LAB MANUAL - JECRC Foundation

JAIPUR ENGINEERING COLLEGE AND RESEARCH CENTRE

JECRC Campus, Shri Ram Ki Nangal, Via-Vatika, Jaipur

LAB MANUAL

Lab Name : Vibration Engineering Lab

Lab Code : 6ME4-22

Branch : Mechanical Engineering

Year : 3rd Year

Department of Mechanical Engineering

Jaipur Engineering College and Research Center, Jaipur

(Rajasthan Technical University, KOTA)



i

INDEX

S.NO CONTENTS PAGE

NO.

1 VISION/MISION III

2. PROGRAM EDUCATIONAL OBJECTIVES (PEOs) IV

3. PROGRAM OUTCOMES (POs) V

4. COURSE OUTCOMES (COs) VI

5. MAPPING OF COs with POs

VII

6. SYLLABUS VIII

7. BOOKS X

8. INSTRUCTIONAL METHODS XI

9. LEARNING MATERIALS XII

10. ASSESSMENT OF OUTCOMES XIII

11 INSTRUCTIONS SHEET XIV

Exp:- 1 Objectives :- To verify relation T = 2π (l/g)1/2 for a simple pendulum. 1

Exp:- 2 Objectives :- To determine radius of gyration of compound pendulum. 6

Exp:-3 Objectives :- To determine the radius of gyration of given bar by using trifilar

suspension.

10

Exp:-4 Objectives: - To determine natural frequency of a spring mass system. 14



ii

Exp:-5 Objectives: - Study of equivalent spring mass system. 19

Exp:-6 Objectives: - To determine natural frequency of free torsional vibrations of

single rotor system.

i. Horizontal rotor

ii. Vertical rotor

23

Exp:-7 Objectives: - To verify the Dunkerley’s rule. 29

Exp:-8 Objectives: - Performing the experiment to find out damping co-efficient in

case of free damped torsional vibration.

34

Exp:-9 Objectives: - To conduct experiment of trifler suspension. 37

Exp:-10 Objectives: - Harmonic excitation of cantilever beam using electro-dynamic

shaker and determination of resonant frequencies

41

Exp:- 11 Objectives: - Study of Vibration measuring instruments.

44

Exp:- 12 Objectives:- Perform study of the following using Virtual Lab

http://www.vlab.co.in/

49

Exp:- 13 Objectives:- Forced Vibration of a Cantilever Beam with a Lumped Mass at

Free End:To calculate the natural frequency and damping ratio for forced

vibration of a single DOF cantilever beam system, experimentally; and

compare the results with theoretical values.

51

Exp:- 14 Objectives:- Harmonicaly Excited Forced Vibration of a Single DOF System:

To analyze the forced vibration response of a single DOF system at different

damping ratio and frequency ratio.

54

Exp:- 15 Objectives:-Perform study of the following using Virtual Lab


58





iii

Exp:- 16 Objectives:- Forced Vibration of a Cantilever Beam with a Lumped Mass at

Free End:

To calculate the natural frequency and damping ratio for forced vibration

of a single DOF cantilever beam system, experimentally; and compare

the results with theoretical values.

60

Exp:- 17 Objectives:- Harmonicaly Excited Forced Vibration of a Single DOF System:

To analyze the forced vibration response of a single DOF system at different


63

1. VISION & MISSION

VISION:

➢ The Mechanical Engineering Department strives to be recognized globally for

outcome based technical knowledge and to produce quality human resource, who can

manage the advance technologies and contribute to society.

MISSION:

1. To impart quality technical knowledge to the learners to make them globally competitive

mechanical engineers.

2. To provide the learners ethical guidelines along with excellent academic environment for a

long productive career.

3. To promote industry-institute relationship.

https://f1mail.rediff.com/cgi-bin/prored.cgi?red=http://1.To&isImage=0&BlockImage=0&rediffng=0&rogue=ad17f086364021c4d5bf7a54708ba224a1c15223



iv

2. PROGRAM EDUCATIONAL OBJECTIVES

1. To provide students with the fundamentals of Engineering Sciences with more

emphasis in Mechanical Engineering by way of analyzing and exploiting engineering

challenges.

2. To train students with good scientific and engineering knowledge so as to

comprehend, analyze, design, and create novel products and solutions for the real life

problems.

3. To inculcate professional and ethical attitude, effective communication skills,

teamwork skills, multidisciplinary approach, entrepreneurial thinking and an ability to

relate engineering issues with social issues.

4. To provide students with an academic environment aware of excellence, leadership,

written ethical codes and guidelines, and the self-motivated life-long learning needed

for a successful professional career.

5. To prepare students to excel in Industry and Higher education by Educating Students

along with High moral values and Knowledge.



v

3. PROGRAM OUTCOMES

1. Engineering knowledge: Apply the knowledge of mathematics, science, engineering

fundamentals, and an engineering specialization to the solution of complex engineering

problems.

2. Problem analysis: Identify, formulate, research literature, and analyze complex engineering

problems reaching substantiated conclusions using first principles of mathematics, natural

sciences, and engineering sciences.

3. Design/development of solutions: Design solutions for complex engineering problems and

design system components or processes that meet the specified needs with appropriate

consideration for the public health and safety, and the cultural, societal, and environmental

considerations.

4. Conduct investigations of complex problems: Use research-based knowledge and research

methods including design of experiments, analysis and interpretation of data, and synthesis of

the information to provide valid conclusions.

5. Modern tool usage: Create, select, and apply appropriate techniques, resources, and modern

engineering and IT tools including prediction and modeling to complex engineering activities

with an understanding of the limitations.

6. The engineer and society: Apply reasoning informed by the contextual knowledge to assess

societal, health, safety, legal and cultural issues and the consequent responsibilities relevant to

the professional engineering practice.

7. Environment and sustainability: Understand the impact of the professional engineering

solutions in societal and environmental contexts, and demonstrate the knowledge of, and need

for sustainable development.

8. Ethics: Apply ethical principles and commit to professional ethics and responsibilities and

norms of the engineering practice.

9. Individual and team work: Function effectively as an individual, and as a member or leader

in diverse teams, and in multidisciplinary settings.

