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SHIP RESPONSE TO WAVES
Types of waves:
1. Incident waves
2. Difracted waves
3. Radiated waves
INCIDENT WAVE
Wave w!ic! is a"read# $resent in t!e %$en sea& $r%$a'atin'
in a $artic("ar directi%n . it is a"s% ca""ed as anA)*ient
wave.
DI++RACTED WAVE
Difracti%n %, waves inv%"ve a c!an'e in directi%n %, waves as
t!e# $ass t!r%('! an %*-ect %, c%nsidera*"esie.
RADIATED WAVES
It is t!e wave 'enerated *# t!e %*-ect ($%n w!ic! t!e incident
wave acts. It is a"s% ca""ed as *%d#'enerated wave.
/et (s c%nsider a *%d# %, )ass ) ,"%atin' %n t!e ,ree s(r,ace %,
water %, densit# 0 .
N%w & ,%rce e(ati%n %, t!e *%d# in directi%n is
m ´ z= F Z ............. 415
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+%rces in directi%n res$%nsi*"e ,%r !eave are
1. Wei'!t 4 W5 actin' vertica""# d%wnwards.
2. 6(%#anc# 4 BO
5 actin' vertica""# ($wards at t!e e(i"i*ri() $%siti%n.
3. C!an'e in *(%#anc# d(e t% !eave δB in vertica""#
($wards.
7. Incident wave ,%rce.
8. Difracti%n wave ,%rce.
9. Radiated wave ,%rce.
m
´ z=W +BO+δB+W incident +W diffracted+W radiated
m ´ z= ρ
gAZ +W incident +W radiated
............. 425
4 since W : −BO and difracted wave ,%rce is ne'"ected ,%r
ver# s)a"" %*-ects i.e.& / ;;
λ 5
m ´ z= ρ
gAZ +W exciting− μ ́z− λ ´ z
On rearran'in' t!e e(ati%n& we 'et&
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4 m+ μ¿ ´ z− ρ
gAZ + λ ́z=W exciting .............
435
W!ere& μ isadded mass &
λ is dampingcoefficient &
4 m+ μ¿ is virtual mass .
W exciting forc e isthe Froude− Krlov force
:
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!= ρg "
2 #cosh $ ( z+h)
cosh$h # e
i($x−%t )
N%w inte'ratin' t!e $ress(re %ver t!e water $"ane area A& we
'et&
W exciting= ρg " 2 #cosh
$ (−d+h)cosh $h # e−i%t # A
............. 475
Ta
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́z= z¿ e−i%t # (−i% )
́z= z¿e−i%t # (% 2 )
We 'et &
−% [¿¿2 (m+ μ )−i%λ+ ρ gA ] z¿ #
e−i%t = F ¿e−i%t
¿
−% [¿¿2 (m+ μ )+ ρ gA]−i%λ
z¿= F
¿
¿
= z¿∨¿ response amplitude oprator
= z¿∨¿ : √ z '
2+ z
(
2
∈=tan−1 z (
z '
z¿
can)e*rittenas
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z¿=
F ¿
'−i(
A,ter rati%na"isati%n we 'et&
z¿= F
¿ '+ i F ¿ ( '
2+ ( 2
CALCULATION: (from VUGT’S experiment)
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ADDED >ASS COE++ICIENT DA>PIN?
COE++ICIENT
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W!ere a33 is added )ass c%e@cient and *33 is da)$in'
c%e@cient.
Va"(es %, t!e c%e@cient are ta
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Res$%nse a)$"it(de %$erat%r vs ,re(enc#
