Introduction 1
CHAPTER
to
Why vibrations
study etc
Vibrations sound
are earthquake
everywhere of
vibration atoms
noise temperature
be
Vibrations diseases
systems
catastrophic
can collapses
dangerous
very failure
fatigue
electronic deices malfunctioning
NUN Vibo
N of
the declination
Vit Acoustics
is automotive
The NUH and harshness
vibration
noise Any irritating noise
an
means
acronym annoying
for It's
of
of
the to
of is NUH
and vehicle
vibration a a Study
object important
passenger the
of that
the
the Nut
individual terms make
understand up acronym
meaning the
Vibration is through senses
as a occur
a
on can
shaking perception
perceived trembling
of and sight objects
tough a watching
touching vibrating the
with to
Noise sand abnormal normal
i is as
unpleasant
an perceived respect
of vehicle
the
operation It
lo the to
to vehicle
refers
Harshness motion refers
in specifically
simply roughness it
to also the
sand to
refers
definitions
and some
quality
perception according for
the
with of
vibrations effect
associated
sensation rigid
physical example
suspension
Degree
ONE Systems
Freedom 2
CHAPTER
or
FREE oscillator
Unbarred di state
Hk MI
vimini elongation
Delta the equilibin
you position
gives
K If the the start
equilibrium
we perturb mass oscillating
b
mi atti eo
va my
m I
I static
load
Foce
mentis
my restoring
We to this
derive
different techniques
can use equations
the
IF of static action
remove
we presence Focus
can
we usually a
of thx
mi
motion io
equation the studies
which
part
initial conditions
considering the of
perturbation equilibrium
Xo
X lo Io of
the
perturbations
o system
of
the
form
the
by schiere Second com
in wean
Dividing genesi
mare creda
Natural
µ
È Un
con where
Eon sola
Frequency
m
Now the
End Solution
we can Asin t
Cont Nn Solution
B
t 1
cos
Where A Be Xo
con
And 1
2
1 11 Fn natural Frequency
Thee fan
also of
alternative Solution
is sn f
X t Solution
X t
con 2
Cos
So È smontsml
to
Out cast cost
cos cos
where Ìn
È Xo of
t oscillator
max
Amplitude amplitude
9
tg 9 Initial Phase
FREE DAMPED oscillator
l'invii Let's the
consider dampen
viscous reaction
dissipata
an energy
the
Face relative
depends velocity
µ on
c F ci
F ri e F
e
M The of motion
equation is thx
mi ci
Eon o
a T e elastic
meta viscous
Ae't
Trial the
solution in
substitute
we com
eat the
A ma coi io
So Leo
ott
ma't Con theo di t in
9 con
29 rotto
con natural
e Frequency
damping
now VF
9
artigianato di In
È
i g
µ
And the solution
general edit Beat
X t a
Damping Ratio
3
We hae solutions
can 44
5
c's di
3 1 him
1 andar rest
s and
are
negative Aperiodic
E motion
Aperiodic damping
tt Beat
X Ae critical
km di
3 1 Aaa
2 rest
and
c and
coincidenti Critical
X E Aperiodic sub
critical
htt
tt
X A Bf damping
f e
e
c'e km di
3 1
e
3 da
and and
are complex
conjugate Sibaritici
E Beat dediti Beat
edit
A
X4 Santos IN to
cont
e
It's the ratio which not the
informations
important danpmgcoeffr.int
damping gives Icon
go.ae
the critical
so coefficient
damping Con 20am
We call treshold
9 it's
because
critical
it 1 a
The I
call here
ratio
why is
we
reason damping
1 9
the who 90
Sometimes e high
in percent
expressed
is very damping
damping
Harmonically Forced oscillator
so of
the motion
contras
nae is Eon in
Fo
città
MI cit
e cos
µ rejma.no
fi
the ed
we prefer in space
making Complex etat
Li
MI Eon
Fo
ci in
M complexioned
domain
indeed
FG cinte Fo
F ti j smart
