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 and conceptual focus

TextBooks

Sr No Title Author Edition Year Publisher Name

T-1 Mechanical vibration S. S. Rao 4th 2003 Pearson

Reference Books

Sr No Title Author Edition Year Publisher Name

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

R-2 MECHANICAL VIBRATIONS Dr. Debabrata Nag 2nd 2011 Wiley-India, New Delhi

R-3 Mechanical Vibrations G.K Grover 8th Nem Chand Brothers

R-4 Mechanical Vibrations and Noise Engineering

A.G Ambekar 5th 2010 PHI (Pretice Hall India)

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

RW-2 http://www.math.psu.edu/tseng/class/Math251/Notes-MechV.pdf Lecture Notes

RW-3 http://www.me.mtu.edu/courses/meem3700/lecture_11.pdf Lecture Notes

RW-4 http://nptel.iitm.ac.in/courses/112104040/pdf/lecture18.pdf Lecture Notes

Detailed Plan For Lectures

LTP week distribution: (LTP Weeks)

Weeks before MTE 7

Weeks After MTE 7

Spill Over 3

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(Vibration terminology)

T-1:1R-1:1R-3:1R-4:1

Introduction to Vibrationand its effects

Students learn theeffects of vibration andcauses of vibrations

Animation of bridge vibrating under heavy winds

Lecture 2 Fundamentals of Vibration(Harmonic motion)

T-1:1R-1:1R-3:1R-4:1

Description aboutHarmonic motion, itsproperties and procedureto add two or moreharmonic motions bothanalytically as

Student learn how tofind resultant of two ormore harmonic motions

Video related to harmonic motion

Fundamentals of Vibration(Periodic motion)

T-1:1R-1:1R-3:1R-4:1

Description aboutHarmonic motion, itsproperties and procedureto add two or moreharmonic motions bothanalytically as

Student learn how tofind resultant of two ormore harmonic motions

Video related to periodic motion

Lecture 3 Fundamentals of Vibration(Modeling of vibration systems)

T-1:1R-1:1R-3:1R-4:1

What are inertiaelements and theirproperties

Student learn aboutdiferent inertiaelements and theirimportance in avibrating system

Animation related to vibrating model

Fundamentals of Vibration(Inertia Elements)

T-1:1R-1:1R-2:1R-3:1

What are inertiaelements and theirproperties

Student learn aboutdiferent inertiaelements and theirimportance in avibrating system

Animation related to vibrating model

Week 2 Lecture 4 Fundamentals of Vibration(Stiffness Elements)

T-1:1R-1:1R-3:1R-4:1

Description aboutstiffness elements of avibrating system

Student learn aboutstiffness elements andtheir differentcombinations

Animation related to vibrating model

Fundamentals of Vibration(Dissipation Elements)

T-1:1R-1:1R-3:1R-4:1

Description aboutstiffness elements of avibrating system

Student learn aboutstiffness elements andtheir differentcombinations

Animation related to vibrating model

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

T-1:2R-1:2R-3:2R-4:2

Description aboutdifferent types ofvibration model and howto make them

Student learn how tomake a model ofvibrating body foranalysis

Whiteboard and Marker

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

T-1:2R-1:2R-3:2R-4:2

RW-1 Description aboutdifferent types ofvibration model and howto make them

Student learn how tomake a model ofvibrating body foranalysis

Whiteboard and Marker

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

T-1:2R-1:2R-3:2R-4:2

Importance of naturalfrequency is discussedalong with methods tofind it

Student learn aboutnatural frequency anddifferent methods offinding it

Whiteboard and Marker

Week 3 Lecture 7 Free Vibration of Single Degree of Freedom Systems(Types of Damping)

T-1:2R-1:3R-3:3R-4:3

RW-1 Description aboutviscous damping, itsdifferential equation andsolution

Student learn aboutviscous damping andsolving differentialequation for the givenproblem

Whiteboard and Marker

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

T-1:2R-1:3R-3:3R-4:3

RW-1RW-2

Description aboutviscous damping, itsdifferential equation andsolution

Student learn aboutviscous damping andsolving differentialequation for the givenproblem

Whiteboard and Marker

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

T-1:2R-1:3R-3:3R-4:3

RW-1 Description aboutviscous damping, itsdifferential equation andsolution

Student learn aboutviscous damping andsolving differentialequation for the givenproblem

Whiteboard and Marker

Lecture 8 Free Vibration of Single Degree of Freedom Systems(Coulomb damping)