10.Communication: Communicate effectively on complex engineering activities with the

engineering community and with society at large, such as, being able to comprehend and write

effective reports and design documentation, make effective presentations, and give and receive

clear instructions.

11. Project management and finance: Demonstrate knowledge and understanding of the

engineering and management principles and apply these to one’s own work, as a member and

leader in a team, to manage projects and in multidisciplinary environments.



vi

12. Life-long learning: Recognize the need for, and have the preparation and ability to engage

in independent and life-long learning in the broadest context of technological change.

4. COURSE OUTCOMES

Vibration Engineering Lab [6ME4-22]

Class: 6th Sem. B.Tech. 3rd Year Branch: Mechanical Engineering

Schedule per Week Practical Hrs.: 2 Examination Time = 2 Hours

Maximum Marks = [Sessional/Mid-term (45 ) & End-term (30 )]

On successful completion of this course the students will be able to:

CO-1 To determine the natural frequency of vibration problems that contains single and multi-

degree of freedom systems.

CO-2 To calculate the damping coefficient of single and multi-degree of freedom systems.



vii

5. MAPPING OF COs with POs

2

COURSE

OUTCOMES

PROGRAM OUTCOMES

1 2 3 4 5 6 7 8 9 10 11 12

I 3 3 2 0 2 1 0 0 2 1 2 2

II 3 3 1 2 3 2 1 1 2 1 3 1



viii

6. SYLLABUS

6ME10A: VIBRATION ENGINEERING LAB

Class: 6th Sem. B. Tech. 3rs year Evaluation

Branch: ME

Schedule per week

Practical Hrs: (2 )

Examination Time=Two ( 2) Hours

Maximum Marks = 75

[Sessional/Mid-term (45 ) & End-term(30 )]

S.N. NAME OF EXPERIMENT

Exp:- 1 Objectives :- To verify relation T = 2π (l/g)1/2 for a simple pendulum.

Exp:- 2 Objectives :- To determine radius of gyration of compound pendulum.

Exp:-3 Objectives :- To determine the radius of gyration of given bar by using bifilar

suspension.

Exp:-4 Objectives: - To determine natural frequency of a spring mass system.

Exp:-5 Objectives: - Study of equivalent spring mass system.

Exp:-6 Objectives: - To determine natural frequency of free torsional vibrations of single

rotor system.

i. Horizontal rotor

ii. Vertical rotor

Exp:-7 Objectives: - To verify the Dunkerley’s rule.

Exp:-8 Objectives: - Performing the experiment to find out damping co-efficient in case of

free damped torsional vibration.

Exp:-9 Objectives: - To conduct experiment of trifler suspension.



ix

Exp:-10 Objectives: - Harmonic excitation of cantilever beam using electro-dynamic shaker

and determination of resonant frequencies

Exp:- 11 Objectives: - Study of Vibration measuring instruments.

Exp:- 12 Objectives:- Perform study of the following using Virtual Lab http://www.vlab.co.in/

Exp:- 13 Objectives:- Forced Vibration of a Cantilever Beam with a Lumped Mass at Free

End:To calculate the natural frequency and damping ratio for forced vibration of a

single DOF cantilever beam system, experimentally; and compare the results with

theoretical values.

Exp:- 14 Objectives:- Harmonicaly Excited Forced Vibration of a Single DOF System: To

analyze the forced vibration response of a single DOF system at different


Exp:- 15 Objectives:-Perform study of the following using Virtual Lab http://www.vlab.co.in/

Exp:- 16 Objectives:- Forced Vibration of a Cantilever Beam with a Lumped Mass at Free

End: To calculate the natural frequency and damping ratio for forced vibration of a

single DOF cantilever beam system, experimentally; and compare the results with

theoretical values.

Exp:- 17 Objectives:- Harmonicaly Excited Forced Vibration of a Single DOF System: To

analyze the forced vibration response of a single DOF system at different damping

ratio and frequency ratio.





x

7. BOOKS

7.1 Text books:-

1) G.K. Grover “Mechanical Vibrations”Nem Chand & Bros

7.2 Reference Books:-

1.) Rattan S.S.: Theory of Machines, Tata McGraw Hill

2.) Kewal Pujara: Vibrations & Noise control, Dhanpat Rai & Co

8. INSTRUCTIONAL METHODS

8.1. Direct Instructions:

I. Black board presentation.

II. Power point presentation.

8.2. Interactive Instruction:

I. Practical on respective equipment.

II. Practical Examples.

8.3. Indirect Instructions:

I. Problem solving



xi

9. LEARNING MATERIALS

9.1. Lab Manual

9.2. Reference Books

10. ASSESSMENT OF OUTCOMES

10.1 End term Practical exam (Conducted by RTU, KOTA)

10.2 Quiz

10.3 Daily Lab interaction.



xii

11. INSTRUCTIONS SHEET

We need your full support and cooperation for smooth functioning of the lab.

DO’s

1. Please switch off the Mobile/Cell phone before entering lab.

2. Intimate the lab incharge whenever you are incompatible in using the system or

in case machine get infected.

3. Arrange all the peripheral and seats before leaving the lab.

4. Properly shutdown the experimental set up before leaving the lab.

5. Keep the bag outside in the racks.

6. Enter the lab on time and leave at proper time.

7. Maintain the decorum of the lab.

8. Utilize lab hours in the corresponding experiment..

DON’TS

1. Don’t mishandle the Machine.

2. Don’t leave the machine ON for long time when in not in use.

3. Don’t bring any external material in the lab.

4. Don’t make noise in the lab.

5. Don’t bring the mobile in the lab. If extremely necessary then keep ringers off.

6. Don’t enter in the lab without permission of lab Incharge.

7. Don’t carry any lab equipments outside the lab.

BEFORE ENTERING IN THE LAB

1. All the students are supposed to prepare the theory regarding the next experiment

2. Students are supposed to bring the practical file and the lab copy.

3. Previous practical should be written in the practical file.

4. Any student not following these instructions will be denied entry in the lab.

WHILE WORKING IN THE LAB

1. Adhere to experimental schedule as instructed by the lab incharge.

2. Get the previously executed program signed by the instructor.

3. Get the output of the current program checked by the instructor in the lab copy.

4. Each student should work on his/her assigned computer at each turn of the lab.



xiii

5. Take responsibility of valuable accessories.

6. Concentrate on the assigned practical and do not play games.

7. If anyone caught red handed carrying any equipment of the lab, then he will have to

face serious consequences



1

Experiment No. 1

AIM:

To Verify the relation of simple pendulam.

