UNIVERSIDAD DE GUANAJUATO DIVISIÓN DE INGENIERÍAS CAMPUS IRAPUATO SALAMANCA DEPARTAMENTO DE INGENIERÍA MECÁNICA DR. JOSÉ COLÍN VENEGAS LABORATORIO DE DINÁMICA Y VIBRACIONES
VIBRACIONES MECÁNICAS PRÁCTICA 1 DETERMINACIÓN DE LA RIGIDEZ DE UN RESORTE
SAÚL GARCÍA HERNÁNDEZ JOSÉ LUIS VARGAS ZAMARRIPA
OBJETIVO
?o'()(+# '(# $"5o!m&!@. D" %& ")0&)(+# &#*"!(o! "#)o#*!&mo' :0"=
Com!"#$"! %&' m"$()(o#"' $" m&#"!& *"+!()&,"-"!(m"#*&% &!& "#)o#*!&! %&' !o("$&$"' m")/#()&' $" 0# '('*"m& M&'&,R"'o!*",Amo!*(0&$o!.
INTRODUCCIÓN S" !"&%(2& "% )/%)0%o $" %& !o("$&$ m")/#()& $" !(($"2 $" 0# !"'o!*" m"$(&#*" m"$()(o#"' !/)*()&', "-"!(m"#*&%"' 3 m"$(&#*" )/%)0%o' *"+!()o'. S" 4&)" %& )om&!&)(+# $" %o' !"'0%*&$o' 3 '" !"'"#*&' %&' !/5()&' $" '0 )omo!*&m("#*o.
MARCO TEÓRICO
=
L& !"&))(+# & %& 50"!2& $"5o!m&$o!& "' %& 50"!2& (#*"!#& $"#om(#&$& 50"!2& !"'*&0!&$o!& )03o 6&%o! "'= = −
C0&#$o 0# !"'o!*" '" "'*(!& o! "5")*o $" 0#& 50"!2& $" *!&))(+# &0m"#*& %& '"&!&)(+# "#*!" '0' "'(!&' '0)"'(6&' $" mo$o :0" "% "'50"!2o :0" 'oo!*& "' "# !"&%($&$ 0# "'50"!2o )o!*&#*" o $" )(2&%%&$0!&.
L& "%&'*()($&$ $"'(#& %& !o("$&$ m")/#()& $" )("!*o' m&*"!(&%"' $" '05!(! $"5o!m&)(o#"' !"6"!'(7%"' )0&#$o '" "#)0"#*!&# '08"*o' & %& &))(+# $" 50"!2&' "-*"!(o!"' 3 $" !")0"!&! %& 5o!m& o!((#&% '( "'*&' 50"!2&' "-*"!(o!"' '" "%(m(#&#.
L& *"o!;& !"'")*(6& "!m(*" !"%&)(o#&! &% m+$0%o "%/'*()o $" !(($"2 G $"% m&*"!(&% )o# %& )o#'*&#*" "%/'*()& $"% !"'o!*" 9 $"% '(0("#*" mo$o=
L& %"3 $" Hoo9" "'*&7%")" :0" $"#*!o $" %o' %;m(*"' "%/'*()o' %& 50"!2& $"5o!m&$o!& < 3 %& m&#(*0$ $" %& $"5o!m&)(+# 'o# $(!")*&m"#*" !oo!)(o#&%"'=
Do#$"=
=
Do#$" → Co#'*&#*" "%/'*()& $"% !"'o!*".
L& $"5o!m&)(+# %%&m&$& *&m7(># "%o#&)(+# "' "% $"'%&2&m("#*o !"'")*o & %& o'()(+# $" ":0(%(7!(o
=
8
→ R(($"2 $"% !"'o!*" → M+$0%o $" "%&'*()($&$ $"% m&*"!(&%. → D(/m"*!o $"% &%&m7!" → D(/m"*!o $" "'(!& m"$(o → C&#*($&$ $" 60"%*&' &)*(6&'
DESARROLLO P&!& "% $"'&!!o%%o $" %& !/)*()& '" "')o(+ 0# !"'o!*" $" %o' "-('*"#*"' "# "% %&7o!&*o!(o $" 6(7!&)(o#"' $" %& 5&)0%*&$. U#& 6"2 '"%"))(o#&$o' '" !o)"$(+ & !"&%(2&! %o' )/%)0%o' 3 %&' m"$()(o#"' #")"'&!(&' &!& %%"6&! & )&7o %& !/)*()&.