T-1:2R-1:3R-2:3R-3:3R-4:3

What is coulombdamping and its use

Student will learn aboutcoulomb damping and structural dampingits applications

Animation of coulomb damping

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

T-1:2R-1:3R-2:3R-3:3R-4:3

What is coulombdamping and its use

Student will learn aboutcoulomb damping and structural dampingits applications

Whiteboard and Marker

Lecture 9 Free Vibration of Single Degree of Freedom Systems(Logarithmic decrement)

T-1:2R-1:3R-2:3R-3:3R-4:3

Discussion aboutlogrithmic decrementand its derivation

Student learn what isLogrithmic decrementand its significance aswell as how to derivean expression of it

Whiteboard and Marker

Week 4 Lecture 10 Forced Vibration of Single Degree of Freedom Systems(Harmonically Forced Vibration)

T-1:3R-1:4R-3:4R-4:4

Discussion onHarmonically ForcedVibrations and theircauses and effects

Student will learn howto find response of asystem underHarmonically forcedvibrations

Whiteboard and Marker

Week 4 Lecture 11 Forced Vibration of Single Degree of Freedom Systems(Magnification factor)

T-1:3R-1:4R-3:4R-4:4

Lecture aboutmagnification factor andits properties

Student will learn whatis magnification factorand its differentproperties underdifferent vibratingconditions

Images related to Magnification factor

Lecture 12 Forced Vibration of Single Degree of Freedom Systems(Rotating and reciprocating unbalance)

T-1:3R-1:4R-2:4R-4:4

RW-3 Description aboutrotating unbalance andits effects along withexpression of response

Student learn abouteffects and causes ofrotating unbalance andhow to find response ofa system vibratingunder rotatingunbalance

Animated video

Week 5 Lecture 13 Forced Vibration of Single Degree of Freedom Systems(Support motion)

T-1:3R-1:4R-4:4

Discussion about theconcept of supportmotion and its differentcases with derivation

Student will learn aboutthe concept of supportmotion in a vibratingbody and also derive itsexpression for differentcases

Whiteboard and Marker

Lecture 14 Forced Vibration of Single Degree of Freedom Systems(Forced Energy dissipated by damping)

T-1:2R-1:3

Description about theenergy dissipation duringdamping and description about forced vibrations with coulomb damping

Student learn aboutcoulomb damping andits effects underdifferent conditions

Whiteboard and Marker

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

T-1:2R-1:3

Description about theenergy dissipation duringdamping and description about forced vibrations with coulomb damping

Student learn aboutcoulomb damping andits effects underdifferent conditions

Whiteboard and Marker

Lecture 15 Forced Vibration of Single Degree of Freedom Systems(Vibration Isolation)

T-1:3R-1:4R-4:4

What is VibrationIsolation and how it isdone and Force Transmissibilityand its effects on avibrating system

Student learn aboutvibration isolation andits various methods and whatis ForceTransmissibilty, itsderivation and how tosolve problems basedon it

Video of Vibration isolation in machines

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

T-1:3R-1:4R-4:4

What is VibrationIsolation and how it isdone and Force Transmissibilityand its effects on avibrating system

Student learn aboutvibration isolation andits various methods and whatis ForceTransmissibilty, itsderivation and how tosolve problems basedon it

Whiteboard and Marker

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

T-1:10R-1:5

Spill Over Spill Over Images for Vibration measurement

Week 6 Lecture 17 Forced Vibration of Single Degree of Freedom Systems(Vibrometer)

T-1:10R-1:4

What is VibrationMeasurement and how itis done

Student will come toknow about vibrationmeasurement and whatparameters of vibrationcan be measured usingdifferent instruments

Whiteboard and Marker

Forced Vibration of Single Degree of Freedom Systems(Accelerometer)

T-1:10R-1:4

What is VibrationMeasurement and how itis done

Student will come toknow about vibrationmeasurement and whatparameters of vibrationcan be measured usingdifferent instruments

Whiteboard and Marker

Lecture 18 Test1

Week 7 Lecture 19 Forced Vibration of Single Degree of Freedom Systems(Frequency Response Curve)

T-1:3R-1:4R-3:4R-4:4

Description about frequency response curves for different cases

Student will learn how to use equations and draw the curves related to them

Images of various curves

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

R-1:4R-4:7

Description aboutwhirling of shaft andfinding expression ofamplitude for it

Student will learn aboutwhirling of shaft, itsrelated derivation alsohow to solve theproblems

Animation for Shafts rotating at Critical Speeds.

Lecture 21 Forced Vibration of Single Degree of Freedom Systems(Whirling of Shaft)

R-1:4R-4:7

Description aboutwhirling of shaft andfinding expression ofamplitude for it

Student will learn aboutwhirling of shaft, itsrelated derivation alsohow to solve theproblems

Animation for Shafts rotating at Critical Speeds.

