Introduction

The main objective of the course is to obtain the dynamic response of single and multiple degree-of-freedom (DOF) systems.

1. Math preliminaries
2. Developing equations of motion
3. Single DOF Vibrations
4. Multiple DOF Vibrations
5. Vibration absorbers
6. Natural frequencies and Mode shapes n
7. Mode shapes normalization and modal analysis
8. Solving for discrete system vibration

Syllabus

Introduction

• Mathematical preliminaries
• Oscillatory motion
• Industrial applications

Single degree of freedom (SDoF) systems

• Derive the equations of motion for SDof system
• Newton’s equation of motion
• Work and energy equation
• Free vibration of undamped SDoF systems
• Forced Vibration of undamped SDoF systems

Types of damping in structures

• Viscous damping
• Coulomb damping
• Structural damping

Single degree of freedom (SDoF) systems

• Free vibration of damped SDoF systems
• Forced vibration of damped SDoF systems
• Vibration isolation
• Transmissibility
• Transient analysis of SDoF systems
• Equation of motion

Multi degrees of freedom (MDoF) systems

• Free vibration of undamped MDoF systems
• Natural frequencies
• Mode shapes
• Time response of MDoF systems
• Forced response of MDoF systems
• Base motion
• Vibration absorbers
• Lagrange’s method
• Modal superposition

Approximation techniques in estimation of natural frequencies and mode shapes

• Dunkerely’s method
• Rayliegh’s method
• Direct iteration method