Mechanical Vibration: Fundamentals with Solved Examples

Mechanical Vibration: Fundamentals with Solved Examples

Ivana Kovacic and Dragi Radomirovic, University of Novi Sad, Serbia

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.

About the authors

Preface

Chapter 1: Preliminaries

Chapter Outline

Chapter Objectives

1.1. From Statics

1.2. From Kinematics

1.3. From Kinetics

1.4. From Strength of Materials

1.4.1. Axial loading

1.4.2. Torsion

1.4.3. Bending

Chapter 2: Lagrange s Equation for Mechanical Oscillatory Systems

Chapter Outline

Chapter Objectives

2.1. About Lagrange s Equation of The Second Kind

2.2. Kinetic Energy in Mechanical Oscillatory Systems

2.3. Potential Energy in Mechanical Oscillatory Systems

2.4. Generalised Forces in Mechanical Oscillatory Systems

2.5. Dissipative Function in Mechanical Oscillatory Systems

References

Chapter 3: Free Undamped Vibration of Single–Degree–of–Freedom Systems

Chapter Outline

Chapter Objectives

Theoretical Introduction

Chapter 4: Free Damped Vibration of Single–Degree–of–Freedom Systems

Chapter Outline

Chapter Objectives

Theoretical Introduction

Chapter 5: Forced Vibration of Single–Degree–of–Freedom Systems

Chapter Outline

Chapter Objectives

Theoretical Introduction

Chapter 6: Free Undamped Vibration of Two–Degree–of–Freedom Systems

Chapter Outline

Chapter Objectives

Theoretical Introduction

Chapter 7: Forced Vibration of Two–Degree–of–Freedom Systems

Chapter Outline

Chapter Objectives

Theoretical Introduction

Chapter 8: Vibration of Systems with Infinite Number of Degrees of Freedom

Chapter Outline

Chapter Objectives

8.1. Theoretical Introduction: Longitudinal Vibration of Bars

8.2. Theoretical Introduction: Torsional Vibration of Shafts

8.3. Theoretical Introduction: Transversal Vibration of Beams

Chapter 9: Additional Topics

Chapter Outline

Chapter Objectives

9.1. Theoretical Introduction

9.2. Equivalent Two–Element System for Concurrent Springs and Dampers

9.3. Nonlinear Springs in Series

9.4. On the Deflection and Potential Energy of Nonlinear Springs: Approximate Expressions

9.5. Corrections of Stiffness Properties of Certain Oscillatory Systems

Appendix: Mathematical Topics

Index