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7/24/2019 AETT ZG 524-L2
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Vehicle Dynamics – Lecture-2
A course on Vehicle Dynamics
By
1Confidential
Prof. Sarvesh Mahajan BITS, PILANI
7/24/2019 AETT ZG 524-L2
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Vehicle Dynamics – Lecture-2
Learning !jec"ives #
Brief History of Vibration
Importance of Study of Vibration
Basic Concept of Vibration
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Classification of Vibration
Vibration #nalysis $rocedure
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Brief $is"ory of Vi!ra"ion #
$eople became interested in %ibration &hen they created the first musical
instruments' probably' &histles or drums(
)he *ree+ philosopher and mathematician $ytha!oras ,.2 /0 B(C( is considered
to be the first person to in%esti!ate musical sounds on a scientific basis(
Vehicle Dynamics – Lecture-2
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#lthou!h the concept of pitch &as de%eloped by the time of $ytha!oras' the
relation bet&een the pitch and the fre3uency &as not understood until the time of
*alileo in the si4teenth century(
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Brief $is"ory of Vi!ra"ion # In about // B(C(' in a treatise called Introduction to Harmonics, Euclid, wrote
briefly about music &ithout any reference to the physical nature of sound(
China e4perienced many earth3ua+es in ancient times'5han! Hen!' &ho ser%ed as a historian and astronomer
in the second century' percei%ed a need to de%elop
an instrument to measure earth3ua+es precisely(
Vehicle Dynamics – Lecture-2
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( (
*alileo &as inspired to study the beha%iour of a
simple pendulum by obser%in! the pendulum
7o%ements of a lamp in a church in $isa
He described the dependence of the fre3uency
of %ibration on the len!th of a simple pendulum'
alon! &ith the phenomenon of sympathetic %ibrations ,resonance(
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Brief $is"ory of Vi!ra"ion #
otable amon! the many contributions of 8aylei!h is the method of findin! the
fundamental fre3uency of %ibration of a conser%ati%e system by ma+in! use of the
principle of conser%ation of ener!y no& +no&n as 8aylei!h s method(
)his method pro%ed to be a helpful techni3ue for the solution of difficult %ibration
problems( #n e4tension of the method' &hich can be used to find multiple natural
-
Vehicle Dynamics – Lecture-2
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' (
In 1:/2 "rahm in%esti!ated the importance of torsional %ibration study in the
desi!n of the propeller shafts of steamships(
#mon! the modern contributers to the theory of %ibrations' the names of Stodola'De La%al' )imoshen+o' and 7indlin are notable(
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Im%or"ance of S"u&y of Vi!ra"ion #
7ost human acti%ities in%ol%e %ibration in one form or other( "or e4ample' &e hear
because our eardrums %ibrate and see because li!ht &a%es under!o %ibration(
Breathin! is associated &ith the %ibration of lun!s and &al+in! in%ol%es ,periodicoscillatory motion of le!s and hands( Human speech re3uires the oscillatory
motion of laryn!es ,and ton!ues(
Vehicle Dynamics – Lecture-2
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'
applications of %ibration' such as the desi!n of machines' foundations' structures'en!ines' turbines' and control systems(
7ost prime mo%ers ha%e %ibrational problems due to the inherent unbalance in
the en!ines(
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Im%or"ance of S"u&y of Vi!ra"ion #
In turbines' %ibrations cause spectacular mechanical failures( <n!ineers ha%e not
yet been able to pre%ent the failures that result from blade and dis+ %ibrations in
turbines(
the structures desi!ned to support hea%y centrifu!al machines' li+e motors and
turbines' or reciprocatin! machines' li+e steam and !as en!ines and reciprocatin!
Vehicle Dynamics – Lecture-2
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' ( '
machine component sub=ected to %ibration can fail because of material fati!ueresultin! from the cyclic %ariation of the induced stress(
"urthermore' the %ibration causes more rapid &ear of machine parts such as
bearin!s and !ears and also creates e4cessi%e noise( In machines' %ibration canloosen fasteners such as nuts( In metal cuttin! processes' %ibration can cause
chatter' &hich leads to a poor surface finish(
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Im%or"ance of S"u&y of Vi!ra"ion #
Vehicle Dynamics – Lecture-2
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Basic 'once%" of Vi!ra"ion #
#ny motion that repeats itself after an
inter%al of time is called vibration or oscillation.