MID-TERMWeek 8 Lecture 22 Two Degree of Freedom System

(Introduction)T-1:5R-1:5R-4:5

Introduction to two degree of freedom system

Student will learn about two degree of freedom systems and their properties

Images for Two DoF Systems

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

T-1:5R-1:5R-4:5

Procedure to find naturalfrequency and principaland normal modes ofvibration

Student will learn howto solve vibrationalproblems of simple twodegree freedomproblem

Whiteboard and Marker

Lecture 24 Two Degree of Freedom System(Degenerating system)

T-1:5R-1:5R-4:5

Procedure to solveproblems forDegenerating and SemiDefinite systems andderivation for Coordinatecouplig, Combinedmodes

Student will learn whatdegenerating systemsare and what is theirimportance

Video related to Semi-definite Systems

Week 8 Lecture 24 Two Degree of Freedom System(Combined rectilinear and angular modes)

T-1:5R-1:5R-4:5

Procedure to solve derivation for Coordinate couplig, Combined modes

Student will learn aboutcombined rectilinearand angular modes andwill be able to solveproblems based on it

Whiteboard and Marker

Two Degree of Freedom System(Coordinate Coupling)

T-1:5R-1:5R-4:5

Procedure to solvederivation for Coordinatecouplig, Combinedmodes

Student will learn aboutcombined rectilinearand angular modes andwill be able to solveproblems based on it

Whiteboard and Marker

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

T-1:6R-1:5R-4:5

Description aboutLagranges equation andits application

Student will learn howto obtain equation ofmotion for a systemusing lagrangesequation

Whiteboard and Marker

Lecture 26 Two Degree of Freedom System(Vibration Absorber)

T-1:9R-1:5R-4:5

Spill Over Spill Over Video demonstration

Two Degree of Freedom System(Frahm Vibration Absorber)

T-1:9R-1:5R-4:5

RW-4 Derivation for FrahmVibration absorber

Student will learn aboutderivation and workingof Frahm Vibrationabsorber and itsconditions foreffectiveness

Video related to vibration absorber

Lecture 27 Two Degree of Freedom System(Frahm Vibration Absorber)

T-1:9R-1:5R-4:5

RW-4 Derivation for FrahmVibration absorber

Student will learn aboutderivation and workingof Frahm Vibrationabsorber and itsconditions foreffectiveness

Video related to vibration absorber

Week 10 Lecture 28 Test2

Lecture 29 Multi Degree of Freedom Systems(Introduction)

T-1:6R-4:6

Description aboutdifferent approaches touse eigen values andeigen vectors forcalculating naturalfrequency and modeshapes

Student will learndifferent methods ofusing eigen values andeigen vectors forcalculating Naturalfrequency and modeshapes

White Board and Marker

Multi Degree of Freedom Systems(Eigen Value and Eigen Vector Problem)

T-1:6R-4:6

Description aboutdifferent approaches touse eigen values andeigen vectors forcalculating naturalfrequency and modeshapes

Student will learndifferent methods ofusing eigen values andeigen vectors forcalculating Naturalfrequency and modeshapes

White Board and Marker

Lecture 30 Multi Degree of Freedom Systems(Influence coefficient)

T-1:6R-1:6R-4:6

Description of procedureto find Flexibilitycoefficients andflexibility matrix

Student will be able tofind flexibilitycoefficients and writeflexibility matrix

Whiteboard and Marker

Week 10 Lecture 30 Multi Degree of Freedom Systems(Flexibility Coefficient and flexibility matrix)

T-1:6R-1:6R-4:6

Description of procedureto find Flexibilitycoefficients andflexibility matrix

Student will be able tofind flexibilitycoefficients and writeflexibility matrix

Whiteboard and Marker

Week 11 Lecture 31 Multi Degree of Freedom Systems(Orthogonality Principle)

T-1:7R-1:6R-4:6

Demonstration aboutOrthogonality Principleand its application

Student will learn howto use orthogonalityprinciple in matrixiteration method

Whiteboard and Marker

Multi Degree of Freedom Systems(Matrix iteration method)

T-1:7R-1:6R-4:6

Description of procedureto find naturalfrequencies and modeshapes using matrixiterations

Student will be able tofind natural frequenciesand mode shapes ofmulti degree freedomsystem using matrixiterations

Whiteboard and Marker

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

T-1:7R-1:6R-4:6

Description of procedureto find naturalfrequencies and modeshapes using matrixiterations

Student will be able tofind natural frequenciesand mode shapes ofmulti degree freedomsystem using matrixiterations

Whiteboard and Marker

Multi Degree of Freedom Systems(Orthogonality Principle)

