questão 1
DESCRIPTION
exemplo de aplicação do MAPLE em problema dinâmico.TRANSCRIPT
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Anexo I - Questo 01Rodrigo Nascimento Barros - 1412828
Comandos de Entrada> with(plots):restart: with(LinearAlgebra):
Termos da Srie de Fourier> a0:=simplify(1/Te*int(P0*sin(2*Pi*t/Te),t=0..Te/2));
:= a0 P0> for n from 1 by 1 to 10 do
a[n]:=simplify(2/Te*int(P0*sin(2*Pi*t/Te)*cos(2*n*Pi*t/Te),t=0..Te/2)); b[n]:=simplify(2/Te*int(P0*sin(2*Pi*t/Te)*sin(2*n*Pi*t/Te),t=0..Te/2)); p[n]:=a[n]*cos(2*n*Pi*t/Te)+b[n]*sin(2*n*t*Pi/Te); end do;
:= a1 0
:= b1P02
:= p112 P0
sin
2 tTe
:= a2 2 P03
:= b2 0
:= p2 23P0
cos
4 tTe
:= a3 0 := b3 0 := p3 0
:= a4 2 P015
:= b4 0
:= p4 215
P0
cos
8 tTe
:= a5 0
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:= b5 0 := p5 0
:= a6 2 P035
:= b6 0
:= p6 235
P0
cos
12 tTe
:= a7 0 := b7 0 := p7 0
:= a8 2 P063
:= b8 0
:= p8 263
P0
cos
16 tTe
:= a9 0 := b9 0 := p9 0
:= a10 2 P099
:= b10 0
:= p10 299
P0
cos
20 tTe
Representao da Fora> Xest:=P0/K;
:= Xest P0K
> P:=a0+add(p[n],n=1..10):> P_normalizada:=P/Xest:
Representao do Deslocamento> for n from 1 by 1 to 10 do
beta[n]:=1/(1-(n*Te/Tp)); xp[n]:=(1/K)*((1/(1-(beta[n]*beta[n])))*(a[n]*cos(2*n*Pi*t/Tp)+b[n]*sin(2*n*Pi*t/Tp)));
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end do:> Xp:=1/K*(a0+odd(xp[n],n=1..10)):> > xp_normalizado:=Xp/Xest:
Dados do problema> Te:=0.2: #Perodo da Fora
K:=400: # Rigidez do sistema M:=25: #Massa do sistema omega0:=evalf(sqrt(K/M)): # Frequncia Natural P0:=20: #Fora Inicial Tp:=evalf(2*Pi/omega0): #Perodo da Estrutura
Espectro da fora> Pmatrix:=Vector(201,2):> count:=0:> for i from 0 by 0.005 to 1 do
count:=count+1: Pmatrix(count,1):=i: Pmatrix(count,2):=evalf(subs(t=i,P_normalizada)); end do:
> Pmatrix:> plot(Pmatrix,color=blue,title=`Espectro da Fora`,labels =
["tempo", "Fora"],titlefont = ["HELVETICA", 20],labelfont = ["HELVETICA", 12],thickness=5);
>
Espectro do deslocamento normalizado> Xmatrix:=Vector(201,2):> count:=0:> for i from 0 by 0.05 to 10 do
count:=count+1: Xmatrix(count,1):=i:
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Xmatrix(count,2):=evalf(subs(t=i,xp_normalizado)); end do:
> plot(Xmatrix,color=red,title=`Espectro do Deslocamento`,labels = ["tempo", "deslocamento"],titlefont = ["HELVETICA", 20],labelfont = ["HELVETICA", 12],thickness=4);
Variao da Resposta> Rmatrix:=Vector(201,2):> count:=0:> for i from 0 by 0.05 to 10 do
count:=count+1: Rmatrix(count,1):=i: Rmatrix(count,2):=evalf(subs(t=i,K*xp_normalizado)); end do:
> for t from 0 by 0.05 to 10 do Rmax:=evalf(K*xp_normalizado) end do:
> Maximum( Rmax );( )Maximum 126.0916804
> plot(Rmatrix,color=green,title=`Espectro da Reao de Apoio`,labels = ["tempo", "Reao"],titlefont = ["HELVETICA", 20],labelfont = ["HELVETICA", 12],thickness=4);