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7/26/2019 Relatorio Vibraes FINAL
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CENTRO FEDERAL DE EDUCAO TECNOLGICA DO RIO DE JANEIRO
DEPARTAMENTO DE ENSINO SUPERIOR
DEPARTAMENTO DE ENGENHARIA MECNICA
TRABALHO DE VIBRAES
Alunos: Gab!"l Ma#"$o S!l%"!a
Ma&'"us Pa&!#( Soa"s )abosa
Po*"sso"s: F"nan$o R!b"!o
Rio de Janeiro,Novembro de 201
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SUMRIO
1 INTRODUO....................................................................................................5
1.1 POSICIONAMENTO......................................................................................5
1.2 OBJETIVOS..................................................................................................... 6
2 EQUACIONAMENTO.......................................................................................6
2.1 MODELO FSICO............................................................................................. 6
2.2 DIAGRAMA DE CORPO LIVRE.........................................................................7
2.3 MODELO MATEMTICO.................................................................................. 8
2.4 PARMETROS TILI!ADOS..........................................................................153 RESULTADO DA SIMULAO.........................................................................15
3.1 ANLISE DOS RESLTADOS NO DOMNIO DO TEMPO..................................16
3.2 FRE"#NCIAS E MODOS NATRAIS DE VIBRA$%O......................................1&
4 COMENTRIOS FINAIS................................................................................... 2'
5 ANEXOS........................................................................................................... 21
5.1 PROGRAMA PRINCIPAL.................................................................................21
5.2 PROGRAMA E"A$%O................................................................................. 22
2
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LISTA DE FIGURAS
F()*+, 1 - V/0* ,.......................................................................................... 6F()*+, 2 - D(,)+,, 0+ (+ )+,* (9+, 0:......7F()*+, 3 - D(,)+,, 0+ (+ ;+*9+,-, ?9,,@.............................................................13F()*+, 6 - D(:0(, ,: >*9+,-, ?9,,@.................................................14F()*+, 7 - A)* 0,++ ,+, 3 ?,@ 1''' N.......................................16F()*+, 8 - A)* 0,++ ,+, 3 ?,@ 1'''' N.....................................16F()*+, & D0,: 0,++ ,+, 3 ?,@ 1''' N............................17F()*+, 1' - D0,: 0,++ ,+, 3 ?,@ 1'''' N........................17
F()*+, 11 - D0,: , ,+, 3 ?,@ 1''' N.......................18F()*+, 12 - D0,: , ,+, 3 ?,@ 1'''' N...................18
3
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LISTA DE TABELAST,9, 1 - P,+:+
*:((,..............................................................................................15
4
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1 INTRODUO
1.1 POSICIONAMENTO
V/0* ,*::+ *:((, :++ 0 ,(
(+ ,0:H *, 0,+,0:+/:(0, 0* :+ : ,
+
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,: ;+,:*+, , 0*, +:9+,. J*:,: 0 , (:* ,+, 0,, (:*,* +0++ :++
+.
1.2 OBJETIVOS
A =,(, : +,:+( ,+ ,,(,+ , ((0, *
/0* ;+ *, 0(:,*9+,-, *
+0*+. O /0* *( * (: , ,,
:+(:,,,)(+ 0(+,, . P+ *:+, ,+((
0 , ,, ++( (:, ,+:0(: , ,,
* ;+, 0(+,. A (H ;( 0(+, :,
0,++H ((, ,( :+0(+ (. P,+, ,( :, , , =)*+, 1.
2 EQUACIONAMENTO
2.1 MODELO FSICO
6
Figura 1 - Veculo plano
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2.2 DIAGRAMA DE CORPO LIVRE
O (,)+,, 0+ (+H (/ , =)*+, 2H :+, ( 0,++ * 3 )+,* (9+,. N, =)*+, 3 : DCL ,;+
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Figura 3 - Diagrama de corpo livre e foras do modelo completo
2.3 MODELO MATEMTICO
A ,+:(+ (,)+,, 0+ (+ , S)*, L( N:H
0), K >*,*,:
,,)(+. O ( +;+Q0(, (:, ,+: 0:+ ,,
/0*H >* : (:,: (,:(+ :+,(+. U (,
8
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>* /0* 0,- 9+ , 9,,H (0(,- 0 )*
+,*H
* 0 * ,+ ()*,( , ++( ,+ )*.