)he s&in!in! of a pendulum and the motion of apluc+ed strin! are typical e4amples of %ibration(
# %ibratory system' in !eneral' includes -
Vehicle Dynamics – Lecture-2
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a means or stor n! potent a ener!y spr n! '
a means for storin! +inetic ener!y ,mass'
and a means by &hich ener!y
is !radually lost ,damper(
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Num!er of Degree of (ree&om #
)he minimum number of independent coordinates re3uired to determine
completely the positions of all parts of a system at any instant of time defines the
number of de!rees of freedom of the system(
#ll systems sho&n belo& and $endulum sho&n in abo%e slide are ha%in! sin!le
de!ree of freedom
Vehicle Dynamics – Lecture-2
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Num!er of Degree of (ree&om #
#ll systems sho&n belo& and $endulum sho&n in abo%e slide are ha%in! t&o
de!ree of freedom
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Num!er of Degree of (ree&om #
#ll systems sho&n belo& and $endulum sho&n in abo%e slide are ha%in! three
de!ree of freedom
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Num!er of Degree of (ree&om #
Some systems' especially those in%ol%in! continuous elastic members' ha%e an
infinite number of de!rees of freedom( # Cantile%er beam is ha%in! infinite no( of
De!ree of "reedom' Since the beam has an infinite number of mass points' &e
need an infinite number of coordinates to specify its deflected confi!uration(
Vehicle Dynamics – Lecture-2
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Systems &ith a finite number of de!rees of freedom are called &iscre"e or lum%e&
%arame"er sys"ems' and those &ith an infinite number of de!rees of freedom are
called con"inuous or &is"ri!u"e& sys"ems.
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'lassifica"ion of Vi!ra"ion #
Vibration can be classified in many &ays but here &e &ill discuss some important
classifications –
(ree an& (orce& vi!ra"ions #
(ree Vi!ra"ion. If a system' after an initial disturbance' is left to %ibrate on its o&n'
Vehicle Dynamics – Lecture-2
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(
system( )he oscillation of a simple pendulum is an e4ample of free %ibration(
(orce& Vi!ra"ion. If a system is sub=ected to an e4ternal force ,often' a repeatin!
type of force' the resultin! %ibration is +no&n as forced %ibration( )he oscillation
that arises in machines such as diesel en!ines is an e4ample of forced %ibration(
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'lassifica"ion of Vi!ra"ion #
Dam%e& an& )n&am%e& vi!ra"ions #
If no ener!y is lost or dissipated in friction or other resistance durin! oscillation'
the %ibration is +no&n as un&am%e& vi!ra"ion(
If any ener!y is lost in this &ay' ho&e%er' it is called &am%e& vi!ra"ion(
#
Vehicle Dynamics – Lecture-2
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If all the basic components of a %ibratory system the sprin!' the mass' and the
damper beha%e linearly' the resultin! %ibration is +no&n as linear vi!ra"ion( If'
ho&e%er' any of the basic components beha%e nonlinearly' the %ibration is called
nonlinear vi!ra"ion(
If the %ibration is linear' the principle of superposition holds' and the mathematical
techni3ues of analysis are &ell de%eloped( "or nonlinear %ibration' the
superposition principle is not %alid' and techni3ues of analysis are less &ell +no&n(
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'lassifica"ion of Vi!ra"ion #
De"erminis"ic an& non*&e"erminis"ic vi!ra"ions #
If the %alue or ma!nitude of the e4citation ,force or motion actin! on a %ibratorysystem is +no&n at any !i%en time' the e4citation is called deterministic( )he
resultin! %ibration is +no&n as &e"erminis"ic vi!ra"ion.
Vehicle Dynamics – Lecture-2
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n some cases' t e e4c tat on s non e"erm n s" c or ran om> t e %a ue o t e
e4citation at a !i%en time cannot be predicted( In these cases' a lar!e collection of
records of the e4citation may e4hibit some statistical re!ularity( It is possible to
estimate a%era!es such as the mean and mean s3uare %alues of the e4citation(
<4amples of random e4citations are &ind %elocity' road rou!hness' and !round
motion durin! earth3ua+es(
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'lassifica"ion of Vi!ra"ion #
De"erminis"ic an& non*&e"erminis"ic vi!ra"ions #
Vehicle Dynamics – Lecture-2
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