Lovely Professional University, Punjab

Course Code Course Title Course Planner Lectures Tutorials Practicals Credits

MEC406 MECHANICAL VIBRATION 15880::Hitesh Dhingra 3.0 1.0 0.0 4.0

Course Category Courses with Numerical focus

TextBooks

Sr No Title Author Edition Year Publisher Name

T-1 Mechanical vibration Thammaiah Gowda, Jagadeesha T and D V Girish

1st 2012 Tata McGraw Hill

Reference Books

Sr No Title Author Edition Year Publisher Name

R-1 Mechanical Vibrations V.P.Singh 9th 2007 Dhanpat Rai

R-2 Mechanical vibration S. S. Rao 4th 2003 Pearson

Relevant Websites

Sr No (Web address) (only if relevant to the course) Salient Features

RW-1 http://www.nptel.iitm.ac.in/courses/Webcourse-contents/IIT-%20Guwahati/ve/index.htm

Lecture Notes

Week Number

Lecture Number

Broad Topic(Sub Topic) Chapters/Sections of Text/reference books

Other Readings,Relevant Websites, Audio Visual Aids, software and Virtual Labs

Lecture Description Learning Outcomes Pedagogical ToolDemonstration/ Case Study / Images / animation / ppt etc. Planned

Week 1 Lecture 1 Fundamentals of Vibration(Modeling of vibration systems)

T-1:Article 1.1-1.5R-1:Article 1.1-1.4R-2:Article 1.1-1.3

Introduction to Vibration and its effects

Students learn the effects of vibration and causes of vibrations

Discussion on the Vibrations and its effects

Detailed Plan For Lectures

LTP week distribution: (LTP Weeks)

Weeks before MTE 7

Weeks After MTE 7

Spill Over 3

Week 1 Lecture 1 Fundamentals of Vibration(Vibration terminology)

T-1:Article 1.4R-1:Article 1.5 and

1.8

Important definition to know about vibrations

Student come to know about the different terms related to a vibrating system

Discussion on the different terms used in vibrational analysis

Fundamentals of Vibration(Harmonic motion)

T-1:Article 1.10-1.11 and Article 1.14R-1:Article 1.9

and1.13

Description about Harmonic motion, its properties and procedure to add two or more harmonic motions both analytically as well as graphically

Student learn how to find resultant of two or more harmonic motions

Discussion on the topic

Lecture 2 Fundamentals of Vibration(Harmonic motion)

T-1:Article 1.10-1.11 and Article 1.14R-1:Article 1.9

and1.13

Description about Harmonic motion, its properties and procedure to add two or more harmonic motions both analytically as well as graphically

Student learn how to find resultant of two or more harmonic motions

Discussion on the topic

Fundamentals of Vibration(Periodic motion)

T-1:Article 1.10R-1:Article 1.9

Description about Periodic Motion and its properties

Student learn about different properties of a periodic motion

Discussion on the topic

Lecture 3 Fundamentals of Vibration(Periodic motion)

T-1:Article 1.10R-1:Article 1.9

Description about Periodic Motion and its properties

Student learn about different properties of a periodic motion

Discussion on the topic

Fundamentals of Vibration(Inertia Elements)

T-1:Article 1.5R-2:Article 1.8

What are inertia elements and their properties

Student learn about diferent inertia elements and their importance in a vibrating system

Discussion on the topic

Fundamentals of Vibration(Stiffness Elements)

T-1:Article 1.6 and Article 2.4-2.7R-1:Article 2.4R-2:Article 1.7

Description about stiffness elements of a vibrating system

Student learn about stiffness elements and their different combinations

video showing effect of stiffness elements, inertia elements,relation between Potential and Kinetic Energies

Week 2 Lecture 4 Fundamentals of Vibration(Stiffness Elements)

T-1:Article 1.6 and Article 2.4-2.7R-1:Article 2.4R-2:Article 1.7

Description about stiffness elements of a vibrating system

Student learn about stiffness elements and their different combinations

video showing effect of stiffness elements, inertia elements,relation between Potential and Kinetic Energies

Fundamentals of Vibration(Dissipation Elements)

T-1:Article 1.7R-2:Article 1.9

Discussion on dampers and their properties

Student learn about different properties of dissipation elements

Discussion on the topic

Lecture 5 Free Vibration of Single Degree of Freedom Systems(Vibration model)

T-1:Article 2.1-2.3R-1:Article 2.2

R-2:Article 2.2-2.5

RW-1 Description about different types of vibration model and how to make them

Student learn how to make a model of vibrating body for analysis

Discussion on the topic

Week 2 Lecture 5 Free Vibration of Single Degree of Freedom Systems(Equations of motion)