T= 2 π

Where T = Periodic time in sec.

L = Length of pendulum in cm.

APPARATUS:

A steel ball, a massless string, a scale, a stopwatch.



2

Figure 1.1: SIMPLE PENDULUM



3

Figure 1.2: Experimental Set up of Simple Pendulum

DESCRIPTION:

For conduction the experiment, a ball is supported by nylon thread into a chuck. It is possible

to change the length of pendulum. This makes it possible to study the effect of variation of

length on periodic time. A small ball may be substituted by large ball to illustrate that period

of oscillation is independent of the mass of ball.

Simple pendulum

By equilibrium of forces we have;



4

mg = T cos dθ ≈ T ……..(1)

By S.H.M equation we have;

T sin dθ = mω2 x ……..(2)

we have; x = l sin dθ

Hence eqn.(2) becomes

T sin dθ = mω2 l sin dθ

T = mω2 l ……..(3)

From (1) and (3)

mg = mω2 l

ω2 = (g / l) ;ω = √(g/l)

We have ; ω = 2 π / T

Hence, T = 2π √(l/g)

PROCEDURE:

1. Attach the ball to one end of the thread.

2. Allow ball to oscillate and determine the periodic time T by knowing the time for say

10 oscillations.

3. Repeat the experiment by changing the length.

4. Complete the observation table given below

STANDARD DATA:

Weight of small ball = 32 gms.

Weight of big ball = 102.34 gms.

Acceleration due to gravity, g = 9.81 m / s².

FORMULAE:



5

1. Time Period, TActual = t / n sec.

2. Time Period, T Theo. = 2 π sec.

Where,

t = Time taken by ‘n ’ oscillations.

n = Nos. of oscillation.

L = Length of the pendulum.

OBSERVATION & CALCULATION TABLE:

Sr. No. Weight of

Ball

L cms. No. of Osc.

‘n’

Time for n Osc.

‘t’ sec.

T sec.

(Expt.) t/n

T sec.

(Theo.)

1.

2.

3.

4.

RESULT:

Plot the graph of T ² Vs. L. It should yield the straight line.

PRECAUTIONS:



6

1. Do not run the motor at low voltage i.e. less than 180 volts.

2. Do not increase the speed at once.

3. Damper is always in perpendicular direction.

4. A motor bolts is properly tightly with weight.

5. A beam is proper tight in bearing with bolt.

6. Always keep the apparatus free from dust.

APPLICATIONS

The pendulum swings back and forth at exact intervals determined by the length at which

thependulum is suspended. To measure time accurately, a pendulum clock must remain

stationary

EXPECTED OUTCOME:

COMMENT BY STUDENT:

VIVA VOCE

1. Define transverse and longitudinal wave?



7

2. Define sound wave in air?

3. Define the frequency?

4. Define dB and dBm?

5. Define noise?



8

Experiment No. 2

AIM:

To determine the radius of gyration 'k' of a given compound pendulum.

T = 2π

Where,

T = Periodic time in sec.

k = Radius of gyration about the C.G. in cm.

OG = Distance of C.G. of the rod from support.

L = Length of suspended pendulum.

APPARATUS:

A compound pendulum, a scale, a stopwatch.



9

Fig. 2 Experimental set up for compound pendulam

DESCRIPTION:

The compound pendulum consists of a steel bar. The bar is supported by knife edge. Two

pendulum of different lengths are provided with the set-up.

PROCEDURE:

1. Support the rod on knife -edge.

2. Note the length of suspended pendulum and detennine OG.

3. Allow the bar to oscillate and determine T by knowing the time for say 10 oscillations.

4. Repeat the experiment with different length of suspension.



10

5. Complete the observation table given below.

STANDARD DATA:

Length of compound pendulum (1) = 80 cm.

Length of compound pendulum (2) = 60 cm.

FORMULAE:

1. Actual time period, T act = t/n

2. Actual radius of gyration, k act from the equation

T = 2π

3. Theoretical radius of gyration, ktheo =


Length of the compound pendulum = ------- cm.

Sr. No. L cm. OG No. of Ocn. Time for Osc. T Expt. k Expt. k



11

n' theoretical

1

2

3

RESULT:

Radius of gyration is calculated and found to match with the relation T = 2π

hence experiment is verified.

PRECAUTIONS:







APPLICATIONS

The compound pendulum is a standard topic in most intermediate physics courses and this

article describes its use to determine the gyradius and center of mass position of Olympic

class sailboat hulls by measuring the oscillation period on two pivot points a known distance

apart.



12

EXPECTED OUTCOME:

COMMENT BY STUDENT:

VIVA VOCE

1. Define vibration?

2. Define degree of freedom?

3. Define damped free vibration and force vibration?

4. Explain spring stiffness?

5. Define damping constant?

6. How is moment of inertia of a rod of uniform section can be found?

7. Why is it important to find moment of inertia of a body of irregular shape (e.g. an

oscillating link of irregular shape used in a mechanism of a machine)?



13

8. Write the formula that relates period of oscillation of a compound pendulum and its

moment of inertia and dimensions.

9. Why do we use a triangular peg resembling a knife-edge as support for suspension of the

connecting rod rather than an object of any other shape? - To minimize friction and to ensure

purely oscillating motion

10.List three sources of errors that can occur during conduct of the real experiment (in real

laboratory situation).



14

Experiment No. 3

AIM:

To determine the radius of gyration of given bar by using Bi-Filar suspension.

APPARATUS:

A uniform rectangular section bar, strings, a scale, a stop watch.

Figure 3: Experimetal set up

DESCRIPTION:



15

A uniform rectangular section bar is suspended from the pendulum support frame by two

parallel cords. Top ends of the cords pass through the two small chucks fitted at the top.

Other ends are secured in the bifilar bar. It is possible to adjust the length of the cord by

loosening the chucks. The suspension may be used to determine the radius of gyration of any

body. In this case the body under investigation is bolted to the centre. Radius of gyation of

the combined bar and body is then determined.

