Mechanical Vibration (eBook)

Fundamentals with Solved Examples

Ivana Kovacic, Dragi Radomirovic (Autoren)

eBook Download: PDF

2017 | 1. Auflage
280 Seiten
Wiley (Verlag)
978-1-118-92757-1 (ISBN)

Infos

Mechanical oscillators in Lagrange's formalism - a thorough problem-solved approach

This book takes a logically organized, clear and thorough problem-solved approach at instructing the reader in the application of Lagrange's formalism to derive mathematical models for mechanical oscillatory systems, while laying a foundation for vibration engineering analyses and design.

Each chapter contains brief introductory theory portions, followed by a large number of fully solved examples. These problems, inherent in the design and analysis of mechanical systems and engineering structures, are characterised by a complexity and originality that is rarely found in textbooks.

Numerous pedagogical features, explanations and unique techniques that stem from the authors' extensive teaching and research experience are included in the text in order to aid the reader with comprehension and retention. The book is rich visually, including numerous original figures with high-standard sketches and illustrations of mechanisms.

Key features:

• Distinctive content including a large number of different and original oscillatory examples, ranging from simple to very complex ones.
• Contains many important and useful hints for treating mechanical oscillatory systems.
• Each chapter is enriched with an Outline and Objectives, Chapter Review and Helpful Hints.

Mechanical Vibration: Fundamentals with Solved Examples is essential reading for senior and graduate students studying vibration, university professors, and researchers in industry.

Ivana Kova?i?, University of Novi Sad, Serbia

Ivana Kova?i? graduated in Mechanical Engineering from the Faculty of Technical Sciences (FTN), University of Novi Sad, Serbia. She obtained her MSc and PhD in the Theory of Nonlinear Vibrations at the FTN. She is currently a Full Professor of Mechanics at the FTN and the head of the Centre of Excellence for Vibro-Acoustic Systems and Signal Processing CEVAS at the same faculty. Kova?i? is the Subject Editor of three academic journals: the Journal of Sound and Vibration, the European Journal of Mechanics A/Solids and Meccanica. Her research involves the use of quantitative and qualitative methods to study differential equations arising from nonlinear dynamics problems mainly in mechanical engineering, and recently also in biomechanics and tree vibrations.

Dragi Radomirovi?, University of Novi Sad, Serbia

Dragi Radomirovi? graduated in Mechanical Engineering from the Faculty of Technical Sciences (FTN), University of Novi Sad (UNS), Serbia. He obtained his MSc and PhD in Analytical Mechanics at the FTN. He is a Full Professor of Mechanics at the Faculty of Agriculture, UNS. His research interests are directed towards Mechanical Vibrations and Analytical Mechanics.

Autor

Ivana Kovacic, University of Novi Sad, Serbia Ivana Kovacic graduated in Mechanical Engineering from the Faculty of Technical Sciences (FTN), University of Novi Sad, Serbia. She obtained her MSc and PhD in the Theory of Nonlinear Vibrations at the FTN. She is currently a Full Professor of Mechanics at the FTN and the head of the Centre of Excellence for Vibro-Acoustic Systems and Signal Processing CEVAS at the same faculty. Kovacic is the Subject Editor of three academic journals: the Journal of Sound and Vibration, the European Journal of Mechanics A/Solids and Meccanica. Her research involves the use of quantitative and qualitative methods to study differential equations arising from nonlinear dynamics problems mainly in mechanical engineering, and recently also in biomechanics and tree vibrations. Dragi Radomirovic, University of Novi Sad, Serbia Dragi Radomirovic graduated in Mechanical Engineering from the Faculty of Technical Sciences (FTN), University of Novi Sad (UNS), Serbia. He obtained his MSc and PhD in Analytical Mechanics at the FTN. He is a Full Professor of Mechanics at the Faculty of Agriculture, UNS. His research interests are directed towards Mechanical Vibrations and Analytical Mechanics.