T-1:Article 2.1-2.3R-1:Article 2.1-2.3R-2:Article 2.1-2.3

RW-1 Discussion on what are equations of motion and their importance

Student learn how to write equations of motion for different vibrating systems using different methods

Solving Derivation on white board

Lecture 6 Free Vibration of Single Degree of Freedom Systems(Natural frequency)

T-1:Article 2.12-2.13R-2:Article 2.1-2.3

Importance of natural frequency is discussed along with methods to find it

Student learn about natural frequency and different methods of finding it

Discussion on the topic

Week 3 Lecture 7 Free Vibration of Single Degree of Freedom Systems(Coulomb damping)

T-1:Article 3.9R-1:Article 3.2R-2:Article 2.7

What is coulomb damping and its use

Student will learn about coulomb damping and its applications

Discussion on the topic

Free Vibration of Single Degree of Freedom Systems(Structural damping)

T-1:Article 3.10R-1:Article 3.2R-2:Article 2.8

What is structural damping and its use

Student will learn about structural damping and its applications

Discussion on the topic

Free Vibration of Single Degree of Freedom Systems(Types of Damping)

T-1:Article 3.9-3.12R-1:Article 3.2

Description about different types of damping

Student will come to know about different types of damping available and their uses

Discussion on the topic

Lecture 8 Free Vibration of Single Degree of Freedom Systems(Viscously damped free vibration)

T-1:Article 3.1-3.5R-1:Article 3.1-3.3

R-2:Article 2.6

RW-1 Description about viscous damping, its differential equation and solution

Student learn about viscous damping and solving differential equation for the given problem

Solving Derivation on white board

Free Vibration of Single Degree of Freedom Systems(Damping ratio)

T-1:Article 3.6R-1:Article 3.3

What is damping ration and its properties

Student learn about damping ratio and effects of different values of damping ratio on a vibrating system

Solving Derivation on white board

Lecture 9 Free Vibration of Single Degree of Freedom Systems(Damping ratio)

T-1:Article 3.6R-1:Article 3.3

What is damping ration and its properties

Student learn about damping ratio and effects of different values of damping ratio on a vibrating system

Solving Derivation on white board

Week 4 Lecture 10 Free Vibration of Single Degree of Freedom Systems(Logarithmic decrement)

T-1:Article 3.7R-1:Article 3.4

R-2:Article 2.6.3

Discussion about logrithmic decrement and its derivation

Student learn what is Logrithmic decrement and its significance as well as how to derive an expression of it

Solving Derivation on white board

Lecture 11 Forced Vibration of Single Degree of Freedom Systems(Harmonically Forced Vibration)

T-1:Article 4.1-4.2R-1:Article 4.1-4.3

RW-1 Discussion on Harmonically Forced Vibrations and their causes and effects

Student will learn how to find response of a system under Harmonically forced vibrations

Solving Derivation on white board

Week 4 Lecture 12 Forced Vibration of Single Degree of Freedom Systems(Magnification factor)

T-1:Article 4.3 Lecture about magnification factor and its properties

Student will learn what is magnification factor and its different properties under different vibrating conditions

Solving Derivation on white board

Week 5 Lecture 13 Forced Vibration of Single Degree of Freedom Systems(Rotating and reciprocating unbalance)

T-1:Article 4.4R-1:Article 4.4R-2:Article 3.7

RW-1 Description about rotating unbalance and its effects along with expression of response

Student learn about effects and causes of rotating unbalance and how to find response of a system vibrating under rotating unbalance

Discussion on the topic

Lecture 14 Forced Vibration of Single Degree of Freedom Systems(Support motion)

T-1:Article 4.5R-1:Article 4.5

RW-1 Discussion about the concept of support motion and its different cases with derivation

Student will learn about the concept of support motion in a vibrating body and also derive its expression for different cases

Solving Derivation on white board

Lecture 15 Forced Vibration of Single Degree of Freedom Systems(Forced Energy dissipated by damping)

T-1:Article 3.8 Description about the energy dissipation during damping

Student will learn to obtain an expression for the energy dissipated during damping under different conditions

Solving Derivation on white board

Forced Vibration of Single Degree of Freedom Systems(Vibration with coulomb damping)

T-1:Article 4.7-4.8R-1:Article 4.8 and

4.10

Description about coulomb damping and its effects

Student learn about coulomb damping and its effects under different conditions

Discussion on the topic

Week 6 Lecture 16 Forced Vibration of Single Degree of Freedom Systems(Vibration Isolation)