1.- Cálculo de la riide! "e#rica de u$ re%or"e U'o' 3 <0#)(o#"' $" 0# R"'o!*"= •
•
•
•
•
P&!& &%m&)"#&! 3 !"*o!#&! "#"!;& )omo "% m")&#('mo $" !"*!o)"'o $" %&' &!m&' $" 50"o. P&!& m&#*"#"! 0#& 50"!2& $"*"!m(#&$& )omo "# %o' &)*0&$o!"' 3 "# %&' 6/%60%&'. Como &('%&$o! $" 6(7!&)(o#"' "# 6"4;)0%o'. P&!& !"*o!#&! o $"'%&2&! ("2&' )omo %o' !"'o!*"' $" 0"!*&' $" "$&%"' $" &)*0&$o!"' m")/#()o' o $" "m7!&0"'. Como &)*0&$o!"' $" )("!!" o $" "m08" )omo %o' !"'o!*"' #"0m/*()o'.
P&!& "% )/%)0%o $" %& !(($"2 '" "m%"+ 0#& ")0&)(+#= =
8
U'&#$o 0# 6"!#("! '" m($("!o# %&' $(m"#'(o#"' !":0"!($&' $"% !"'o!*" o7*"#("#$o %o' '(0("#*"' !"'0%*&$o'= = 2.8 = 38.3 1 = 2 3
D" &)0"!$o &% !"'o!*" '"%"))(o#&$o '" o7'"!6+ :0" '0 )omo'()(+# "' 0# &)"!o )o# )o#'($"!&7%" )o#*"#($o $" )&!7o#o o! %o :0" '" *("#" %o '(0("#*"= = 30 10 20! = 0.2"2
Do#$" → R&2+# $" Po(''o#
P&!& )&%)0%&! "% m+$0%o "%/'*()o $" !(($"2 '" *("#" %& '(0("#*" !"%&)(+#= =
2#1 $ %
P&!& *"#"! 0# !"'0%*&$o m/' "-&)*o '" '"%"))(o#&!o# o78"*o' )o# $(5"!"#*"' m&'&' 3 '" 50"!o# )o%o)&#$o $" 0#& o! 0#& 'o7!" "% !"'o!*" &'; '" 6&!;& %& 50"!2& &%()&$& 3 %& $"5%"-(+# $"% !"'o!*" )omo '" m0"'*!& "# %& 5(0!& '(0("#*"=
20! 10& = 2#1 $ 0.2"2% = 8.01 10'( )
E#*o#)"' S" !o'(0" )o# "% )/%)0%o $" %& !(($"2= 8.01 10'( #2.1* 10+ % = ,#,%#0.03-0* % = /. /
E# %& '(0("#*" *&7%& '" m0"'*!&# %o' !"'0%*&$o' o7*"#($o'=
&.- Cálculo e'(eri)e$"al de la riide! de u$ re%or"e
P&!& "#)o#*!&! %& !(($"2 $"% !"'o!*" '"%"))(o#&$o '" 0*(%(2+ %& %"3 $" Hoo9" !"6(&m"#*" "-%()&$& $o#$" '0 "-!"'(+# "'=
Ma%a "o"al *+,
e%o To"al *N,
Dele'i#$ *),
Riide! *+N,
.1 . 1. 1.1 .F .F
. . 11. 1. . .
1.,0 4 10+ 3.00 4 10+ *.00 4 10+ 8.00 4 10+ 1.03 4 10+5 1.*3 4 10+5
.FF . .F . .11 .
= −
P&!& o$"! "#)o#*!&! %& !(($"2 "' #")"'&!(o 'om"*"! &% !"'o!*" & 0#& 50"!2& 3 m"$(! '0 $"5o!m&)(+# $" "'*& m&#"!& '" 0"$" "#)o#*!&! %& !(($"2 '(m%"m"#*" $"'"8&#$o $" %& ")0&)(+# :0"$&#$o= =−
P&!& mo'*!&! "% )omo!*&m("#*o "#)o#*!&$o $"% !"'o!*" '" 0*(%(2&!o# %o' $&*o' o7*"#($o' :0" '" m0"'*!&# "# %& *&7%& &#*"!(o! &!& !"&%(2&! 0#& !/5()& $" $"5%"-(+# )o#*!& 50"!2& &%()&$& 0'&#$o %& &30$& $" M&*%&7.
