Vibrations and Stability: Advanced Theory, Analysis, and Tools

This book ties together classical and modern topics of advanced vibration analysis in an interesting and lucid manner. It is intended for advanced students, university teachers, and researchers in mechanical/structural engineering dynamics, and professional engineers aiming at strengthening their theoretical foundation. Assuming background knowledge in elementary vibrations, it provides a set of useful tools for understanding and analyzing the more complex dynamical phenomena that can be met in engineering and scientific practice. Summarizing first basic linear vibration theory, it progresses over various types of nonlinearity and nonlinear interaction to bifurcation analysis, chaotic vibrations, and special high-frequency effects. It trains the student to analyze simple models, recognize nonlinear phenomena, and work with advanced tools such as perturbation analysis and bifurcation analysis. Focusing attention on a limited number of simple, generic models, the book covers the qualitative behavior of a wide variety of mechanical/structural systems; the key examples dealt with can be fabricated as simple physical models for classroom demonstrations. Explaining theory in terms of relevant examples from real systems, this book is user-friendly and meets the increasing interest in, and significance of, nonlinear dynamics in mechanical/structural engineering. This 3rd edition adds many new topics, sections, figures, exercise problems, literature references, and other updates; it is backed up by a separately available booklet with worked out solutions to exercise problems.

"1139042265"
Vibrations and Stability: Advanced Theory, Analysis, and Tools

This book ties together classical and modern topics of advanced vibration analysis in an interesting and lucid manner. It is intended for advanced students, university teachers, and researchers in mechanical/structural engineering dynamics, and professional engineers aiming at strengthening their theoretical foundation. Assuming background knowledge in elementary vibrations, it provides a set of useful tools for understanding and analyzing the more complex dynamical phenomena that can be met in engineering and scientific practice. Summarizing first basic linear vibration theory, it progresses over various types of nonlinearity and nonlinear interaction to bifurcation analysis, chaotic vibrations, and special high-frequency effects. It trains the student to analyze simple models, recognize nonlinear phenomena, and work with advanced tools such as perturbation analysis and bifurcation analysis. Focusing attention on a limited number of simple, generic models, the book covers the qualitative behavior of a wide variety of mechanical/structural systems; the key examples dealt with can be fabricated as simple physical models for classroom demonstrations. Explaining theory in terms of relevant examples from real systems, this book is user-friendly and meets the increasing interest in, and significance of, nonlinear dynamics in mechanical/structural engineering. This 3rd edition adds many new topics, sections, figures, exercise problems, literature references, and other updates; it is backed up by a separately available booklet with worked out solutions to exercise problems.

66.99 In Stock
Vibrations and Stability: Advanced Theory, Analysis, and Tools

Vibrations and Stability: Advanced Theory, Analysis, and Tools

by Jon Juel Thomsen
Vibrations and Stability: Advanced Theory, Analysis, and Tools

Vibrations and Stability: Advanced Theory, Analysis, and Tools

by Jon Juel Thomsen

eBook3rd ed. 2021 (3rd ed. 2021)

$66.99  $89.00 Save 25% Current price is $66.99, Original price is $89. You Save 25%.

Available on Compatible NOOK devices, the free NOOK App and in My Digital Library.
WANT A NOOK?  Explore Now

Related collections and offers


Overview

This book ties together classical and modern topics of advanced vibration analysis in an interesting and lucid manner. It is intended for advanced students, university teachers, and researchers in mechanical/structural engineering dynamics, and professional engineers aiming at strengthening their theoretical foundation. Assuming background knowledge in elementary vibrations, it provides a set of useful tools for understanding and analyzing the more complex dynamical phenomena that can be met in engineering and scientific practice. Summarizing first basic linear vibration theory, it progresses over various types of nonlinearity and nonlinear interaction to bifurcation analysis, chaotic vibrations, and special high-frequency effects. It trains the student to analyze simple models, recognize nonlinear phenomena, and work with advanced tools such as perturbation analysis and bifurcation analysis. Focusing attention on a limited number of simple, generic models, the book covers the qualitative behavior of a wide variety of mechanical/structural systems; the key examples dealt with can be fabricated as simple physical models for classroom demonstrations. Explaining theory in terms of relevant examples from real systems, this book is user-friendly and meets the increasing interest in, and significance of, nonlinear dynamics in mechanical/structural engineering. This 3rd edition adds many new topics, sections, figures, exercise problems, literature references, and other updates; it is backed up by a separately available booklet with worked out solutions to exercise problems.