T-1:Article 4.10-4.11 and 4.14

R-1:Article 4.6-4.7

What is Vibration Isolation and how it is done

Student learn about vibration isolation and its various methods

Discussion on the topic

Forced Vibration of Single Degree of Freedom Systems(Force Transmissibility)

T-1:Article 4.10-4.11R-1:Article 4.6-4.7

Force Transmissibility and its effects on a vibrating system

Student will learn what is Force Transmissibilty, its derivation and how to solve problems based on it

Solving Derivation on white board

Lecture 17 Forced Vibration of Single Degree of Freedom Systems(Motion Isolation)

T-1:Article 4.12-4.13 Description of Motion Isolation and its effects

Student will learn about Motion Isolation and its effects as well as obtain an expression for it

Solving Derivation on white board

Forced Vibration of Single Degree of Freedom Systems(Motion Transmissibility)

T-1:Article 4.12-4.13 Motion Transmissibility and its effects on a vibrating system

Student will learn what is Motion Transmissibilty, its derivation and how to solve problems based on it

Solving Derivation on white board

Lecture 18 Test 1

Week 7 Lecture 19 Forced Vibration of Single Degree of Freedom Systems(Vibration Measuring Instruments)

T-1:Article 5.1-5.3R-1:Article 4.11

R-2:Article 10.3.1-10.3.2

What is Vibration Measurement and how it is done

Student will come to know about vibration measurement and what parameters of vibration can be measured using different instruments

Discussion on the topic

Forced Vibration of Single Degree of Freedom Systems(Vibrometer)

T-1:Article 5.1-5.3R-1:Article 4.11

R-2:Article 10.3.1-10.3.2

How to use Vibrometer for measuring vibrations

Student learn how to measure vibrations using vibrometer

Solving Derivation on white board

Forced Vibration of Single Degree of Freedom Systems(Accelerometer)

T-1:Article 5.1-5.3R-1:Article 4.11

R-2:Article 10.3.1-10.3.2

How to use Accelerometer for measuring vibrations

Student learn how to measure vibrations using Acceleroometer

Solving Derivation on white board

Lecture 20 Forced Vibration of Single Degree of Freedom Systems(Whirling of Shaft)

T-1:Article 5.5R-1:Article 4.14-4.15

Description about whirling of shaft and finding expression of amplitude for it

Student will learn about whirling of shaft, its related derivation also how to solve the problems

Solving Derivation on white board

Lecture 21 Forced Vibration of Single Degree of Freedom Systems(Frequency Response Curve)

Spill Over

MID-TERMWeek 8 Lecture 22 Two Degree of Freedom System

(Introduction)T-1:Article 6.1R-1:Article 5.1R-2:Article 5.1

Introduction to two degree of freedom systems

Student will learn what is a two degree of freedom system and how they are identified

Discussion on the topic

Two Degree of Freedom System(Principal and Normal modes of Vibration)

T-1:Article 6.2R-1:Article 5.2-5.6R-2:Article 5.2-5.4

and 5.6

Procedure to find natural frequency and principal and normal modes of vibration

Student will learn how to solve vibrational problems of simple two degree freedom problem

Discussion on the topic

Lecture 23 Two Degree of Freedom System(Principal and Normal modes of Vibration)

T-1:Article 6.2R-1:Article 5.2-5.6R-2:Article 5.2-5.4

and 5.6

Procedure to find natural frequency and principal and normal modes of vibration

Student will learn how to solve vibrational problems of simple two degree freedom problem

Discussion on the topic

Lecture 24 Two Degree of Freedom System(Degenerating system)

T-1:Article 6.4R-1:Article 5.7R-2:Article 5.7

Procedure to solve problems for Degenerating and Semi Definite systems

Student will learn what degenerating systems are and what is their importance

Solving Derivation on white board

Two Degree of Freedom System(Combined rectilinear and angular modes)

T-1:Article 6.5R-1:Article 5.8R-2:Article 5.5

Description and derivation for Coordinate couplig, Combined modes

Student will learn about combined rectilinear and angular modes and will be able to solve problems based on it

Solving Derivation on white board

Week 8 Lecture 24 Two Degree of Freedom System(Coordinate Coupling)

T-1:Article 6.13 Description of different cases of coordinate coupling

Student will learn about coordinate coupling and will be able to solve problems for different cases of coupling

Discussion on the topic

Week 9 Lecture 25 Two Degree of Freedom System(Langrange method)

T-1:Article 6.15R-1:Article 5.15R-2:Article 6.7

Description about Lagranges equation and its application

Student will learn how to obtain equation of motion for a system using lagranges equation

Discussion on the topic

Lecture 26 Two Degree of Freedom System(Vibration Absorber)

