Modelagem e Simulação da Dinâmica de Alto

Modelagem e Simulação da Dinâmica de Alto

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rE
rA
rR
m
CM
I
rM
M
L
CE
CA
CR
rA
rE
Evc (s) = [RE + Red (ω) + sLe (ω)]Ivc (s) + βlV (s),
1
+ Sd2 ZA (s)),
βlIvc = V (s)(Rms + sMms +
sCms
!
• Evc (s) " #$%#$&$'() ) ($'&*+ )%,-.)/) ') 0+0-') /+ ),(+ 1),)'($2
• RE " ) %)#.$,) .+'&()'($ $3 #$,)4*+ 5 1#$678'.-) /) #$&-&(8'.-) /) 0+0-') /+
),(+"1),)'($2
• Red (ω) " ) %)#.$,) /) #$&-&(8'.-) /) 0+0-') 9)#-:9$, .+3 ) 1#$678'.-)2
• Le (ω)" ) -'/7(;'.-) /) 0+0-') /+ ),(+"1),)'($< 67$ = 9)#-:9$, .+3 ) 1#$678'.-)2
• Ivc (s) " ) .+##$'($ 67$ .-#.7,) ') 0+0-') /$9-/+ ) Evc (s)2
• βl " + %#+/7(+ $'(#$ ) /$'&-/)/$ /$ >7?+ 3)@'=(-.+ %$,+ .+3%#-3$'(+ /) 0+0-')
/$'(#+ /+ .)3%+ 3)@'=(-.+2
• Rms " ) #$&-&(8'.-) 3$.;'-.) /+ ),(+"1),)'($2
• Mms " ) 3)&&) 3A9$, /+ ),(+"1),)'($2
• Cms " ) .+3%,-;'.-) /+ ),(+"1),)'($2
• V (s) " ) 9$,+.-/)/$ /$ /$&,+.)3$'(+ /+ .+'$ /+ ),(+"1),)'($2
• Sd " ) :#$) $1$(-9) /+ .+'$2
• ZA (s) " ) -3%$/;'.-) ).B&(-.) /+ 3$-+2
• U (s) " ) .+##$'($ 67$ .-#.7,) ') -3%$/;'.-) ).B&(-.)C
D$&($ 3+/$,+< Evc (s)< RE < Red (ω)< Le (ω) $ βlV (s) #$%#$&$'()3 ) %)#($ $,=(#-.) /+
),(+ 1),)'($< +& -($'& Rms < Mms < Cms $ βlIvc (s) #$%#$&$'()3 ) %)#($ 3$.;'-.) $ ZA (s)
#$%#$&$'() ) %)#($ ).B&(-.) /+ ),(+"1),)'($C E ).+%,)3$'(+ $'(#$ ) %)#($ $,=(#-.) $ ) %)#($
3$.;'-.) = 1$-() )(#)9=& /$ 73 @-#)/+#< 67$ %+/$ &$# /$F'-/+ .+3+ 73 67)/#-%+,+ +'/$
) ($'&*+ $3 73 %)# /$ ($#3-')-& = /-#$()3$'($ %#+%+#.-+'), 5 .+##$'($ '+ +7(#+ %)#
/$ ($#3-')-&C E ).+%,)3$'(+ $'(#$ )& %)#($& 3$.;'-.) $ ).B&(-.) = 1$-() )(#)9=& /$ 73
(#)'&1+#3)/+# -/$), .+3 73) #$,)4*+ /$ $&%-#)& Sd : 1 G !"#$< HHIJC
K#$67$'($3$'($< )/+()"&$ 73) )'),+@-) .+3 + &-&($3) 3)&&)"3+,) 1+#4)/+
)3+#($.-/+ .+3+ 3+/$,+ &-3%,-F.)/+ %)#) 73 ),(+"1),)'($ G %$&'!$< LMMNJC O+3 $,$<
&$ $&(7/) ) /-';3-.) /+ 17'.-+')3$'(+ 3$.;'-.+ /+ ),(+"1),)'($ $3 +%+&-4*+ )+ %#-3$-#+
3+/$,+< 67$ &$ %#$&() 3)-& %)#) + $&(7/+ $,$(#+/-';3-.+ /+ 3$&3+C E &-&($3) 3)&&)
]< %#$&) /$ 73
3+,) .+3 )3+#($.-3$'(+ -/$), .+'&-&($ /$ 73) 3+,) .+3 .+'&()'($ k[ N
m
,)/+ ) 73) %)#$/$ F?) $< /+ +7(#+< ) 73) 3)&&) M [Kg]C P)#),$,+ 5 3+,)< %#$&+ ') 3$&3)
%)#$/$ $ ') 3$&3) 3)&&) M [Kg]< $?-&($ 73 )3+#($.$/+# .+3 .+'&()'($ /$ )3+#($.-3$'(+
c[ Nms ]C Q&($ &-&($3) $&(: $&67$3)(-R)/+ ') F@7#) LCN< +'/$ &$ %$#.$0$ 73) 1+#4) $?($#')
)+ &-&($3)< #$%#$&$'()/) %+# F [N ]C
Fs = −kx;
Fd = −cv = −c
dx
.
dt
x[m]
v[ ms ]
Fs [N ]
Fd [N ]
Fm = M a = M
d2 x
.
dt2
a[ sm2 ]
M [Kg]
x[m]
t[s]
F
Fm = Fs + Fd + F ;
d2 x
dx
M 2 + c + kx = F.
dt
dt
ω0 [ rad
]
s
!