PROCEDURE:

1. Suspend the bar from chuck, and adjust the length of the cord 'L' conveniently. Note the

suspension length of each cord must be same . .

2. Allow the bar to oscillate about the vertical axis passing through through centre and

Measure the periodic time T by knowing the time for say 10 oscillations.

3. Repeat the experiment by mounting the weights at equal distance from centre.

4. complete the observation table given below.

STANDARD DATA:

Distance between two rods = 46 cm.

FORMULAE:

1. Actual time period, T act = t/n sec.

2. Actual radius of gyration, k act from the equation

T = 2π

3. Theoretical radius of gyration, k theo =



16

Where,

t = Time taken by ‘ n ’ oscillations.

n = Nos. of oscillation.

L = Length of the suspended string.

2a = Distance between the two string.

g = Acceleration due to gravity.

k = Radius of gyration of Bi-Filler suspension.

OBSERVATION & CALCULATION TABLE :

S. No. L in cm. a in cm. Tact kact ktheo

1.

2.

3.

RESULT:

1. As length of cord decreases the radius of gyration decreases.

2. Differences in the theoretical ‘k’ experimental values of ‘k’ are due to error in nothing

down the time period.



17

PRECAUTIONS :

1. Tight the drill chucks properly.

2. Length of each cord should be equal.

APPLICATIONS

The bifilar suspension is a technique used to determine the moment of inertia of any type of

object about any point on the object.

EXPECTED OUTCOME:

COMMENT BY STUDENT:



18

VIVA VOCE

1. Define radius of gyration?

2. Define resonance?

3. Define amplitude?

4. Define pack value?

5. Define single degree of vibration?



19

Experiment No. 4

AIM:

To determine natural frequency of a spring mass system.

.'APPARATUS:

A spring mass system, a stop watch, a scale.


DESCRIPTION:

One end of open coil spring is fixed to the nut having a hole which itself is mounted on a MS

strip fixed on one side of the main frame. The lower end of the spring is attached to the



20

platform carrying the weights. The stiffness of the spring can be find out by varying the

weights on the platform and by measuring the deflection of the spring. The time period of

vibrations can be calculated by measuring the nos. of oscillation and time taken by them.

PROCEDURE:

1. Fix one end of the helical spring to upper screw.

2. Determine free length.

3. Put some weight to platform and note down the deflection.

4. Stretch the spring through some distance and release.

5. Count the time required in Sec. for say 10, 20 oscillations.

6. Determine the actual period.

7. Repeat the procedure for different weights.

STANDARD DATA:

1. Length of spring. =

2. Mean dia. of spring. =

3. Wire dia. =

.

FORMULAE:

1. Stiffness, k = kg / cm.

2. Mean Stiffness, = kg / cm.

3. Theoretical time period, Ttheo = 2π



21

4. Therotical frequency, ftheo = Hz

5. Experimental time period, T expt. = sec

6. Experimental frequency, f expt. = Hz

Where,

K = Stiffness of the spring

W = Weight applied

δ = Deflection of the spring.

= Mean Stiffness

g = Acceleration due to gravity = 9.81 m/s²

n = No. of oscillations.

t = Time taken by ‘n’ oscillation

OBSERVATION & CALCULATION TABLE - 1

Sr. No. Wt. Attached, Deflection in spring Stiffness Mean Stiffness

W kg δ cm k kg/cm Km kg/cm



22

OBSERVATION & CALCULATION TABLE - 2

Sr. No.

Wt.

Attached, No. of Osc.

Time reqd.

For T theo

T

expt f theo f expt

W kg n' n osc. (sec) (sec) (Hz) (Hz)

t sec

RESULT:

The difference in F exp & F theoretical is due to

1] Observation human error

2] Damping effect of air.

PRECAUTIONS :





23

EXPECTED OUTCOME:

COMMENT BY STUDENT:

VIVA VOCE

1. What are the common types of damping?

2. Define centre of percussion?



24

3. Define damping ratio?

4. What is critical damping?

5. What is SHM?



25

Experiment No.5

AIM:-

Equivalant spring mass system.

APPARATUS:

The general arrangement of experiment setup. It’s consist of fixed support of which there is

hole where spring can be attached through the hook.


DECCRIPTION:



26

The equipment is designed to study free damped and undamped vibrations. It consists of

M.S. rectangular beam supported at one end by a trunion pivoted in ball bearing. The bearing

housing is fixed to the side member of the frame. The other end of beam issupported by the

lower end of helical spring, upper end of the spring is attached to screw which engage with

screwed hand wheel. The screw can be adjusted vertically in any convenient position and can

be clamped with the help of lock nut.The exciter unit can be mounted at any position along

the beam. Additional known weights may be added to the weight platform under side exciter.

PROCEDURE:

1. First the tension spring is attached is attached to the support with load no attached to it and

its length is measure (pitch).

2. Then dead wt is attached to that spring with the help of hook and again length is measured.

3. Same procedure is applied for the spring 2 of different stiffness.

4. Then spring i.e spring 1 and spring 2 connected in series and length is measured then dead

wt. is attached to spring and length is measured.

FORMULAE:

1. Time Period, T (Theoretical) = 2π

2. Equivalent mass at the spring, = m

3. m =

4. Actual Time period, Tact =



27

Where,

W = Weight of exciter assembly along with wt. platform = 13.2 kg.

w = Weight attached on exciter assembly.

= Distance of w from pivot.

k = Stiffness of spring.

L = Distance of spring from pivot = Length of beam = 94 cm.

m = Mass of exciter assembly along with wt. platform.

g = 9.81

OBSERVATION TABLE & CALCULATION TABLE:

wt. L1 No. of Osc. Time for n Osc. Periodic Time (expt.) Natural Freq. fn (expt.)

N T = t/n

RESULTS

The theoretical and experimental value of equivalent stiffness were found to almost equal.

PRECAUTIONS:





28





APPLICATIONS

To this end, a technique to replace each two‐dof spring–mass system by a set of rigidly

attached equivalent masses is presented, so that the free vibration characteristics of a loaded

beam can be predicted from those of the same beam carrying multiple rigidly attached

equivalent masses.