cosa
the is Fully
problem equivalent
So the
the solution
state
write
invest
domani we
con can particular
Steady
considering È Latt
Che cos
the domani
com in
now complenifical
considering Feint
X f
Then those
between
is a solutions
perfect equivalence X
1
Factor
amplifica non
afte manipulation
a U
U
Fo Fo
e e
e
X µ
i
mail tieni f
r II è
25
define Factor
we amplification 1 1
1 1 1
IG a i
x t.in fa E
25
The the the
term
this
of initial
is
physical displacement
over
amplitude
meaning
We that the value
notice depends
can on
amplification Frequency
that
We has
here
can maximum
a
see tamping
fa Ci_ call
that
condition
ho in a we
such don't
if hai
in condition we
resonance
G to
damping tre
Here scout shot
di
another
we can
When it's the
the 0.707
damping critical
tamping
Facta at
maximum is zero
amplification Frequency
So the
static
those conditions have
in
in maximum
cose displacement
you
To sommare if
Wto Glo 1
1 1hr2
3 s
Tyif3I1 TT
Gloves
r2
live.nu
2 51
9
il is sms 1
g cives 29 the in
is
PHASE movement
contea with the
phase Fare
the has to
Near
the it
a
resonance phase equal
jump
The isn't
when
Function
a
is
phase regular damping
it
of
absence
zero in a
presents
damping
at
the
discontinuity resonance the in
is
movement
with fare
the
phase
VIBRATION
da Isolation NN
Fare excited trasmissibility
as support
the ti
c
here to
able
is so
a we wanna
being
point suspension
design
this
hae the
trasmits
if and to
oscillata Force
evolsivate base m
the
Let's start with oscillata Io t
the
nè ci cosa FG
v
so edit È coatti
mai g
The Fare the ebstrsndtompmgfo
by
exceeded c.es
is given 1 città
the Foce
non complex edit
t.XCjwc.tk Foce
complex
We the H
ratio
define between
transuassibility
can as working
the of Forceand
the
the transmitted amplitude
amplitude region
of the excitation Itt
Fa È
1 25 Hunt
e 2
when
C ietteseli
f
Vibration From excitation
the
transmitted sismico
support etat
Yo
Y i
the
we
m I
z Cat
K mai
Gr
c Gesù
i
i e i
i f that
EXAMPLE
io ROADS
OF CORRUGATED
Wash
boarding 2T
i wavelength FASTER stater
is
IF GO
YOU slow
too I
That's result
the H
working
region
Periodic Fourier
Forcing Series
to SUPER
Position principle Xo
Consider the o
system halt Fit
f ci Where
µ e Ìo
o
if F Fe tbh t with
t cost
t b
a a e
the
then Solution is b X
Lt X f
a t t
linea
This if
True it said
the system a
is principle
is is superposition
ad Fourier Series Flt of Fourier
be the
Function
Any can
period
periodic a
expressed through series
The
of il the
function function
series suitably
is
periodic
trigonometric Series convenga
smooth
Consider function
harmonic Coot
sin
an Note
the snoot txt
cio 2T
sn
period a
the
consider time
dimensionless
we 7 Got
2ft e
the become
precedent son sn Etait
of of
without
loss the
so consider function
can 2T
period
we
generality a Fran T to
period
HE bus
in re
ar rt
a Zenith
cos
n period
E 2 t
The the
bir
and be terminated
coefficient by
ao an can ortogandity properties
considering
ofthe function
trigonometric Fit rwotdtv.co
an cos 1,2
Fit
bn ott
root re 1,2
sn of
the
Favore the each
coefficients
series trigonometric
weight importance
represent
term
the
Function harmonic
each of
value the function
mesi
Dirichlet X
conditions
The Dirichlet
the
if
f
Fourier and
Lt
of exists
Function only
certain
series cangent
a is
satisfied
conditions are
F the
I of
Finite
it within
discontinuities
t castra number
is on presenta
