• Foreword

• Preface

• Acknowledgement

• PART 1: Basic Concepts

• Fundamentals of Vibrations

• Free Vibrations

• Damped Free Vibrations

• Fundamentals of Forced Vibrations

• Advanced Concepts of Forced Vibrations

• Torsional Vibrations

• Transverse Vibrations

• PART 2: Advanced Theory of Vibrations

• Transient Vibrations

• Vibrations of Two Degrees of Freedom Systems

• Vibration Absorbers

• Properties of Vibrating Systems

• Multi-Degrees of Freedom Systems

• Vibrations of Continuous Systems

• Numerical Methods

• Matrix Methods

• PART 3: Advanced Systems

• Finite Element Method

• Nonlinear Vibrations–I

• Nonlinear Vibrations–II

• Random Vibrations

• Vibrations in Plates

Part 1: Basic Concepts

Focuses on single-degree-of-freedom systems, providing a solid foundation in mathematical concepts and terminology. This section covers:

• Free and damped vibrations, including Viscous and Coulomb damping.

• Forced vibrations with harmonic, rotating, and reciprocating unbalance.

• Vibration isolation and measuring instruments.

• Dedicated discussions on torsional and transverse modes of vibration.

Part 2: Advanced Theory of Vibrations

Transitions into multi-degree of freedom and continuous systems. Key highlights include:

• The use of Laplace transforms for transient vibration analysis.

• In-depth exploration of vibration absorbers and influence coefficients.

• Advanced numerical approaches such as Holzer’s, Myklestad’s, and Stodola’s methods.

• A robust introduction to Matrix Methods, including matrix iteration and transfer matrix methods suitable for computer programming.

Part 3: Advanced Systems

Explores modern and complex vibration phenomena using high-level analytical tools:

• Finite Element Method (FEM): Fundamentals and applications in vibration analysis.

• Nonlinear Vibrations: Detailed coverage of the phase plane method, Duffing and Mathieu equations, and the "jump phenomenon".

• Random Vibrations: A statistical approach using probability distribution, power spectral density, and Fourier transforms.

• Vibrations in Plates: Introductory theory for both rectangular and circular thin plates.