Product Details

ISBN-13: 9783030680459
Publisher: Springer-Verlag New York, LLC
Publication date: 03/18/2021
Sold by: Barnes & Noble
Format: eBook
File size: 29 MB
Note: This product may take a few minutes to download.

About the Author

PhD (1988) and dr.techn. (2003) in mechanical vibrations and dynamics; associate professor at the Technical University of Denmark, Dept. of Mechanical Engineering. Author of 100+ peer reviewed scienti­fic publications, covering many aspects of theoretical and experimental vibration analysis, in particular nonlinear effects and analysis. 30+ years of university teaching in advanced and basic vibration theory, dynamics, computer modeling, and experimental mechanics. Fundamental and applied research with a special focus on the description, analysis and synthesis of nonlinear phenomena, e.g. vibration suppression using nonlinearity, object transport using vibrations, non-trivial effects of high-frequency excitation, deterministic chaos, wave propagation in periodic media, discontinuous processes (e.g. vibro-impact, friction, clearance), fluid flow affected vibrations, vibration analysis for non-destructive testing and structural health monitoring, and nonlinear modal interaction; see more on www.staff.dtu.dk/jjth.

Table of Contents

PrefaceVII
ContentsXIII
NotationXXI
1Vibration Basics1
1.1Introduction1
1.2Single Degree of Freedom Systems2
1.2.1Undamped Free Vibrations2
1.2.2Damped Free Vibrations2
1.2.3Harmonic Forcing3
1.2.4Arbitrary Forcing4
1.3Multiple Degree of Freedom Systems4
1.3.1Equations of Motion5
1.3.2Undamped Free Vibrations6
1.3.3Orthogonality of Modes7
1.3.4Damped Free Vibrations7
1.3.5Harmonically Forced Vibrations, No Damping7
1.3.6Harmonically Forced Vibrations, Damping Included8
1.3.7General Periodic Forcing9
1.3.8Arbitrary Forcing, Transients9
1.4Continuous Systems10
1.4.1Equations of Motion10
1.4.2Undamped Free Vibrations11
1.4.3Orthogonality of Modes12
1.4.4Normal Coordinates13
1.4.5Forced Vibrations, No Damping13
1.4.6Forced Vibrations, Damping Included14
1.4.7Rayleigh's Method15
1.4.8Ritz Method16
1.5Energy Methods for Setting Up Equations Of Motion17
1.5.1Lagrange's Equations17
1.5.2Hamilton's Principle18
1.5.3From PDEs to ODEs: Mode shape Expansion21
1.5.4Bypassing PDEs: Using Lagrange's Equations with Continuous Systems23
1.6Problems25
2Eigenvalue Problems of Vibrations And Stability27
2.1Introduction27
2.2The Algebraic EVP27
2.2.1Mathematical Form28
2.2.2Properties of Eigenvalues and Eigenvectors28
2.2.3Methods of Solution29
2.3The Differential EVP29
2.3.1Mathematical Form30
2.4Stability-Related EVPs31
2.4.1The Clamped-hinged Euler Column31
2.4.2The Paradox of Follower-loading34
2.4.3Buckling by Gravity35
2.5Vibration-Related EVPs36
2.5.1Axial Vibrations of Straight Rods36
2.5.2Flexural Vibrations of Beams37
2.6Concepts of Differential EVPs39
2.6.1Multiplicity40
2.6.2Classes of Boundary Conditions: Essential and Suppressible40
2.6.3Function-classes: Eigen-, Test-, and Admissible functions41
2.6.4Adjointness41
2.6.5Definiteness42
2.6.6Orthogonality43
2.6.7Three Classes of EVPs43
2.6.8The Rayleigh Quotient43
2.7Properties of Eigenvalues and Eigenfunctions44
2.7.1Real-valueness of Eigenvalues44
2.7.2Sign of the Eigenvalues44
2.7.3Orthogonality of Eigenfunctions45
2.7.4Minimum Properties of the Eigenvalues46
2.7.5The Comparison Theorem47
2.7.6The Inclusion Theorem for One-term EVPs48
2.8Methods of Solution49
2.8.1Closed-form Solutions50
2.8.2The Method of Eigenfunction Iteration50
2.8.3The Rayleigh-Ritz Method51
2.8.4The Finite Difference Method54
