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Question: problem with subs rule

Question:problem with subs rule

9009134 110 Maple 2017
subs
July 28 2017
1

subs.mw

hi...i have a problem with subs rule

please help me.

thanks

> 

eq81a:=m*diff(w(x,t),t$2)+c*diff(w(x,t),t)+E*Is*diff(w(x,t),x$4)+(P-f[p]*cos(Omega*t)-E*A/(2*l)*int(diff(w(x,t),x)^2,x=0..l))*diff(w(x,t),x$2)=0;

m*(diff(diff(w(x, t), t), t))+c*(diff(w(x, t), t))+E*Is*(diff(diff(diff(diff(w(x, t), x), x), x), x))+(P-f[p]*cos(Omega*t)-(1/2)*E*A*(int((diff(w(x, t), x))^2, x = 0 .. l))/l)*(diff(diff(w(x, t), x), x)) = 0

 (1)

 

> 

bc81a:=B[1](w(0,t))=0,B[2](w(0,t))=0,B[3](w(l,t))=0,B[4](w(l,t))=0;

B[1](w(0, t)) = 0, B[2](w(0, t)) = 0, B[3](w(l, t)) = 0, B[4](w(l, t)) = 0

 (2)

 

 

> 

nondimRule1:=w(x,t)=l*w[n](x/l,t/T);

w(x, t) = l*w[n](x/l, t/T)

 (3)
> 

nondimRule2:=x=l*x[n],t=T*t[n],Omega=Omega[n]/T,P=P[n]*E*Is/l^2,f[p]=f[n]*E*Is/l^2,c=c[n]*sqrt(E*Is*m)/l^2,A=2*alpha*Is/l^2;

x = l*x[n], t = T*t[n], Omega = Omega[n]/T, P = P[n]*E*Is/l^2, f[p] = f[n]*E*Is/l^2, c = c[n]*(E*Is*m)^(1/2)/l^2, A = 2*alpha*Is/l^2

 (4)
> 

intRule1:=Int(D[1](w[n])(x[n],t[n])^2,l*x[n]=0..l)=l*int(D[1](w[n])(x[n],t[n])^2,x[n]=0..1);

Int((D[1](w[n]))(x[n], t[n])^2, l*x[n] = 0 .. l) = l*(int((D[1](w[n]))(x[n], t[n])^2, x[n] = 0 .. 1))

 (5)
> 

dropnRule:=w[n]=w,x[n]=x,t[n]=t,c[n]=c,P[n]=P,f[n]=f,Omega[n]=Omega;

w[n] = w, x[n] = x, t[n] = t, c[n] = c, P[n] = P, f[n] = f, Omega[n] = Omega

 (6)

 

> 

eq81b:=convert(expand(l^3/(E*Is)*subs(int=Int,nondimRule2,intRule1,dropnRule,value(subs(nondimRule1,eq81a)))),diff);

Error, invalid input: diff received T*t, which is not valid for its 2nd argument

  

 

> 

``
> 

TRule;=solve(coeff(lhs(eq81b),diff(w(x,t),t$2))=1,{T})[1];

TRule

  

Error, `=` unexpected

  

``


 

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