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0</ (&1+05 =+> #$0&1-+ %&$ -+1 "#$%&'()*+ 9 .+.+ 4/#?
ω0 =
r
k
.
M
@ 5AB
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4/(-/ I3/5 6$0-$ 0*0-$,+8 + 4/0*;</ .$ $%&*1>E#*/ 0$ .2 %&+(./ / I/ 0$ $()/(-#+ (+ :$#-*)+15
J,+ :$D .$01/)+.+ .$0-+ 4/0*;</8 + K#+:*.+.$ +K$ .$ "/#,+ #$0-+&#+./#+8 4#/:/)+(./ &,
,/:*,$(-/ /0)*1+-L#*/ +(21/K/ +/ 0*0-$,+ ,+00+7,/1+ 1*:#$ .$ "/#;+0 $3-$#(+05 M19,
.+ K#+:*.+.$8 4/.$70$ )/(0*.$#+# $"$*-/0 .$ +,/#-$)*,$(-/0 $ "/#;+0 $3-$#(+08 .$ ,/./
+(21/K/ +/ 0*0-$,+ ,+00+7,/1+ +,/#-$)*./ $ "/#;+./5 6/ )+0/ ./ 4'(.&1/8 (+ $%&+;</
@ 5NB8 x #$4#$0$(-+ / .$01/)+,$(-/ .+ ,+00+ )/, #$1+;</ O 4/0*;</ .$ $%&*1>E#*/ $ k +
+;</ .+ K#+:*.+.$5
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$%&*1>E#*/ @+&0'()*+ .$ )/##$(-$ +1-$#(+.+B8 .+./ 4/# x[m]5 C0-+ +(+1/K*+ 4/.$ 0$# :*0-+
$, @
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Mef f
dx
d2 x
+ Rm
+ kef f (x)x = βlI0 cos(ωt),
2
dt
dt
/(.$?
• x[m] 7 .$01/)+,$(-/ ./ .*+"#+K,+ $, #$1+;</ O 4/0*;</ .$ $%&*1*E#*/S
• Mef f [Kg] 7 ,+00+ ,L:$1S
• Rm [ Kg
] 7 +,/#-$)*,$(-/ ./ 0*0-$,+8 .+./ 4$1+0 4$#.+0 ,$)F(*)+0S
s
] 7 #*K*.$D .+.+ 4$1/ +($1 .+ 0&04$(0</ $ 4$1+ +#+(G+S
• kef f [ N
m
• β[T ] 7 )+,4/ ,+K(9-*)/8 -/,+./ )/,/ G/,/K'(*/ ($0-$0 $0-&./0S
• l[m] 7 -+,+(G/ ./ I/ .+ E/E*(+S
• I0 [A] 7 )/##$(-$ +1-$#(+.+ .$ $3)*-+;</ )/, + *("/#,+;</ 0/(/#+S
• f [Hz] 7 "#$%&'()*+ .+ )/##$(-$ .$ $3)*-+;</ I0 S
• ω = 2πf 5
@ 5Q!B
!
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70&+' :#.0(' 0 +0.%4. (' 4&9 +#.&06#6%#; < .4:4(#= (0(0 +#)' 06#) (0 $2$+#6$9' #
+#)0 0.06>0* 0124 .#+.#$#6%0(0 +'. kef f (x)* 7'&+?# 2& 4&+'.%06%# 4%#& 6#$%# &'(#)';
@'. #3#&+)'* $# 0+.'34&0.&'$ ' 06#) (0 $2$+#6$9' # 0 0.06>0 +'. (20$ &')0$* kef f (x)
$2.:# 7'&' 2& +0.A&#%.' .#+.#$#6%06(' #$%0$ (20$ &')0$; B# 0)C& (4$$' )#/0.&'$ #&
7'6$4(#.089' 0 #)0$%474(0(# (' 7'6#* 0)C& (0 0.06>0 # (' 06#) (0 $2$+#6$9'* kef f (x) +0$$0
0 .#+.#$#6%0. ' 7'6D26%' (#$$#$ '$74)0('.#$* ' 12# 02&#6%0 046(0 &04$ 0 7'&+)#34(0(# ('
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0)%',50)06%#$ F !"#$%& '( )*+* GGHI* $#6(' 2&0 4&+'.%06%# 5'6%# (# (4$%'.8?#$ 6' $'&
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Mef f
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+
R
+ kef f (x)x + F = βlI0 Cos(ωt).
m
dt2
dt
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dt
dt
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