2.8.5Collocation58
2.8.6Composite EVPs: Dunkerley's and Southwell's Formulas59
2.8.7Other Methods60
2.9Problems60
3Nonlinear Vibrations: Classical Local Theory65
3.1Introduction65
3.2Sources of Nonlinearity66
3.2.1Geometrical Nonlinearities66
3.2.2Material Nonlinearities68
3.2.3Nonlinear Body Forces69
3.2.4Physical Configuration Nonlinearities70
3.3Main Example: Pendulum with an Oscillating Support71
3.3.1Equation of Motion72
3.4Qualitative Analysis of the Unforced Response73
3.4.1Recasting the Equations into First-order Form73
3.4.2The Phase Plane74
3.4.3Singular Points76
3.4.4Stability of Singular Points77
3.4.5On the Behavior of Orbits near Singular Points79
3.5Quantitative Analysis85
3.5.1Perturbation Methods85
3.5.2The Straightforward Expansion86
3.5.3The Method of Multiple Scales88
3.5.4The Method of Harmonic Balance92
3.5.5The Method of Averaging94
3.6The Forced Response--Multiple Scales Analysis96
3.6.1Posing the Problem96
3.6.2Perturbation Equations97
3.6.3The Non-resonant Case99
3.6.4The Near-resonant Case100
3.6.5Stability of Stationary Solutions102
3.6.6Discussing Stationary Responses105
3.7Externally Excited Duffing Systems110
3.7.1Two Physical Examples111
3.7.2Primary Resonance, Weak Excitations116
3.7.3Non-resonant Hard Excitations122
3.7.4Obtaining Forced Responses by Averaging128
3.8Concluding Remarks130
3.9Problems130
4Nonlinear Multiple-DOF Systems: Local Analysis137
4.1Introduction137
4.2The Autoparametric Vibration Absorber138
4.2.1The System138
4.2.2First-order Approximate Response140
4.2.3Frequency and Force Responses144
4.2.4Concluding Remarks on the Vibration Absorber147
4.3Nonlinear Mode-Coupling of Non-Shallow Arches147
4.3.1The Model148
4.3.2Linear Response and Stability149
4.3.3Nonlinear Response and Stability150
4.4Other Systems Possessing Internal Resonance154
4.5The Follower-loaded Double Pendulum155
4.5.1The Model156
4.5.2The Zero Solution and its Stability158
4.5.3Periodic Solutions160
4.5.4Non-periodic and Non-zero Static Solutions164
4.5.5Summing Up164
4.6Pendulum with a Sliding Disk165
4.6.1Introduction165
4.6.2The System165
4.6.3Equations of Motion166
4.6.4Inspecting the Equations of Motion167
4.6.5Seeking Quasi-statical Equilibriums by Averaging167
4.7String with a Sliding Pointmass168
4.7.1Model System and Equations of Motion169
4.7.2Illustration of System Behavior172
4.7.3Response to Near-resonant Base Excitation174
4.7.4Response to Slow Frequency-sweeps177
4.7.5Response to Near-Resonant Axial Excitation179
4.7.6Non-trivial Effects of Rotary Inertia182
4.7.7Summing Up182
4.8Vibration-Induced Fluid Flow in Pipes183
4.9Problems185
5Bifurcations189
5.1Introduction189
5.2Systems, Bifurcations, and Bifurcation Conditions190
5.2.1Systems190
5.2.2Bifurcations190
5.2.3Bifurcation Conditions: Structural Instability191
5.3Codimension One Bifurcations of Equilibriums192
5.3.1The Pitchfork Bifurcation192
5.3.2The Saddle-node Bifurcation194
5.3.3The Transcritical Bifurcation195
5.3.4The Hopf Bifurcation196
5.4Codimension One Bifurcations for N-Dimensional Systems197
5.4.1Saddle-Node Conditions198
5.4.2Transcritical and Pitchfork Conditions199
5.4.3Hopf Conditions200
5.5Center Manifold Reduction201
5.5.1The Center Manifold Theorem202
5.5.2Implications of the Theorem203
5.5.3Computing the Center Manifold Reduction204
5.5.4An Example206
5.5.5Summing up on Center Manifold Reduction207
5.6Normal Form Reduction208
5.7Bifurcating Periodic Solutions209
5.8Grouping Bifurcations According to their Effect210
5.9On the Stability of Bifurcations to Perturbations211
5.9.1Stability of a Saddle-node Bifurcation211
