Unit 4 Forced Vibration

Dynamics of Machines R 2017

1. Unit IV
FORCED
VIBRATION
DYNAMICS OF MACHINES
FORCED
VIBRATION
DOM - B.K.P1
B.K.Parrthipan, M.E., M.B.A., (Ph.D).,
Assistant Professor / Mechanical Engineering
Kamaraj College of Engineering and Technology.

2. Forced Vibration
Whenthebodyvibratesundertheinfluenceof
external force, then the body is said to be
underforcedvibration.
Example
:
Example
:
1.Ringingofelectricalbell
2.Vibrationsofaircompressors

3. Types of External Excitation
Three types of external forces applied are
(i) Periodic forces
(ii) Impulsive type of forces, and
(iii) Random forces

4. Harmonic Disturbances
(Spring mass system)
The amplitude of the forced vibration is given by
F
ois the excited forceand is the phase lag

5. Harmonic Disturbances
(Spring mass system)
The maximum amplitude of the forced vibration is
given by
ω is the angular velocity of the excited force or applied force.

6. Harmonic Disturbances
(Spring mass system)
The amplitude of the forced vibration is given by

F
ois the excited forceand

is the phase lag
The maximum amplitude of the forced vibration is
given by

7. 1.PhaseLagφ
Asthedisplacementtakesplaceafterapplying
force, the displacement vector lags the force
vector
by
some
angle
φ
.
This
angle
is
known
Harmonic Disturbances
(Spring mass system)
vector
by
some
angle
φ
.
This
angle
is
known
asphaselag.
Mathematically,
where r is the frequency ratio

8. Harmonic Disturbances
(Spring mass system)
2. Magnification factor or Dynamic Magnifier
The ratio of maximum displacement of the
forcedvibration(X
max)tothestaticdeflection
(X
)
due
to
static
force
and
it
is
denoted
by
(X
o
)
due
to
static
force
and
it
is
denoted
by
M.F.

9. Harmonic Disturbances
(Spring mass system)
It is clear that the magnification factor depends u p on
(i) The ratio of circular frequencies and
(ii) The damping factor

10. 1. Frequency response curve
Acurvedrawnbetweenmagnificationfactor
and frequency ratio is known as frequency
response
curve
.
Harmonic Disturbances –
Characteristics Curve
response
curve
.

11. 2.Phase-frequencyresponsecurve
A curve drawn between phase angle and
frequencyratioisknownasphasefrequency
response
curve
.
Harmonic Disturbances –
Characteristics Curve
response
curve
.

12. Disturbance caused by unbalance
Almost in all rotating and reciprocating
machinerylikeanelectricmotor,aturbine,an
IC engine, etc have some amount of
unbalanced
force
left
in
them
even
after
unbalanced
force
left
in
them
even
after
correcting their unbalance on precision
balancingmachines.Thisunbalanceproduces
theexcitingforceinamachine.

13. Disturbance caused by unbalance
The amplitude of the forced vibration is given by
m
u
-
unbalanced
mass, and e
-
eccentricity
m
u
-
unbalanced
mass, and e
-
eccentricity
The maximum amplitude of the forced vibration is
given by

14. PhaseLagφ
Asthedisplacementtakesplaceafterapplying
force, the displacement vector lags the force
vectorbysomeangleφ.Thisangleisknown
as
phase
lag
.
Disturbance caused by unbalance as
phase
lag
.
Mathematically,
where r is the frequency ratio

15. Forced Vibration due to the excitation
of the support (Support Motion)
•Absolute amplitude
The amplitude of the forced vibration is given
by
where Y is the amplitude

16. Forced Vibration due to the excitation
of the support (Support Motion)
•Relative amplitude
Inmanycases,itisusefultoknowtheresponseofthe
systemrelativetoamovingsystem.
The steady state relative amplitude of the forced The steady state relative amplitude of the forced vibration is given by
where z is the relative motion of the mass with res pect
to support

17. Transmissibility
•Transmissibility is a measure of the effectiveness
of the vibration isolating material.
•Types
1. Force Transmissibility 1. Force Transmissibility 2. Motion Transmissibility

18. Force Transmissibility
•ForceTransmissibilityisdefinedastheratioof
theforcetransmitted(F
T)totheforceapplied
onthesystem(F
O).
•
This
ratio
is
also
known
as
isolating
factor
.
•
This
ratio
is
also
known
as
isolating
factor
.
•Itisdenotedbyepsilon.

19. Force Transmissibility

20. Motion Transmissibility
•Motiontransmissibilityisdefinedastheratio
ofabsoluteamplitudeofthemass(F
T)tothe
base(orsupport)baseexcitationamplitute(Y).
•
This
ratio
is
also
known
as
Amplitude
•
This
ratio
is
also
known
as
Amplitude
Transmissibility.
•Itisdenotedby
A

21. Vibration Isolation
•The process of reducing the vibrations of
machines and hence reducing the transmitted
force to the foundation using vibration
isolating
materials
is
called
as
vibration
isolating
materials
is
called
as
vibration
isolation.
•Thematerialsusedforvibrationisolationare
(i)Rubber(ii)Corkand(iii)MetallicSprings

22. Types of Isolation
1. Isolationofforces
Vibrations produced in unbalanced machines
should be isolated from the foundations so that
theadjoiningstructureisnotsetintovibrations.
Thistypeofisolationisknownasforceisolation.
2. Isolationofmotions
Theunbalancedmachinesareisolatedfromtheir
foundations so that there should not be any
damageeithertothemachineorthefoundations.
This type of isolation is known as motion
isolation.