## COURSE OBJECTIVES

Students will have a good understanding of the modelling of vibratory motion of mechanical systems using both single and multiple degree of freedom concepts. Students will be able to design simple vibration isolation systems. They will understand the concepts of natural frequencies and mode shapes and their significance in the solution of multiple degree of freedom problems. Students will have an introduction to the use of Laplace Transforms as a solution to differential equations of motion. They will be able to complete basic system modelling tasks. Students will acquire the ability to:

(1) Formulate mathematical models of problems in vibrations using Newton’s second law or energy principles.
(2) Determine a complete solution to the modelled mechanical vibration problems.
(3) Correlate results from the mathematical model to physical characteristics of the actual system.
(4) Design of a mechanical system using fundamental principles developed in the class.

## COURSE LEARNING OUTCOMES (CLO)

CLO-1: Analyze the type of vibration (desirable or undesirable) its attributes. (C4)
CLO-2: Apply the knowledge to different mechanical translational, rotational and other applications (C3)
CLO-3: Design and analyze the system response by using the different techniques of Mechanical Vibrations with the application of mathematical modeling. (C5)

## COURSE CONTENTS

• Origin of vibration, basic concepts, classification of vibration, analysis and elements of vibratory system. – Two Lectures
• Harmonic and harmonic analysis. Example Using Matlab – Two Lectures
• Free vibration of an undamped translational system, stability conditions – Two Lectures
• Free with viscous damping, Coulomb damping – Two Lectures
• Problem Solving from Ch-1 and Ch-2 – Two Lectures
• Introduction to Forced Vibration with Harmonic Excitation – Two Lectures
• Response of damped system with under F(t)=Feiwt – Two Lectures
• Forced vibration with coulomb damping, self-Excitation and Stability Analysis – Two Lectures
• Whirling of rotating shafts. Balancing of rotator machinery – Two Lectures
• Forced and free vibrations, coordinate coupling, principle coordinate – Two Lectures
• Coordinate coupling, principle coordinate – Two Lectures
• System with two degrees of freedom, analysis and response, with mode shapes – Two Lectures
• Problem solving regarding two degree of freedom system – Two Lectures
• Modeling of continuous system as multi-degree. Holzer Method – Two Lectures
• Influence coefficient, potential and kinetic energy – Two Lectures
• Introduction to Eigen-value problems and problem solving – Two Lectures