EXPECTED OUTCOME:

COMMENT BY STUDENT:



29

VIVA VOCE

1. Define the term magnification factor?

2. Define peak amplitude and resonant amplitude?

3. Why is viscous damping used in most cases?

4. Define displacement transmissibility?

5. Define vibration isolation?



30

Experiment No.6

AIM:

To study the Torsional Vibrations (Undamped) of Single Rotor Shaft System.

A. Horizontal rotor

B. Vertical rotor

APPARATUS:

A single rotor shaft system, a scale, a stop watch.

Figure 6.1: Experimental set up for Single Rotor Shaft Horizontal System



31

Figure 6.1: Experimental set up for Single Rotor Shaft Vertical System

DESCRIPTION:

Figure shows the general arrangement for carrying out the experiments. One end of the shaft

is gripped in the chuck & heavy flywheel free to rotate in ball bearing is fixed at the other end

of the shaft. The bracket with fixed end of the shaft can be clamped at any convenient

position along lower beam. Thus length of the shaft can be varied during the experiments.

The ball bearing support to the flywheel provides negligible damping during experiment. The

bearing housing is fixed to side member of the main frame.

PROCEDURE:

1 . Fix the bracket at convenient position along the lower beam.



32

2. Grip one end of the shaft at the bracket by chuck.

3. Fix the rotor on the other end of shaft.

4. Twist the rotor through some angle & release.

5. Note down the time required for 10,20 oscillations.

6. Repeat the procedure for different length of shaft.

7. Make the following observations:-

STANDARD DATA:

1. Shaft Dia. = 3 mm.

2. Dia. of Disc, D = 225 mm.

3. Wt. of the Disc, w = 3 kg.

4. Modulus of rigidity for shaft = 0.8 × kg/

FORMULAE:

1. Torsional stiffness, =

2. Theoretical Time period, Ttheo = 2

3. Moment of Inertia of disc, I = ×

4. Experimental Time period, Texp =

5. Theoretical Frequency, ftheo =

6. Experimental Frequency, fexp =

Where,

L = Length of shaft

= Polar M.I. of shaft =



33

d = Dia. of shaft.

G = Modulus of rigidity of shaft = 0.8 × kg/cm2

w = weight of the disc in kg.

D = Diameter of disc.

OBSERVATION TABLE:

S. No. Length of shaft No. of Osc. Time for n Osc Periodic

Time

L cm. n t sec T= t/n

(expt.)

CALCULATION TABLE:

S. No. Length of shaft kt Ttheo Texp. ftheo fexp

L cm. Sec sec Hz Hz



34

RESULTS

PRECAUTIONS:







APPLICATIONS

In ideal power generation, or transmission, systems using rotating parts, not only

the torques applied or reacted are "smooth" leading to constant speeds, but also the rotating

plane where the power is generated (or input) and the plane it is taken out (output) are the

same. In reality this is not the case. The torques generated may not be smooth (e.g., internal

combustion engines) or the component being driven may not react to the torque smoothly

(e.g., reciprocating compressors), and the power generating plane is normally at some

distance to the power takeoff plane. Also, the components transmitting the torque can

generate non-smooth or alternating torques (e.g., elastic drive belts, worn gears, misaligned

shafts). Because no material can be infinitely stiff, these alternating torques applied at some

distance on a shaft cause twisting vibration about the axis of rotation.

https://en.wikipedia.org/wiki/Torque

https://en.wikipedia.org/wiki/Internal_combustion_engines

https://en.wikipedia.org/wiki/Internal_combustion_engines

https://en.wikipedia.org/wiki/Reciprocating_compressor



35

EXPECTED OUTCOME:

COMMENT BY STUDENT:

VIVA VOCE

1. Define principal models of vibration?



36

2. Define first and second mode of oscillation?

3. What is the function of a vibration isolator?

4. What is a vibration absorber?

5. What is the difference between a vibration isolator and a vibration absorber?



37

Experiment No. 7

AIM: To verify the Dunkerley's Rule.

= =

Where,

F = Natural frequency of given beam (considering the weight of beam) with central load

W.

= Natural frequency of given beam (neglecting the weight of beam) with central load

W.

F =

Where,

W = Central load of the beam, OR weight attached.

L = Length of the beam.

= Natural frequency of the beam.



38

FIGURE 7: Experimental set for Dunkerley's Rule.

DESCRIPTION:

Figure shows the general arrangement for carrying out the experiment. A rectangular bar is

supported in trunion fitting at each end. Each trunion is pivoted in a ball bearing carried in

housing. Each bearing housing is fixed to the vertical frame member. The beam carries at its

centre a weight platform.

PROCEDURE:

1. Arrange the set up as shown in fig. 10 with some weight W clamped to weight

platform.

2. Pull the platform & release it to set the system in to natural vibrations.

3. Find periodic time T & frequency of vibrations F by measuring time for some

oscillations.

4. Repeat experiment by putting additional masses on weight platform.



39

5. Plot graph of vs. W

STANDARD DATA:

1. Length of beam = L =105 cm.

2. Weight per cm of the beam = w = W/ L .

3. Section of the beam = Small - 2.5 x 0.6 cm. Big 2.5 x 1.2 cm.

4. Weight of the beam. = Small-1.12 kg. Big- 2.45

FORMULAE:

1. Natural frequency of the beam, =

2. Moment of Inertia of beam section, I =

3. Experimental Time Period, =

4. Experimental frequency, =

5. Plot the graph of Vs. intercept of the graph with W = 0 gives the value of

frequency of the beam.

6. Compare the values of natural frequency of the beam obtained by using theoretical

expression and obtained from graph.

To verify Dunkerley's Rule proceed as follows:

Find ‘ ’ from expression given above.

1. Find ‘ ’ by using formula given above.

2. Find' F' by using Dunkerley's equation.

3. Compare this with experimental values of F.

Where,



40

w = weight of beam per unit length =

E = Modulus of elasticity of beam material (to be taken as 2 × 106 kg/cm2)


S. No. Wt. attached – W No. of Osc Time for n Osc Frequency of

Osc

Kg n t' l/Texp

RESULT:

Thus Dunkerley’s rule is verified, since theoretical and experimental values are closer.

