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

1. Introduction
   1. Mathematical preliminaries
   2. Oscillatory motion
   3. Industrial applications
2. Single degree of freedom (SDoF) systems
1. Derive the equations of motion for SDof systems
   1. Newton’s equation of motion
   2. Work and energy equation
2. Free vibration of undamped SDoF systems
3. Forced Vibration of undamped SDoF systems
4. Types of damping in structures
1. Viscous damping
2. Coulomb damping
3. Structural damping
4. Free vibration of damped SDoF systems
5. Forced vibration of damped SDoF systems
6. Vibration isolation
7. Transmissibility
8. Transient analysis of SDoF systems
1. Equation of motion
2. Free vibration of undamped MDoF systems
   1. Natural frequencies
   2. Mode shapes
   3. Time response of MDoF systems
3. Forced response of MDoF systems
4. Base motion
5. Vibration absorbers
6. Lagrange’s method
7. Modal superposition
1. Dunkerely’s method
2. Rayliegh’s method
3. Direct iteration method
4. Multi degrees of freedom (MDoF) systems
5. Approximation techniques in estimation of natural frequencies and mode shapes