5.9.2Stability of a Supercritical Pitchfork Bifurcation212
5.10Summing up on Different Notions of Stability213
5.11Examples215
5.11.1Midplane Stretching (Duffing's Equation)215
5.11.2Pendulum with a Moving Support (Parametric Excitation)217
5.11.3The Autoparametric Vibration Absorber219
5.11.4The Partially Follower-loaded Double Pendulum221
5.12Problems222
6Chaotic Vibrations225
6.1Introduction225
6.2A First Example227
6.3Tools for Detecting Chaotic Vibrations229
6.3.1Phase Planes229
6.3.2Frequency Specters231
6.3.3Poincare Maps231
6.3.4Lyapunov Exponents234
6.3.5Horizons of Predictability238
6.3.6Attractor Dimensions240
6.3.7Basins of Attraction241
6.3.8Summary on Detecting Tools242
6.4Universal Routes to Chaos242
6.4.1The Period-doubling Route243
6.4.2The Quasiperiodic Route245
6.4.3The Transient Route246
6.4.4The Intermittency Route248
6.4.5Summary on the Routes to Chaos249
6.5Tools for Predicting the Onset of Chaos249
6.5.1Criteria Related to the Universal Routes of Chaos249
6.5.2Searching for Homoclinic Tangles and Smale Horseshoes251
6.5.3The Melnikov Criterion255
6.5.4Criteria Based on Local Perturbation Analysis259
6.5.5Criteria for Conservative Chaos263
6.6Mechanical Systems and Chaos263
6.6.1The Lorenz System (D = 3)263
6.6.2Duffing-type Systems (D = 3)264
6.6.3Pendulum-type Systems (D = 3)265
6.6.4Piecewise Linear Systems (D [greater than or equal] 3)267
6.6.5Coupled Autonomous Systems (D [greater than or equal] 4)268
6.6.6Autoparametric Systems (D [greater than or equal] 5)273
6.6.7High-order Systems (D [greater than sign] 5)277
6.6.8Other Systems277
6.7Elastostatical Chaos278
6.8Spatial and Spatiotemporal Chaos281
6.9Controlling Chaos282
6.10Closing Comments283
6.11Problems284
7Special Effects of High-Frequency Excitation287
7.1Introduction287
7.2The Method of Direct Partition of Motions (MDPM)288
7.2.1Outline of the MDPM288
7.2.2The Concept of Vibrational Force291
7.2.3The MDPM Compared to Other Perturbation Approaches291
7.3Simple Examples292
7.3.1Pendulum on a Vibrating Support (Stiffening and Biasing)292
7.3.2Mass on a Vibrating Plane (Smoothening and Biasing)297
7.3.3Brumberg's Pipe (Smoothening and Biasing)300
7.4A Slight but Useful Generalization302
7.5A Fairly General Class of Discrete Systems303
7.5.1The System303
7.5.2Example Functions304
7.5.3The Averaged System Governing the 'Slow' Motions304
7.5.4Interpretation of Averaged Forcing Terms307
7.5.5The Effects308
7.5.6Stiffening309
7.5.7Biasing312
7.5.8Smoothening315
7.6A General Class of Linear Continuous Systems318
7.6.1The Generalized No-Resonance Prediction (GNRP)320
7.6.2The Generalized Analytical Resonance Prediction (GARP)322
7.6.3Example 1: Clamped String With HF Base Excitation324
7.6.4Example 2: Square Membrane with In-Plane HF Excitation325
7.7Specific Systems and Results--Some Examples327
7.7.1Using HF Excitation to Quench Friction-Induced Vibrations327
7.7.2Displacement due to HF Excitation and Asymmetric Friction329
7.7.3Chelomei's Pendulum--Resolving a Paradox329
7.7.4Stiffening of a Flexible String332
7.8Concluding Remarks333
7.9Problems334
Appendix APerforming Numerical Simulations339
A.1Solving Differential Equations339
A.2Computing Chaos-Related Quantities340
A.3Interfacing with the ODE-Solver340
A.4Locating Software on the Internet343
Appendix BMajor Exercises347
B.1Tension Control of Rotating Shafts347
B.1.1Mathematical Model348
B.1.2Eigenvalue Problem, Natural Frequencies and Mode Shapes348
B.1.3Discretisations, Choice of Control Law349
B.1.4Local Bifurcation
From the B&N Reads Blog

Customer Reviews