period
Flt and
has of
I within
Fornite the
number max non period
a Ìl
f
I Idt
the t'A
t io
is absolutely on period
integrable
In the
such Fourier ofthe
condition period
series in point
any
converge
0 Res
Ponce Forcina
OF an a
oscillator periodic
to
Let's costola fa
µ ao Hor
in t
f root
di sn
cos va
the
From the
of
the and
oscillates
analyse
we can
spa
position Following
principle response
solution
the
superimpose cio the forced
Koch
mio da
t t
t e statically
system
the sdutto
patata is I
24
For
the harmonics
other mira Cip the
Lt alti ar t
Xv nwo
t
t cos
Èh ci Lt tkxnblts.br
Lt nw.li
t
m b sin
the solution
and patata Luo
1 Gu Ya
an t
Xp t
va
cos
K
1 il
ben Yr
salvo.tt
b Gufo
the
So of the Fourier
harmonic
oscillator by
is
response given
È IGut basis
X arcos
20
t t va va
Where 1 14
25W
1Gt yu
tg
i lucidanti
Brodo a
radon
e Nothin
Fa E the
the the
small
We 1
that condition is
a
cansee resonance
damping of
to
excitation infinite
number
rise conditions
periodic resonance
sn
gives
EXAMPLE SQUAREWAVE
Ten of of
the
One
terms terns
the hundred Series
Series effect
Gibbs
fit
the
of
Gibbs whit
doesn't
the
effect the
the ogni
series
discontinuity
in proximity
the
that's not
the
Function Function deemed
because ogni
in discontinuity is
Check fa
29 of notes
lecture mea
pag
ARBITRARY Excitation time
i Domain approach
THE
da THE di
Impulse Rac Function
Unit E
È
Let's the F Edt
I Face within
of tormentarsi
consider a
a o
impulse o face
Fare
if and
veryshort time intensi
that Fase the
E
consider
we impulsive
now acting
impulse
conrspond.mg 1
folli
IF F a 1
Ie
because
o Dirac
this the Delta
of
Fare
kind be by unitary
con symbolically impulse
represented a
special
S fa t.fr
t z o
a S E dt 1
t o tra
fa
5 T t.to
t not deemed
X DIRAC Function recall X SH
S
the
mathematics tetto
Dmc o
II de a
see
the let's
delta often
Function why
deemed see
unitary
is impulse
as SE t
Let called ti
define E
o
Emotion
discontinuous Fornite o
us a impulse se lei telo E
The Disc
Anatra of
Innit
the Finite
the
is impulse
I Iim Scelti
8 t
Function
not
is s o
Response An an impulse
to
oscillator
of unitary A
F in un
We the
have situation SCH
mi citta
let's Innit
the
the to
and
now integrale Impact
di
mi tcitkddt.jp
E s
a
hit t
E
the terms
and three
consider separately
In Ot
mi
i
mi un
Io a Free
dampedoscillation
E
o so
lmcIozf
cidE o
È.io E so
o s
t
Holt
Io 5Wh
1
44 Udt
e sn
the miti mud
applying conditions t so
etico I
è
o where
a a 11 3
cod
m un
THE convolution INTEGRAL Flt
Consider oscillata
harmonic
excitation an
sn a
arbitrary
non aol.mg FA
Milt thx
tcx.lt t
Initial the rest
conditions oscillata in
is
are homogeneous
t.ro
upto
This indeed
of
doesn't generality non
implies
loosing
assumption throated
be
initial by
conditions taking
can
homogeneous
from the
advantage principle
superposition
FG of
by
be described
can a series
mathematically each
impulseforces acts
infinite
Scarica il documento per vederlo tutto.
Scarica il documento per vederlo tutto.
Scarica il documento per vederlo tutto.
Scarica il documento per vederlo tutto.
Scarica il documento per vederlo tutto.
Scarica il documento per vederlo tutto.
Scarica il documento per vederlo tutto.
Scarica il documento per vederlo tutto.
-
Riassunto esame Mechanical Vibrations, Prof. Del Mas Lieta, libro consigliato Vocabulary, Amir Hamza
-
Mechanical vibrations
-
Mechanical Vibrations
-
Mechanical Vibrations