PRECAUTIONS :



APPLICATIONS

The elastic properties of the shaft will act to restore the “straightness”. If the frequency of

rotation is equal to one of the resonant frequencies of the shaft, whirling will occur. In order

to save the machine from failure, operation at such whirling speeds must be avoided.

EXPECTED OUTCOME:



41

COMMENT BY STUDENT:

VIVA VOCE

1. Define longitudinal vibration?

2. Define torsional vibration?

3. Define multi degree of freedom?

4. What is the unit of damping coefficient?

5. Define pendulum?



42

EXPERIMENT No. 8

AIM: Performing the experiment to find out damping co-efficient in case of free damped

torsional vibration

APPARATUS:

Spring mass system, damper, exciter unit, voltage regulator and strip recorder.

THEORY:

The vibration that the system executes under damping system is known as damped vibrations.

In general all the physical systems are associated with one or the other type of damping. In

certain cases amount of damping may be small in other case large. In dam a reduction in

amplitude over every cycle of vibration. This is due to the fact that a certain amount of

energy possessed by the vibrating system is always dissipated in overcoming frictional

resistances to the motion. The rate at w upon the type and amount of damping in the system.

Damped vibrations can be free vibrations or forced vibrations. Shock absorber is an example

of damped vibration. Mainly the following two aspects are important while studying damped

free vibrations: 1. The frequency of damped free vibrations and 2. The rate of decay.

FIGURE:



43

PROCEDURE:

1. Connect the exciter to D.C. motor.

2. Start the motor and allow the system to vibrate.

3. Wait for 3 to 5 minuets for the amplitude to build for particular forcing frequency.

4. Adjust the position of strip chart

5. Take record by changing forcing frequency.

6. Repeat the experiment for different damping. Damping can be changed adjusting the

position of the exciter.

7. Plot the graph of amplitude Vs frequency for each damping condition.



44

Sr. No. Number of

oscillations, n

Time

required for

n oscillations,

t

Periodic

Time, T

Forcing

frequency, f

= 1/T

Amplitude,

mm

CONCLUSION:

1. From the graph it can be observed that the amplitude of vibration decreases with time.

2. Amplitude of vibration is less with damped system as compared to undamped system.

Result: The frequency of damped forced vibration is………

PRECAUTIONS:







EXPECTED OUTCOME:



45

COMMENT BY STUDENT:

Viva-Voce:

1. Define vibration absorbers?

2. Define loudness and its unit?

3. What is the major source of noise?

4. What are the noise control sources?

5. Define decibel scale?



46

Experiment no. 9

AIM:

To conduct experiment of trifler suspension.

APPARATUS REQUIRED: Main frame, Trifler suspension, Weights, Stopwatch, and

Thread.

DESCRIPTION:

The set up consists of a disc having a weight W is suspended by three long parallel flexible

chord of length ‘l’. The three strings being placed symmetrically about the centre of gravity

‘G’ at a radius ‘r’ and disposed at 120º to each other. When the disc is twisted through a

small angle θ about a vertical axis through the center of gravity ‘G’, it will vibrate with

simple harmonic motion in a horizontal plane.

Figure 9: Experimental set up for trifler suspension.



47

FORMULAE:

1. Radius of gyration, k =

2. Mass moment of inertia of body about a vertical axis =

STANDARD DATA:

1. Weight of the disc, W = 2.26 kg

2. Weight of Ring = 0.988 kg

3. Weight of block = 0.454 kg

4. Radius of disc = 11.2 cm

OBSERVATION TABLE:

S.

No.

Wt. attached

– W

No. of

Osc

Length of

cord

Time

required

Frequency

n=t/n

Radius of

gyration

Kg n Cm t cm osc/sec k(cm)

PRECAUTIONS:




48


RESULT:

APPLICATIONS

The trifilar suspension is a technique used to determine the moment of inertia of any type of

object about any point on the object.

EXPECTED OUTCOME:

COMMENT BY STUDENT:



49

VIVA-VOCE

1. How is the moment of inertia of a solid body of regular shape (e.g. a disc or a

cylinder) found?

2. How will you recommend the length of wire compared to the size of the base

of the trifiliar suspension to be? – longer or shorter. Why?

3. Why do we need to find moment of inertia of solid bodies of irregular shapes

in real life?

4. Write the formula that relates dimensions of a trifiliar suspension, MI of the

oscillating base and period of oscillation of the trifiliar suspension.

Explain the meaning of terms used in the formula.

5. What will be the effect of increasing or decreasing the length of suspension

and MI of base on the period of oscillation of the trifiliar suspension?



50

Experiment No. 10

AIM: Harmonic excitation of cantilever beam using electro-dynamic shaker and

determination of resonant frequencies.

INTRODUCTION

The passive vibration absorber is an important device used for vibration reduction in

structures. The linear vibration absorber is limited in that it reduces vibration over a very

narrow frequency range. This range is not enough to correspond to changes in speed for a

rotating unbalanced source due to load, motor power supply or source variations. A technical

benefit of the NDVA has been hypothesized that they can operate efficiently over a broader

range of forcing frequencies.

APPRATUS

The schematic diagram of the experimental setup is shown in Figure 8. The electro-dynamic

shaker was driven by a signal generator producing a stepped-sine signal. The accelerometers

(PCB type 352C22) were attached to the support structure and to the mass of the absorber,

while the oscilloscope was used to observe the system response.



51

Figure 10 : Photograph of the actual experimental system consisting of a nonlinear absorber

attached to a cantilever beam excited by an electro-dynamic shaker.

ERXPERIMENTAL PROCEEDURE

1. The cantilever beam was made of aluminium with a total length L = 0.09 m , cross-

sectional area A = 0.04 m=0.004 m , density =2700 kg/m3 , and Young’s modulus E

= 70 GN/m2 . In addition, the circular plate was made of brass with thickness 0.2103

m , area A =0.0262 m2 , density =8500 kg/m3 , and Young’s modulus E =110

GN/m2 .

2. The parameters for the systems tested were required in order to compare the

experimental results with the model predictions. These parameters ( s m , s c , s k , m ,

c , 1 k , 3 k ) were measured independently and were estimated as follows.

