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# Mechanical Vibration

**Introduction**

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

- Math preliminaries
- Developing equations of motion
- Single DOF Vibrations
- Multiple DOF Vibrations
- Vibration absorbers
- Natural frequencies and Mode shapes n
- Mode shapes normalization and modal analysis
- 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

Prerequisites:

Dynamics

Engineering Mathematics

Differential Equations

Grading Policy:

40% Midterm Exam

50% Final Exam

10% Homeworks + Quiz

Teacher Assistants:

Miss S Rashidi, PhD student

Time:

Saturday 9:30 -11:00

Monday 9:30 -11:00

Class 3, Mechanical Engineering Department

Homeworks:

Term:

Spring 2020

Grade:

Undergraduate