T-1:7R-1:6R-4:6

Demonstration aboutOrthogonality Principleand its application

Student will learn howto use orthogonalityprinciple in matrixiteration method

Whiteboard and Marker

Lecture 33 Multi Degree of Freedom Systems(Dunkerley's Method)

T-1:7R-1:6R-4:6

Derivation of dunkerleyequation

Student will learn howto derive DunkerleyEquation and how tofind natural frequencyusing it

Whiteboard and Marker

Week 12 Lecture 34 Multi Degree of Freedom Systems(Holzer Method)

T-1:7R-1:6R-4:6

Description about how to use Holzer's method to find natural frequencies

Student will be able to learn about finding natural frequencies by using Holzer's Procedure

Whiteboard and Marker

Lecture 35 Multi Degree of Freedom Systems(Stodola Method)

R-1:6R-4:6

Description about how to use Stodola's method to find natural frequencies

Student will be able to learn about finding natural frequencies by using Stodola's Procedure

Whiteboard and Marker

Lecture 36 Test3

Week 13 Lecture 37 Vibration of Continuous Systems(Vibrating String)

T-1:8R-1:7R-4:8

Introduction toContinuous system andderivation of generalsolution for a vibratingstring

Student will learn aboutcontinuous system andits properties Alsostudent will be able tomake solution for sucha system depending ongiven conditions

Video demonstration

Week 13 Lecture 38 Vibration of Continuous Systems(Longitudinal Vibration of Rods)

T-1:8R-1:7R-4:8

Derivation Solving ofgeneral solution for avibrating rod

Student will be able tomake solution for sucha system depending ongiven conditions

Whiteboard and Marker

Lecture 39 Vibration of Continuous Systems(Torsional Vibration of rods)

T-1:8R-1:7R-4:8

Spill Over Spill Over Animations

Vibration of Continuous Systems(Euler equation for beams)

T-1:8R-1:7R-4:8

Solution for TorsionalVibration of rods and Euler's Equation for Transverse Vibration

Student will be able tomake solution for sucha system depending ongiven conditions

Whiteboard and Marker

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

T-1:8R-1:7R-4:8

Solution for TorsionalVibration of rods and Euler's Equation for Transverse Vibration

Student will be able tomake solution for sucha system depending ongiven conditions

Whiteboard and Marker

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

T-1:8R-1:7R-4:8

Solution for TorsionalVibration of rods and Euler's Equation for Transverse Vibration

Student will be able tomake solution for sucha system depending ongiven conditions

Whiteboard and Marker

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

T-1:8R-1:7R-4:8

Solution for TorsionalVibration of rods and Euler's Equation for Transverse Vibration

Student will be able tomake solution for sucha system depending ongiven conditions

Whiteboard and Marker

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 30 60

Total :- 30 60

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

Test1 To Prepare the Students for Mid Term Exam

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 Damping Forced Vibration of Single Degree of Freedom Systems : Harmonically Forced Vibration, Magnification factor, Rotating and reciprocating unbalance

Individual Step Marking 4 / 6

Test2 To test analytically the understanding and knowledge gained by student.

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

Individual Step Marking 8 / 10

Test3 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 Method, Stodola Method and Holzers Method

Individual Step Marking 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)

Tutorial1 Addition of Harmonic Motion Work done by Harmonic Force

Problem Solving

Tutorial2 Natural Frequency of Undamped Single Degree of Freedom System

Problem Solving

Tutorial3 Natural Frequency of Damped Single Degree of Freedom System

Problem Solving

Tutorial4 Logrithmic Decrement, Damping Ratio Amplitude Ratio Problem Solving

Tutorial5 Harmonically Forced Vibration, Magnification factor, Rotating and reciprocating unbalance

Problem Solving

Tutorial6 Support motion, Forced Energy dissipated by damping, Vibration with coulomb damping, Vibration Isolation

Problem Solving

Tutorial7 Force Transmissibility, Vibration Measuring Instruments,Vibrometer, Accelerometer

Problem Solving

After Mid-TermTutorial8 Principal and Normal modes of Vibration, Degenerating

systemProblem Solving

Tutorial9 Combined rectilinear and angular modes, Langrange method

Problem Solving

Tutorial10 Eigen Value and Eigen Vector Problem Problem Solving

Tutorial11 Absorber,Influence coefficient, Flexibility Coefficient and flexibility matrix

Problem Solving

Tutorial12 Matrix iteration method,Orthogonality Principle Problem Solving

Tutorial13 Dunkerleys Method, Stodola Method and Holzers Method

Problem Solving

Tutorial14 Vibrating String, Longitudinal Vibration of Rods, Torsional Vibration of rods, Euler equation for beams

Problem Solving