.1
RESULTADOS
.1 .1
Como '" 0"$" o7'"!6&! *&#*o &!& "% m>*o$o *"+!()o )omo &!& "% m>*o$o "-"!(m"#*&% %&' )&#*($&$"' "#)o#*!&$&' &!& %& !(($"2 'o# m03 )"!)&#&'. Co# "'*o '" 0"$" )o#)%0(! :0" %o' !o)"$(m("#*o' '" !"&%(2&!o# $" m&#"!& )o!!")*&.
M .1 m L . # + ( .F " % 5 " D
. . .
1
1 <0"!2& &%()&$& N
CONCLUSIONES
Como '" 0"$" &!")(&! %& !(($"2 $"% !"'o!*" *("#" 0# )omo!*&m("#*o %(#"&% o! %o :0" '" 0"$" *om&! 0# 6&%o! m"$(o $" o7*"#($o "# %&' m"$()(o#"' :0"$&#$o "#*o#)"'= = /. 67
U*(%(2&#$o "% m>*o$o $" m;#(mo' )0&$!&$o' '" !"&%(2+ 0# !o!&m& "# m&*%&7 &!& o7*"#"! %& ")0&)(+# $" %& !")*& "#)o#*!&$&. Lo' !"'0%*&$o' o7*"#($o' 'o#= D"5o!m&)(+#,<0"!2& . D&*o' $(')!"*o' .1F- .1F
.1F .1 .1 M .1 m L . # + .1 ( " % 5 " D .F
. . .
1
1 <0"!2& &%()&$& N
P&!& "% )/%)0%o $" %&' )&!&)*"!;'*()&' m")/#()&' $" %o' !"'o!*"' 4"%()o($&%"' "' 0#& 70"#& &!o-(m&)(+# !"&%(2&! m>*o$o' !/)*()o' o *"+!()o'. P"!'o#&%m"#*" '" !")om("#$& 0*(%(2&! "% m>*o$o "-"!(m"#*&% 0"' %o' $&*o' o7*"#($o' '" 7&'&!/# "# %o :0" '" o7'"!6& "# %& !/)*()&. S(# "m7&!o &!& "% m>*o$o *"+!()o '" $"7"# )o#o)"! !o("$&$"' m/' "'");5()&' $"% m&*"!(&% )o# "% :0" "'*/ 4")4o "% !"'o!*" '( '" )o#o)" !"'0%*& '"! m0)4o m/' '"#)(%%o $" )&%)0%&! 3 '( #o "'*o 0"$" !"!"'"#*&! 0# !o7%"m&B &5o!*0#&$&m"#*" &!& %& !/)*()& '" '&7;& "% m&*"!(&% $"% !"'o!*" 3 '" 0$o !"&%(2&! "% )/%)0%o '(# #(#K# !o7%"m&.
ANE/O P!o!&m& 1., G!/5()& $" $&*' "-"!(m"#*&%"' 3 ")0&)(+# o! m;#(mo' )0&$!&$o'. clear all clc syms t Y=[1.4e-3, 3e-3, 5e-3, 8e-3,1.03e-2,1.53e-2]; X=[4.04172,7.37712,11.79162,16.79472,22.42566,37.63116]; N=6; S Syy Sy S Sy
= = = = =
0; 0; 0; 0; 0;
!"r #=1$6 Sy = S = Sy = S = Syy = e*+
Y%#&'X%#&(Sy; X%#&(S; Y%#&(Sy; X%#&)2(S; Y%#&)2(Syy;
m=%N'Sy-S'Sy&%N'S-S)2&; *=%S'Sy-S'Sy&%N'S-S)2&; y=m't(*; l"t%X,Y,/--"& r+ "* "l+ "* set%el"t%y,[0 40]&,"l"r,r&; as%[0 40 0 20e-3]&; yla/el%e!le*, [m]&; la/el%era alca+a, [N]&; ttle%e!"rmac*-era&; Sal+a=[*m2str%m&, ( ,*m2str%*&]; lee*+%at"s +scret"s,Sal+a&; "l+ "!!