T-1:Article 6.7R-1:Article 5.9 and

5.11

Introduction to Vibration absorber

Student will learn about vibration absorber and its applications

Discussion on the topic

Two Degree of Freedom System(Frahm Vibration Absorber)

T-1:Article 6.7R-1:Article 5.9 and

5.11

Derivation for Frahm Vibration absorber

Student will learn about derivation and working of Frahm Vibration absorber and its conditions for effectiveness

Solving Derivation on white board

Lecture 27 Multi Degree of Freedom Systems(Introduction)

Spill Over

Week 10 Lecture 28 Test 2

Lecture 29 Multi Degree of Freedom Systems(Flexibility Coefficient and flexibility matrix)

T-1:Article 7.3-7.4R-1:Article 6.2R-2:Article 6.4

Description of procedure to find Flexibility coefficients and flexibility matrix

Student will be able to find flexibility coefficients and write flexibility matrix

Discussion on the topic

Multi Degree of Freedom Systems(Influence coefficient)

T-1:Article 7.1 and 7.3-7.4

R-1:Article 6.1-6.2R-2:Article 6.1-6.2

and 6.4

Introduction to Multi Degree of freedom systems and procedure to find influence coefficients will be discussed

Student will understand how to find influence coefficients and what is their importance in finding natural frequency of multi degree freedom system

Discussion on the topic

Lecture 30 Multi Degree of Freedom Systems(Flexibility Coefficient and flexibility matrix)

T-1:Article 7.3-7.4R-1:Article 6.2R-2:Article 6.4

Description of procedure to find Flexibility coefficients and flexibility matrix

Student will be able to find flexibility coefficients and write flexibility matrix

Discussion on the topic

Week 11 Lecture 31 Multi Degree of Freedom Systems(Eigen Value and Eigen Vector Problem)

T-1:Article 7.6R-1:Article 6.11

R-2:Article 6.9-6.10

Description about different approaches to use eigen values and eigen vectors for calculating natural frequency and mode shapes

Student will learn different methods of using eigen values and eigen vectors for calculating Natural frequency and mode shapes

Solving Derivation on white board

Week 11 Lecture 32 Multi Degree of Freedom Systems(Matrix iteration method)

T-1:Article 7.8R-1:Article 6.6R-2:Article 7.5

Description of procedure to find natural frequencies and mode shapes using matrix iterations

Student will be able to find natural frequencies and mode shapes of multi degree freedom system using matrix iterations

Discussion on the topic

Multi Degree of Freedom Systems(Orthogonality Principle)

T-1:Article 7.7R-1:Article 6.5

Demonstration about Orthogonality Principle and its application

Student will learn how to use orthogonality principle in matrix iteration method

Discussion on the topic

Lecture 33 Multi Degree of Freedom Systems(Orthogonality Principle)

T-1:Article 7.7R-1:Article 6.5

Demonstration about Orthogonality Principle and its application

Student will learn how to use orthogonality principle in matrix iteration method

Discussion on the topic

Multi Degree of Freedom Systems(Matrix iteration method)

T-1:Article 7.8R-1:Article 6.6R-2:Article 7.5

Description of procedure to find natural frequencies and mode shapes using matrix iterations

Student will be able to find natural frequencies and mode shapes of multi degree freedom system using matrix iterations

Discussion on the topic

Week 12 Lecture 34 Multi Degree of Freedom Systems(Dunkerley's Method)

T-1:Article 8.1R-2:Article 7.2

Derivation of dunkerley equation

Student will learn how to derive Dunkerley Equation and how to find natural frequency using it

Solving Derivation on white board

Lecture 35 Vibration of Continuous Systems(Vibrating String)

T-1:Article 9.1-9.2R-1:Article 7.1-7.2

Introduction to Continuous system and derivation of general solution for a vibrating string

Student will learn about continuous system and its properties Also student will be able to make solution for such a system depending on given conditions

Solving Derivation on white board

Lecture 36 Vibration of Continuous Systems(Longitudinal Vibration of Rods)

T-1:Article 9.3R-1:Article 7.3

Derivation Solving of general solution for a vibrating string

Student will be able to make solution for such a system depending on given conditions

Solving Derivation on white board

Week 13 Lecture 37 Test 3

Lecture 38 Vibration of Continuous Systems(Torsional Vibration of rods)

Spill Over

Lecture 39 Vibration of Continuous Systems(Euler equation for beams)

T-1:Article 9.4-9.5R-1:Article 7.4-7.5

Solution for Torsional Vibration of rods and Euler equation of beams

Student will be able to make solution for such a system depending on given conditions