3. The Frequency Response Function (FRF) of the support frame attached to the

cantilever beam without the absorber was measured using pseudo random force

measurements. It is noted that the system was designed such that by simply adjusting

the thickness of the plate, in the vibration absorber, the nonlinear stiffness and natural

frequency of the absorber could be varied.



52

OBSEVATION TABLE

Equivalent non-dimensional system parameters for the model predictions.

Amplitute

Results: It was found that the frequency response curve of the NDVA has the effect of

moving the second resonant peak to a higher frequency away from the tuned frequency, so

that the device is robust to mistuning.

PRECAUTIONS:







EXPECTED OUTCOME:



53

COMMENT BY STUDENT:

VIVA-VOCE

1. What are beats?

2. Define spring mass system?

3. Define dynamic coupling?

4. Define the number of degrees of freedom of a vibration system?



54

EXPERIMENT NO.11

AIM:

Study of Vibration measuring instruments.

DESCRIPTION:

The primary purpose of vibration measuring instruments is to give an output signal which

represents, as closely as possible, the vibration phenomenon. This phenomenon may be

displacement , velocity or acceleration of the vibratin system and accordingly the instruments

which reproduce signals proportional to these are called vibrometers, velocity pickups

(Techometer) or accelerometers.

Figure shows the schematic of a seismic instrument which is used to

measure any of the vibration phenomenon. It consists of aframe in which the seismic mass m

is supported by means of spring k and dashpot C . The frame is mounted on a vibrating body,

vibrates along with it. This system reduces to a spring mass dashpot system having base or

support excitation.

Consider the vibrating body (base) to have a sinusoidal motion

y = γ sinωt

Then the steady state relative amplitude z of the seismic mass with respect to the frame is

obtained from equation,

=

and phase difference between exciting motion & relative motion is given by

Φ= tan-1

Imagine that a scale is fixed on the frame and a pointer on the seismic mass. Then the

amplitude of the motion of mass over the scale represents the relative motion z having

amplitude z. This motion is also harmonic. Plot of equation 1 and 2 for relative response &

phase shift in figure 2 and 3.



55

1. Vibrometers:

If input motion y in figure 1 is harmonic then relative motion z that can be recorded by means

of a secondary strainsensing transducer, is also harmonic. The ratio of recorded motion to

exciting motion is given by equation 1 and plot by figure 2

if in equation 1, >> 1

then tends to unity irrespective of the value of damping. This is also seen in figure 2.

The ratio = 1 means that the relative amplitude recorded z, is equal to excitation amplitude

Y or the amplitude of vibrating system. Thus, provided is large, the amplitude

recorded is approximately equal to the amplitude of the vibrating body.

It can also seen from figure 2, if damping factor about 0.7 or a little lower, it is possible to

have a better approximation of relation ( ) over a larger range of frequency ratio.

In most vibrometers damping is kept as small as possible (for reason of reduced distortion),

but is lage enough to ensure that the recorded motion is a good approximation of

input motion. The ratio of can be made large by having the instruments of low

natural frequency, the average value of which may be about 4Hz.

We have seen that if vibrating body has a harmonic motion of a frequency such that then the amplitude recorded is a good approximation of the amplitude of

vibrating body. However, output signal is not in phase with the input motion and so, there is

some time delay depending upon the time of damping in the system. But that is immaterial as

long as output signal is a true representation of input signal.

Now consider that vibrating bidy has a non-harmonic periodic motion of fundamental

frequency ω such that then the fundamental will be transmitted with the same

accuracy as before any higher harmonic has a higher frequency than the fundamental and will

be recorded still more precisely. But if we look back to phase angle plot of figutr4, we see the

phase shift for different values of is different.



56

This will mean that although each harmonic separately, is recorded accurately it has different

phase angle relationship with the fundamental in the recorded motion than what it had in the

input motion.

The result is that the output motion will be distorted motion and not a true representation of

input motion. This can be seen in figure 4 , where the fundamental in the recorded wave has

suffered a log of Φ3 .The final output wave is distorted.

This difficulty can be overcome by making the damping in the system to be zero. Under this

condition , the phase difference is 180˚ whatever the frequency ratio. So each

harmonic motion , seperatly apart from being recorded accurately is also transmitted with the

same phase angle relationship. The resulting output signal is a true reproduction of the input

signal.

2. Velocity Pickups:

The relative motion z could be measured by means of secondary strain sensing

transducer. We can have a velocity sensing secondary transducer of the type of a magnet

rigidly fixed to the seismic mass moving in a coil fixed to the frame, then the output

voltage at two ends of the coil will be proportional to the relative velocity since the output

voltage is proportional to the rate at which the lines of force are cut. The relative velocity

is equal to the input velocity of the support of the vibrating system at large values of

.

Hence the instruments behaves as a ‘ velocity pick up ’.

3. Accelerometers:

The instrument in figure1 can also behave as an accelerometer under certain conditions.

In equation 1 if << 1 ; then

≈

or z ≈

The expression in the above equation is equal to the acceleration amplitude of the

body vibrating with frequency ω and having a displacement Y. Hence the amplitude

recorded z, under these conditions is proportional to the acceleration of the vibrating



57

body. Since is a constant of the instrument actually represents the accelerations at

various frequencies.

The ratio can be made small by having large as possible.

The natural frequency of the accelerometer should be at least twice as high as the highest

frequency of the acceleration to be recorded.

There is a possibility of some difficulty in case of non-harmonic periodic vibrations

where the harmonics of higher frequency may not be recorded accuretly unless is

much higher than the highest frequencies of harmonics. For this reason the natural

frequency of most of the good accelerometer is above 10,000 Hz , much above the range

of frequency of mechanical vibrations.

4. Frequency Measurement instrument s or Techometer:

(Frahm’s Reed Techometer)

It consists of a system having a no. of reeds fixed over it in the form of cantilevers

carrying small masses at their free end, as shown in figure. The natural frequencies of the

set of these reeds is adujested to give a definite series of known frequencies. When this

instrument is attached to the body where frequency of vibration is to be measuired the

reed whose natural frequency is nearest to the excitation frequency vibrates near resonate

condition and has a large amplitude of vibration. The frequency of the vibrating body is

then given by the known frequency of reed vibrating with maximum amplituide.

