 Dynamics of Infinite Nonlinear Chains [Seite 175]
6.1.1 - 3.1.1 Long-Wavelength Approximation. Equation of Supersonic Extension Solitons in an Infinite FPU Chain [Seite 175]
6.1.2 - 3.1.2 Zigzag Chain and Long-Wave Solitons [Seite 177]
6.1.3 - 3.1.3 Envelope Solitons [Seite 179]
6.1.4 - 3.1.4 Optical Breathers in a Zigzag Chain [Seite 184]
6.1.5 - 3.1.5 Torsional Solitons [Seite 194]
6.1.6 - 3.1.6 Approximation of Immobile Neighbour Chains [Seite 196]
6.2 - 3.2 Dynamics of Essentially Nonlinear and Vibro-Impact Chains [Seite 200]
6.2.1 - 3.2.1 Oscillatory Chain with Rigid Barriers [Seite 201]
6.2.2 - 3.2.2 Discrete Breathers in a Vibro-Impact Chain [Seite 206]
6.2.2.1 - 3.2.2.1 System of Klein-Gordon (KG) Type [Seite 207]
6.2.2.2 - 3.2.2.2 System of Fermi-Pasta-Ulam (FPU) Type [Seite 211]
6.3 - 3.3 The Problem of Heat Conduction in Dielectrics [Seite 215]
6.4 - 3.4 Solitons in Energetically Nondegenerate Quasi-One-Dimensional Models [Seite 225]
6.4.1 - 3.4.1 Quasi-One-Dimensional Model of a Molecular Crystal: Soliton Modes of Motion in a Bistable Nonlinear System [Seite 227]
6.5 - 3.5 Dynamics of Ensembles of Interacting Nonlinear Chains [Seite 233]
6.6 - 3.6 Concluding Remarks [Seite 241]
6.7 - References [Seite 241]
7 - 4 Continuous Systems [Seite 245]
7.1 - 4.1 One-Dimensional Models [Seite 245]
7.1.1 - 4.1.1 Bolotin Model [Seite 245]
7.1.1.1 - 4.1.1.1 Exercises [Seite 249]
7.1.2 - 4.1.2 Simplification of the Timoshenko Beam [Seite 249]
7.2 - 4.2 The Planar Dynamical Problem and Tractable One-Dimensional Models of an Elastic Solid [Seite 256]
7.2.1 - 4.2.1 Exercises [Seite 261]
7.3 - 4.3 The Two-Dimensional Orthotropic Model and Its Application to a Complex Contact Problem [Seite 261]
7.3.1 - 4.3.1 Basic Asymptotic Decomposition of the Orthotropic Plate Problem [Seite 261]
7.3.2 - 4.3.2 The Contact Problem for a Planar Orthotropic Strip [Seite 267]
7.4 - 4.4 Models of Elastic Foundation [Seite 272]
7.4.1 - 4.4.1 General Equations and Asymptotic Analysis [Seite 272]
7.4.2 - 4.4.2 Example -- Dynamical Problem [Seite 276]
7.4.3 - 4.4.3 Example -- An Axisymmetric Stamp [Seite 278]
7.5 - 4.5 On the Concept of Solids [Seite 289]
7.6 - 4.6 Models of Non-Fourier Heat Conduction [Seite 292]
7.7 - 4.7 Concluding Remarks [Seite 299]
7.8 - References [Seite 299]
8 - Afterword [Seite 302]
9 - Index [Seite 304]