Solving Derivation on white board

Week 14 Lecture 40 Vibration of Continuous Systems(Euler equation for beams)

T-1:Article 9.4-9.5R-1:Article 7.4-7.5

Solution for Torsional Vibration of rods and Euler equation of beams

Student will be able to make solution for such a system depending on given conditions

Solving Derivation on white board

Week 14 Lecture 41 Vibration of Continuous Systems(Euler equation for beams)

T-1:Article 9.4-9.5R-1:Article 7.4-7.5

Solution for Torsional Vibration of rods and Euler equation of beams

Student will be able to make solution for such a system depending on given conditions

Solving Derivation on white board

Lecture 42 Vibration of Continuous Systems(Euler equation for beams)

T-1:Article 9.4-9.5R-1:Article 7.4-7.5

Solution for Torsional Vibration of rods and Euler equation of beams

Student will be able to make solution for such a system depending on given conditions

Solving Derivation on white board

SPILL OVERWeek 15 Lecture 43 Spill Over

Lecture 44 Spill Over

Lecture 45 Spill Over

Scheme for CA:Component Frequency Out Of Each Marks Total Marks

Test 2 3 10 20

Total :- 10 20

Details of Academic Task(s)

AT No. Objective Topic of the Academic Task Nature of Academic Task(group/individuals/field

work

Evaluation Mode Allottment / submission Week

Test 1 To Prepare the Students for Mid Term Test

Fundamentals of Vibration : Modeling of vibration systems, Vibration terminology, Harmonic motion, Periodic motion, Inertia Elements, Stiffness Elements, Dissipation Elements Free Vibration of Single Degree of Freedom Systems : Vibration model, Equations of motion, Natural frequency, Viscously damped free vibration, Damping ratio, Logarithmic decrement, Coulomb damping, Structural damping, Types of DampingForced Vibration of Single Degree of Freedom Systems : Harmonically Forced Vibration, Magnification factor, Rotating and reciprocating unbalance

Individual Step Marking 4 / 6

Test 2 To test analytically the understanding and knowledge gained by student.

Vibration Measuring Instruments, Vibrometer, Accelerometer, Whirling of ShaftTwo Degree of Freedom System : Introduction, Principal and Normal modes of Vibration, Degenerating system, Combined rectilinear and angular modes, Langrange method, Vibration Absorber, Frahm Vibration Absorber, Coordinate Coupling

Individual Step Marking 8 / 10

Test 3 To check analytically the knowledge gained by the students

Multi Degree of Freedom Systems : Introduction, Influence coefficient, Flexibility Coefficient and flexibility matrix, Eigen Value and Eigen Vector Problem, Matrix iteration method, Orthogonality Principle, Dunkerley's MethodVibration of Continuous Systems : Vibrating String, Longitudinal Vibration of Rods.

Individual StepbMarking 10 / 12

Plan for Tutorial: (Please do not use these time slots for syllabus coverage)Tutorial No. Lecture Topic Type of pedagogical tool(s) planned

(case analysis,problem solving test,role play,business game etc)

Tutorial 1 Addition of Harmonic MotionWork done by Harmonic Force

Problem solving

Tutorial 2 Natural Frequency of Undamped Single Degree of Freedom System

Problem solving

Tutorial 3 Natural Frequency of Damped Single Degree of Freedom System

Problem solving

Tutorial 4 Logrithmic Decrement, Damping Ratio Amplitude Ratio Problem solving

Tutorial 5 Harmonically Forced Vibration, Magnification factor, Rotating and reciprocating unbalance

Problem solving

Tutorial 6 Support motion, Forced Energy dissipated by damping, Vibration with coulomb damping, Vibration Isolation

Problem solving

Tutorial 7 rgy dissipated by damping, Vibration with coulomb damping, Vibration Isolation, Force Transmissibility, Motion Isolation, Motion Transmissibility, Frequency Response Curve, Vibration Measuring Instruments,Vibrometer, Accelerometer, Whirling of Shaft

Problem solving

After Mid-TermTutorial 8 Principal and Normal modes of Vibration, Degenerating

systemProblem solving

Tutorial 9 Combined rectilinear and angular modes, Langrange method

Problem solving

Tutorial 10 Frahm Vibration Absorber,Influence coefficient, Flexibility Coefficient and flexibility matrix

Problem solving

Tutorial 11 Eigen Value and Eigen Vector Problem Problem solving

Tutorial 12 Matrix iteration method,Orthogonality Principle Problem solving

Tutorial 13 Vibrating String, Longitudinal Vibration of Rods Problem solving

Tutorial 14 Torsional Vibration of rods, Euler equation for beams Problem solving