The accuracy of instrument depends upon the difference between the natural frequencies

of the successive reeds. The smaller the difference, more accurate is the instruments and

vice-versa . Of course with a more accurate instrument of this type, the range of

frequencies that can be measured , will be smaller.

RESULT:

We have studied about Vibrometer, Velocity pickup, Accelerometer and Techometer.

APPLICATIONS



58

The information about ground vibrations due to earthquakes, fluctuating wind velocities on

structures, random variation of ocean waves, and road surface roughness are important in the

design of structures, machines, oil platforms, and vehicle suspension systems.

EXPECTED OUTCOME:

COMMENT BY STUDENT:

VIVA VOCE

1. What are vibratometers?



59

2. Define Frahm’s Reed Techometer?

3. Define dynamic coupling?

4. Define the number of degrees of freedom of a vibration system?



60

Experiment No. 12

AIM: Perform study of the following using Virtual Lab http://www.vlab.co.in/

Objectives of the Virtual Labs:

To provide remote-access to Labs in various disciplines of Science and Engineering. These

Virtual Labs would cater to students at the undergraduate level, post graduate level as well

as to research scholars.

To enthuse students to conduct experiments by arousing their curiosity. This would help

them in learning basic and advanced concepts through remote experimentation.

To provide a complete Learning Management System around the Virtual Labs where the

students can avail the various tools for learning, including additional web-resources, video-

lectures, animated demonstrations and self evaluation.

To share costly equipment and resources, which are otherwise available to limited number

of users due to constraints on time and geographical distances

Welcome to Vibration and Acoustics!

In this lab vibration related techniques are demonstrated like MI of connecting rod, force

response and free response of SDOF, Trifiliar suspension, tuned vibration absorber and many

more

APPLICATIONS

A concept and a structure of a Virtual Laboratory for technical engineering education that

relies on self-directed, directed and collaborative learning methods has been developed.



61

EXPECTED OUTCOME:

COMMENT BY STUDENT:

VIVA VOCE

1.What is virtual lab

2.What the role of virtual in vibration lab



62



63

Experiment No.13

AIM: Forced Vibration of a Cantilever Beam with a Lumped Mass at Free End: To calculate

the natural frequency and damping ratio for forced vibration of a single DOF cantilever beam

system, experimentally; and compare the results with theoretical values.

DESCRIPTION:

Figure shows the general set up. Slightly heavy rectangular section bar than used in Expt. no.

10 is supported at both ends in trunnion fittings. Exciter unit with the weight platform can be

clamped at any convenient position along the beam. Exciter unit is connected to the damper

which provides the necessary damping.

PROCEDURE :

1. Arrange the setup as shown in Figure.

2. Connect the exciter Motor to control panel.

3. Start the Motor and allow the system to vibrate.

4. Wait for 5 minuts for amplitude to build up for particular forcing frequency.

5. Adjust the position of strip chart recorder. Take the record of amplitude Vs. time on

strip chart recorder by starting recorder motor.


7. Repeat the experiment for different dampng.



64

8. Plot the graph of amplitude Vs. frequency for each damping.

OBSERVATION TABLE:

Forcing frequency Amplitude

SAMPLE CALCULATION:

OBSERVATION TABLE:




65

RESULT:

PRECAUTIONS:







EXPECTED OUTCOME:

COMMENT BY STUDENT:



66

VIVA VOCE





5. Define pendulum?



67

Experiment No.14

AIM:

Harmonicaly Excited Forced Vibration of a Single DOF System: To analyze the forced

vibration response of a single DOF system at different damping ratio and frequency ratio

DESCRIPTION:





PROCEDURE :












68

OBSERVATION TABLE:


SAMPLE CALCULATION:

OBSERVATION TABLE:




69

RESULT:

PRECAUTIONS:



70







EXPECTED OUTCOME:

COMMENT BY STUDENT:



71

VIVA VOCE





5. Define pendulum?



72

Experiment No. 15

AIM: Perform study of the following using Virtual Lab http://www.vlab.co.in/

Objectives of the Virtual Labs:

To provide remote-access to Labs in various disciplines of Science and Engineering. These

Virtual Labs would cater to students at the undergraduate level, post graduate level as well

as to research scholars.

To enthuse students to conduct experiments by arousing their curiosity. This would help

them in learning basic and advanced concepts through remote experimentation.

To provide a complete Learning Management System around the Virtual Labs where the

students can avail the various tools for learning, including additional web-resources, video-

lectures, animated demonstrations and self evaluation.

To share costly equipment and resources, which are otherwise available to limited number

of users due to constraints on time and geographical distances

Welcome to Vibration and Acoustics!

In this lab vibration related techniques are demonstrated like MI of connecting rod, force

response and free response of SDOF, Trifiliar suspension, tuned vibration absorber and many

more

EXPECTED OUTCOME:

COMMENT BY STUDENT:



73

VIVA VOCE

1.What is virtual lab

2.What the role of virtual in vibration lab



74



75

Experiment No.16

AIM: Forced Vibration of a Cantilever Beam with a Lumped Mass at Free End: To calculate

the natural frequency and damping ratio for forced vibration of a single DOF cantilever beam

system, experimentally; and compare the results with theoretical values.

DESCRIPTION:





PROCEDURE :











76


OBSERVATION TABLE:


SAMPLE CALCULATION:

OBSERVATION TABLE:




77

RESULT:

PRECAUTIONS:







EXPECTED OUTCOME:

COMMENT BY STUDENT:



78

VIVA VOCE





5. Define noise?



79

Experiment No.17

AIM:

Harmonicaly Excited Forced Vibration of a Single DOF System: To analyze the forced

vibration response of a single DOF system at different damping ratio and frequency ratio

DESCRIPTION:





PROCEDURE :












80

OBSERVATION TABLE:


SAMPLE CALCULATION:

OBSERVATION TABLE:




81

RESULT:

PRECAUTIONS:









82

EXPECTED OUTCOME:



83

COMMENT BY STUDENT:

VIVA VOCE





5. Define noise?

LAB MANUAL - JECRC Foundation

Documents

Transcript of LAB MANUAL - JECRC Foundation