N, 0(*
,,)(+ : , *, (:0(, c +,*H ,: /0* ,:()(+ , 9,,H
*+,: :+,: DH , , :,+(, :(0,, >* *+,: , ,,)
, 9,, * 0,: X2 :,+(, +(:, , (+*(/9+( , ;+
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P (,)+,, 0+ (+H 9+,- >* , W(0, ;+*
,:*, 9+ ,,)(+ * ++( , ;+* X2 , ,(+ >*
X1 . L)
KP(X2X1c . )m2 . g=m2 . X2
m2 . X2+KP (X2X1c . )=m2 . g
P+:,:
m2. X2+KP. X2KP . X1KP . c . =m2 . g
2.3.2 VECLO PLANO
1'
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O ,:, ,+, ++:,+ /0* , ,+:, ,,
*(;+: (:+(9*/, m1 : (+0(, I +,*,( 0:, , , ,+:0+H
(:. A * (,:(+, : , *, (:0(, a 0:+
,,H , 0:,: :(0, ,+:0(: ,, + KD
BD H +0:(,:. P+ *, H , * :+,(+, : , *,
(:0(, b 0:+ ,,H 0=0(: :(0
,+:0(: KT B T . O 0=0(: ,+:0(:
* ;( +,H ( ,+:, ,+ *(: ,( 9,( >*
0=0(: ,+:0(: ,+:0+.
O 0,: +:(0, 0:+ ,, /0*H X1 H
(+0(, ,+, 0(, 0(+,- >* , , :, :+,0(,,H
,( 0 ,,)(+. C /0*
0(+, 0 * 0+ +/)(H 0,: +:(0, (,:(+
:+,(+ : *, +,
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T 0,: (,:(+ :+,(+H 0,0*,+ ,
;+
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m1
. X1+( BT+BD) . X1+( BD . bB T. a ) .+ (KT+KD+KP ) . X1(KP ) . X2+ (KD. bKT. a+KP . c ) . =
O ,:+( : ,:*,: /0* , ,9,(
+ T=I
E:
KT(X1a .YT) a+BT( X1a .YT)aKD(X1+b .YD) bBD( X1+b . YD)b+KP (X2X1c . )
P+:,:
I+( BD . bBT. a ) X1+( B T. a2+BD . b
2)+(KD . bKT. a+KP . c )X1(KP . c )X2+(KT. a2+KD .b
2+KP . c2)
C , >*,
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B T+BD BD . bBT.a 0
BD . bB T. a BT. a2+BD . b
20
0 0 0
Y B
KT KDKT. a KD .b
0 0
YK
BT BDBT. a BD . b
0 0
Y B
2.3.3 "EBRA-MOLAS O LOMBADA
P,+, >*9+,-, : >* )* +**9+,-, :+ 'H'8 ,:*+, 0+(: 1H5. O , )*(: , ,) , ;** = ,
0*+, >*9+,-,.
Figura 5 - Perl !uebra-molas "lombada#
f=y
0
2[1cos(t)]
S >* =(+ 0
14
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=v , com = 2
lamb[ciclos /m]
OH
' ,:*+, , 9,,Z
;+>*Q0(, ,,) , 9,,Z
0(, /0* *+,: , ,,) , 9,,Z
0+(: , 9,,Z
: : ,,).
S,9 >* , +, , ;+: (+ ,,+ ,: >* , +, :+,H
- (0*(+ : >* , +, :+ +, , 0),+. N: >* (+
((*(+ , >*,* , +, :+ 0), ( >* , , ;+: 0)*.
T,9 (0*(+ : >* 0,++ +, ,+, 0),+ ,
>*9+,-,. F, ( *9:+,( , ;**9+, ,
(((, , 0(,.
t =
D
v
D (:0(, , /0* ,: >*9+,-,Z
:[[ : ,: >*9+,-,.
15
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Figura $ - Dist%ncia at& !uebra-molas "lombada#
L) =0, >* ,+, , +, , ;+: :+ :H +0:(,:H, ;*
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2.4 PARMETROS TILI!ADOS
P,+, : +,:+( ,:, )*(: ,+
'abela 1 - Par%metros utili(ados
Letra a!"r
U#$%a%e
De&'r$()"
15'' L,+)*+, >*9+,-,\ 8' A:*+, >*9+,-,
A B 1&'' D(:,0(, 0:+ ,, ,:,+:0+
C 15'' D(:,0(, 0:+ ,, ,: ,,)(+D 1'''
'
D(:0(, , +, , ;+: ,: >*9+,-
,V 5 V0(, 0,++
M0 1''' ) M,, 0,++M 8' ) M,, ,,)(+0 1'''
'N C:,: :(0, 0,++
1''' N C:,: :(0, ,,)(+B0 5''' N C:,: ,+:0(: 0,++J 24 )] M: (+0(, /0*
T,9 ,++, = 0,+,:( ,:, * ))* 0, , 0:,: :(0, , , 1' ,(+.
3 RESULTADO DA SIMULAO
O +*:, ;+, 9:( , ,+:(+ +)+,, 0+(, )+*
*:((, ;:,+ MATLAB. E +*:, W+(0H ;+,
+()(, , ,) +9, ;+, ,::(0,H
;+, >* 0*:,+ 0)*( :+ ;,+ 0,0*. O+)+,, : ,, , = : +,:+(. P,+, ;(:
0,+,:( ,(0(, * )* 0, >* , 0:,:
:(0, , , 1' ,(+.
