Chapter 1

Single Degree of Freedom Systems

Undamped and damped free vibrations

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Logarithmic decrement and critical damping

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Forced harmonic vibrations and resonance

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Response to periodic and arbitrary excitations

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Duhamel's integral formulation

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Chapter 2

Multi-Degree of Freedom Systems

Equations of motion for MDOF systems

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Evaluation of mass, stiffness, and damping matrices

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Free vibration analysis and eigenvalue problems

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Orthogonality of mode shapes

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Mode superposition method for dynamic response

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Chapter 3

Continuous Systems

Vibration of strings and cables

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Longitudinal and torsional vibration of bars

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Transverse vibration of beams

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Rayleigh-Ritz and Galerkin methods

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Effect of rotary inertia and shear deformation

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Chapter 4

Numerical Evaluation of Dynamic Response

Time-stepping methods overview

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Central difference method

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Newmark's beta method

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Wilson-theta method

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Stability and accuracy analysis of numerical methods

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Chapter 5

Vibration Control and Applications

Principles of vibration isolation

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Tuned mass dampers (TMDs)

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Base isolation techniques

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Dynamic testing of structures

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Aeroelastic and hydrodynamic dynamic effects

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