Menl

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15 years, 321 days

MaplePrimes Activity


These are answers submitted by Menl

Here the equations I try to solve. Hope this might solicit more response as you indicated.

PDEtools[declare]( (w,g)(x), prime=x );

var:={g(x),w(x)};

odew3:=diff(w(x),`$`(x,4))-(lambda/L)^2*diff(w(x),`$`(x,2)) = 1/B*(lambda/L)^2*(M(x)+beta*L^2*q);

odeg3:=diff(g(x),`$`(x,2))-(lambda/L)^2*g(x) = -1/B*(lambda)^2*Q(x);

sys:={odew3,odeg3,w(L)=0,w(0)=0,(D@@2)(w)(L)=0,(D@@2)(w)(0)=0,D(g)(0)=0,D(g)(0.99*L)=0};

R1:=dsolve(sys);

Without the boundary conditions it will produce a solution with 6 constants with exponentials. I know how I can express two constants into the others, which reduces the number of constants to solve to four. I need then only 4 boundary conditions and might get a more compact result.  To use this knowledge I would like to propose the solotion form with the constants. Is this possible.

Furthermore the last boundary condition cannot be D(g)(L)=0 as this will result in R1:= with nothing after this. Using a value extremely close to 1 is OK though. any ideas on this.

 

Doug,

Thank you very much. This is a much simpler function than the one I found. Sometimes it's easier to do the complex things right that it is to do the simpler things. ;)

I found a way to do it. This evaluates to true when the first result is fout and it results false when its u2.

if op(ddmax[1])[1]='fout'
 

But I still like to hear if there is an easier method.

M.

Thank you all for your solutions. I will try them both.

 

 

This is the function I talk about. The parameters plotted are u2 (x axis) and fout(y-axis).

 Ferr:=-10*(.7845815999*u2+3.141592654)*sinh(10*(.7845815999*u2+3.141592654)/((100+fout)^(1/2)*(.1998118316*u2+1)))*cos(10*(.7845815999*u2+3.141592654)/((100+fout)^(1/2)*(.1998118316*u2+1)))*u2/((100+fout)^(1/2)*(.1998118316*u2+1))+200*(.7845815999*u2+3.141592654)^2*sinh(10*(.7845815999*u2+3.141592654)/((100+fout)^(1/2)*(.1998118316*u2+1)))*sin(10*(.7845815999*u2+3.141592654)/((100+fout)^(1/2)*(.1998118316*u2+1)))/((100+fout)*(.1998118316*u2+1)^2)+10*(.7845815999*u2+3.141592654)*cosh(10*(.7845815999*u2+3.141592654)/((100+fout)^(1/2)*(.1998118316*u2+1)))*u2*sin(10*(.7845815999*u2+3.141592654)/((100+fout)^(1/2)*(.1998118316*u2+1)))/((100+fout)^(1/2)*(.1998118316*u2+1))

If you use the plot command:

implicitplot(Ferr,u2=0..50,fout=-1..1,numpoint=30000, gridlines=true);

you can visually see the min and max.

 

I've attached the expressions from both maple 9.5 and Maple 10. I've reinstalled 9.5 for this. Version 11 acts like Maple 10 b.t.w.

I've verified that both equations are the same only in a different form.

Regarding your solution using simplify I've used it in various ways simplify (%,trig) etc. If you have other ideas I would very much like to hear them as I would rather use the newer versions.

Maple 9.5

 

A1 = A4*(cosh(B*L)*v-cos(B*L)*v+2*B*L*sin(B*L))/((sinh(B*L)-sin(B*L))*v)

Maple10

A1 = A4*((exp(B*L))^2*v+v-2*cos(B*L)*exp(B*L)*v+4*sin(B*L)*exp(B*L)*B*L)/(v*((exp(B*L))^2-1-2*sin(B*L)*exp(B*L)))

 

 

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