17
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3.1 ANLISE DOS RESLTADOS NO DOMNIO DO TEMPO
Figura ) - *ngulo carro para +3 "pessoa# de 1,,, .m
Figura / - *ngulo carro para +3 "pessoa# de 1,,,, .m
18
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Figura 0 Deslocamento carro para +3 "pessoa# de 1,,, .m
Figura 1, - Deslocamento carro para +3 "pessoa# de 1,,,, .m
1&
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Figura 11 - Deslocamento pessoa para +3 "pessoa# de 1,,, .m
Figura 12 - Deslocamento pessoa para +3 "pessoa# de 1,,,, .m
2'
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P+09 >* )+=0 ,+:, * 0+:,:
0(: 0 , +,(,. P+09 *, *,* ,9 0,H >*, *:((0, + 1' , 0:,: ,
,H +09 >* 0,++ 0(, * *0 ,( (:,:H (
,+: , , , , + ,( ;+: +:,: ,(0,+
,( ;+* :H
,,+ +H ,(, ()(=0,:(.
3.2 FRE"#NCIAS E MODOS NATRAIS DE VIBRA$%O
O +)+,, +:+* )*(: ,+ ,+, , ;+>*0(, ,:*+,(
1- P,+, ^3 , , 1''' N
-F+>*0(, N,:*+, 1Y55.7.
-M 1Y'.'5.
-F+>*0(, N,:*+, 2Y4.7'553.
-M 2Y-1.54&47-2'.
-F+>*0(, N,:*+, 3Y3.3'87&.
-M 3Y'.'141421.
2- P,+, ^3 , , 1'''' N
-F+>*0(, N,:*+, 1Y63.'775.
-M 1Y'.'5.
21
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-F+>*0(, N,:*+, 2Y4.26611.
-M 2Y1.6&464-1&.
-F+>*0(, N,:*+, 3Y1'.1&12.
-M 3Y'.'141421.
P+09 * ;(: ()(=0,:( , ;+>*Q0(, ,:*+,(H + . P +09+ >* 2 :+,: >* + ,+(, ,+, + ?, +,(, + +H +0 ;( *:((,, *, 0:,: 0 *9 +0(( _,:()-(:H +*:, ;( 0,0*, 0 , +0( ()(,H >* 0, , *9 1'-3'8H ,+, +:+,+ ,+ +@.
4 COMENTRIOS FINAIS
P ,=+,+ >* ,::(0 +)+,,
0*:,0(,( ( ,+:, +*:, ,:(;,:+( ,+, ,
,( , * 0;+: (0*,+.
A ( - :,+ >* , ;0( *:((,*,
*:((, , ;, ((0(,(. P+(:( , 0+ 0+:,:
((0 /0*H :+, 9;/0( , +**(: 0;+: )*+,
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5 ANEXOS
5.1 PROGRAMA PRINCIPAL
%Programa Principal%clearclose allglobala b bb d da db dq g kb m1 m3 yo vc%%%%%%%%%%GRAUS DE L!ERDADE%%%%%%%%%%ngl"3#%%%%%%%%%%%%%%%%$ASSAS%%%%%%%%%%%%%%%%m1"1# %dian&eira 'kg(
m)")*# %momen&o inercia 'kg(
m3"+# %pessoa 'kg(%%%%%%%%%,-E.,E/0E ELAS0,-%%%%%%%%%k1"1# %dian&eira '/m(
k)"1# %&raseira '/m(k3"1# %pesssoa '/m(
%%%%%%%,-E.,E/0E A$-R0E,$E/0-%%%%%%%!1"2# %dian&eira '/ms
!)"2# %&raseira!3"# %pesssoa
%%%%%%%%%%%%%%DAD-S ,ARR-%%%%%%%%%%%%%%da"14# %dis&ancia a 'm(db"14# %dis&ancia b 'm(dc"12# %dis&ancia c 'm(
dq"1# %dis&ancia roda da 5ren&e a&6 q7ebra8mola 'm(vc"2# %velocidade do carro 'ms(%%%%%%%%%%%DAD-S 9UE!RA8$-LAS%%%%%%%%%%yo"2# %al&7ra q7ebra molas 'm(d"2# %comprimen&o q7ebra molas 'm(%%%%%%%%%%%%%%%%$A0R:ES%%%%%%%%%%%%%%%m";m1
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&span";
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y)&"'yo)(@'')@pi@vcd(@sin'')@pi@vcd(@'&8''da?db?dq(vc((((# %roda&raseira derivada &empoelse y1"# y)"#
y1&"# y)&"#endyy";y1#y)=#
yy&";y1y)&=#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
.&1"kb@yy# %Para / gra7s de liberdade adicionar .&n
.&)"bb@yy
.&3";8m1@g##8m3@g=#
.&".&1?.&)?.&3# %al&erar ma&ri> &amb6m
yp"'a@y(?'b@.&(#