Inhalt

Title Page 5
Copyright Page 6
Contents 7
Preface 13
About the Authors 11
Chapter 1 Preliminaries 15
Chapter Outline 15
Chapter Objectives 15
1.1 From Statics 15
1.1.1 Mechanical Systems and Equilibrium Equations 15
1.1.2 Constraints and Free-Body Diagrams 15
1.1.3 Equilibrium Condition Via Virtual Work 16
1.2 From Kinematics 18
1.2.1 Kinematics of Particles 18
1.2.2 Kinematics of Rigid Bodies 19
1.2.2.1 Rigid Body in Translatory Motion 19
1.2.2.2 Rigid Body in Fixed-Axis Rotation 19
1.2.2.3 Rigid Body in General Plane Motion 20
1.2.3 Kinematics of Particles in Compound Motion 21
1.3 From Kinetics 22
1.3.1 Kinetics of Particles 22
1.3.2 Kinetics of Rigid Bodies 23
1.3.2.1 Kinetics of Rigid Bodies in Translatory Motion 23
1.3.2.2 Kinetics of Rigid Bodies in Fixed-Axis Rotation 24
1.3.2.3 Kinetics of Rigid Bodies in General Plane Motion 24
1.4 From Strength of Materials 27
1.4.1 Axial Loading 27
1.4.2 Torsion 28
1.4.3 Bending 28
Chapter 2 Lagrange´s Equation for Mechanical Oscillatory Systems 31
Chapter Outline 31
Chapter Objectives 31
2.1 About Lagrange´s Equation of the Second Kind 31
2.2 Kinetic Energy in Mechanical Oscillatory Systems 33
2.3 Potential Energy in Mechanical Oscillatory Systems 35
2.3.1 Gravitational Potential Energy 36
2.3.2 Potential Energy of a Spring (Elastic Potential Energy) 38
2.3.2.1 On the Approximations for Linear Spring Deflection 39
2.4 Generalised Forces in Mechanical Oscillatory Systems 41
2.5 Dissipative Function in Mechanical Oscillatory Systems 42
References 44
Chapter 3 Free Undamped Vibration of Single-Degree-of-Freedom Systems 45
Chapter Outline 45
Chapter Objectives 45
Theoretical Introduction 45
Chapter 4 Free Damped Vibration of Single-Degree-of-Freedom Systems 81
Chapter Outline 81
Chapter Objectives 81
Theoretical Introduction 81
Chapter 5 Forced Vibration of Single-Degree-of-Freedom Systems 115
Chapter Outline 115
Chapter Objectives 115
Theoretical Introduction 115
Chapter 6 Free Undamped Vibration of Two-Degree-of-Freedom Systems 141
Chapter Outline 141
Chapter Objectives 141
Theoretical Introduction 141
Chapter 7 Forced Vibration of Two-Degree-of-Freedom Systems 167
Chapter Outline 167
Chapter Objectives 167
Theoretical Introduction 167
Chapter 8 Vibration of Systems with Infinite Number of Degrees of Freedom 197
Chapter Outline 197
Chapter Objectives 197
8.1 Theoretical Introduction: Longitudinal Vibration of Bars 197
8.2 Theoretical Introduction: Torsional Vibration of Shafts 211
8.3 Theoretical Introduction: Transversal Vibration of Beams 221
Chapter 9 Additional Topics 239
Chapter Outline 239
Chapter Objectives 239
9.1 Theoretical Introduction 239
9.2 Equivalent Two-Element System for Concurrent Springs and Dampers 240
9.2.1 Concurrent Springs 241
9.2.2 Concurrent Dampers 245
9.3 Nonlinear Springs in Series 252
9.3.1 Purely Nonlinear Springs in Series 253
9.3.2 Equal Duffing Springs in Series 253
9.3.3 Two Different Nonlinear Springs 254
9.4 On the Deflection and Potential Energy of Nonlinear Springs: Approximate Expressions 256
9.4.1 Duffing-Type Spring Deformed in the Static Equilibrium Position 256
9.4.2 Duffing-Type Spring Undeformed in the Static Equilibrium Position 256
9.5 Corrections of Stiffness Properties of Certain Oscillatory Systems 258
9.5.1 One-Degree-of-Freedom Systems 259
9.5.1.1 Linear–Linear System 259
9.5.1.2 Duffing–Linear System 260
9.5.1.3 Duffing–Duffing System 262
9.5.2 Two-Degree-of-Freedom Systems 262
9.5.2.1 System with Two Pairs of Orthogonal Duffing Springs 262
9.5.2.2 System with Two Pairs of Equal and Orthogonal Duffing Springs 266
9.5.2.3 System with Two Pairs of Equal and Symmetrically Attached Duffing Springs 267
Appendix Mathematical Topics 269
A.1 Geometry 269
A.2 Trigonometry 271
A.3 Algebra 272
A.4 Vectors 272
A.5 Derivatives (Notation: fdfdt) 273
A.6 Variation (Virtual Displacements) 274
A.7 Series 274
Index 275
EULA 277

Produkt-Details

• Erscheint lt. Verlag: 17.7.2017
• Sprache: englisch
• Themenwelt: Informatik ► Weitere Themen ► CAD-Programme
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Bauingenieur- u. Bauwesen • Baustatik • Baustatik u. Baumechanik • Beating oscillations • Civil Engineering & Construction • Damped oscillations • Equation of Motion • Equivalent stiffness' Dynamic absorber • Festkörpermechanik • Forced Vibrations • Lagrange's equation of the second kind • Maschinenbau • Maschinenbau - Entwurf • mechanical engineering • Mechanical Engineering - Design • Mechanical oscillators • potential energy • solid mechanics • Structural Theory & Structural Mechanics • Transversal vibrations • Vibration
• ISBN-10: 1-118-92757-5 / 1118927575
• ISBN-13: 978-1-118-92757-1 / 9781118927571