md7007

15 Reputation

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13 years, 5 days
Sharif University of Technology

Ph.D Student

MaplePrimes Activity


These are replies submitted by md7007

Attach your maple code

@Joe Riel 

I recieved your email. i have some problem, i asked them in another email.

Thanks

@Joe Riel 

Dear

thanks a lot, but there is just a file by the name of NaturalFrequenc.msim and it is not available. when i click on it, nothing is available

404 - File or directory not found.

The resource you are looking for might have been removed, had its name changed, or is temporarily unavailable.

please send them again

if it is possible, please send them to my email: mohammadhojjati@yahoo.com

thanks for your kind attention

BR

@Joe Riel 

Dear, can you help me plz???

@Joe Riel 

Thanks for your attention

I have MapleSim 6.2

@Joe Riel 

I try to create a linearized model, but i faced a lot of problem, can you help me plz? i'm wondering if you have a tutorial or video or everything that explain how to create a linearized model.

BR

@Christopher2222 

I'm an expert on Vibration and Maple. I'm going to be an expert on mapleSim too, so i want to learn the necessary analysis in mapleSim,BR

@Joe Riel 

as the first step, i want to determine natural frequencies of the simplest cases. for example i attach one of them that is a spring and a mass and the analytical natural frequency is (k/m)^0.5. Please give me more explain about your solution with LinearAnalysis. Thanx

prob1.msim

@Carl Love 

That's ok and I'm sorry.

do you know where can i find MapleSIm experts?

Hi dear

Here is the text of the code

restart;
v[Theta0] := proc (r, theta) options operator, arrow; -U*(1+a^2/r^2)*sin(theta)-(1/2)*Omega/(Pi*r)-r*Omega end proc:
v[R0] := proc (r, theta) options operator, arrow; U*(1-a^2/r^2)*cos(theta) end proc:
a1 := -(-S*V[R(n)](r)*r*n+(2*I)*Omega*r*V[R(n)](r)+(2*I)*Omega*r^2*(diff(V[R(n)](r), r))-r*v[R0](r, theta)*(diff(V[R(n)](r), r))*n-r*V[R(n)](r)*(diff(v[R0](r, theta), r))*n-I*v[Theta0](r, theta)*V[R(n)](r)*n^2-I*(diff(v[R0](r, theta), theta))*V[R(n)](r)-I*(diff(v[R0](r, theta), theta))*r*(diff(V[R(n)](r), r))+(2*I)*v[Theta0](r, theta)*V[R(n)](r)+(2*I)*v[Theta0](r, theta)*r*(diff(V[R(n)](r), r)))/(n*r) = -I*(I*(diff(v[Theta0](r, theta), theta, r))*V[R(n)](r)+I*r^2*S*(diff(V[R(n)](r), r, r))+I*r^2*v[R0](r, theta)*(diff(V[R(n)](r), r, r, r))+V[R(n)](r)*(diff(v[Theta0](r, theta), r))*n+r*V[R(n)](r)*(diff(v[Theta0](r, theta), r, r))*n-v[Theta0](r, theta)*n*(diff(V[R(n)](r), r))-v[Theta0](r, theta)*n*r*(diff(V[R(n)](r), r, r))+I*r^2*(diff(v[R0](r, theta), r))*(diff(V[R(n)](r), r, r))+I*(diff(v[R0](r, theta), r))*V[R(n)](r)+2*Omega*V[R(n)](r)*n+2*Omega*r*(diff(V[R(n)](r), r))*n+(4*I)*v[R0](r, theta)*(diff(V[R(n)](r), r))+(3*I)*r*S*(diff(V[R(n)](r), r))+(3*I)*r*(diff(v[R0](r, theta), r))*(diff(V[R(n)](r), r))+I*S*V[R(n)](r)+(5*I)*r*v[R0](r, theta)*(diff(V[R(n)](r), r, r))+(2*I)*(diff(v[Theta0](r, theta), theta))*(diff(V[R(n)](r), r))+I*(diff(v[Theta0](r, theta), theta, r))*r*(diff(V[R(n)](r), r))+I*(diff(v[Theta0](r, theta), theta))*r*(diff(V[R(n)](r), r, r)))/n^2:
a2:=isolate(a1, V[R(n)](r)):
a3:=simplify(a2, 'size'):
dsolve(a3, {V[R(n)](r)});

 

and this the main code,you can download the .mw either in the end of the page

``

restart

v[Theta0] := proc (r, theta) options operator, arrow; -U*(1+a^2/r^2)*sin(theta)-(1/2)*Omega/(Pi*r)-r*Omega end proc

proc (r, theta) options operator, arrow; -U*(1+a^2/r^2)*sin(theta)-(1/2)*Omega/(Pi*r)-r*Omega end proc

(1)

v[R0] := proc (r, theta) options operator, arrow; U*(1-a^2/r^2)*cos(theta) end proc

proc (r, theta) options operator, arrow; U*(1-a^2/r^2)*cos(theta) end proc

(2)

a1 := -(-S*V[R(n)](r)*r*n+(2*I)*Omega*r*V[R(n)](r)+(2*I)*Omega*r^2*(diff(V[R(n)](r), r))-r*v[R0](r, theta)*(diff(V[R(n)](r), r))*n-r*V[R(n)](r)*(diff(v[R0](r, theta), r))*n-I*v[Theta0](r, theta)*V[R(n)](r)*n^2-I*(diff(v[R0](r, theta), theta))*V[R(n)](r)-I*(diff(v[R0](r, theta), theta))*r*(diff(V[R(n)](r), r))+(2*I)*v[Theta0](r, theta)*V[R(n)](r)+(2*I)*v[Theta0](r, theta)*r*(diff(V[R(n)](r), r)))/(n*r) = -I*(I*S*V[R(n)](r)+I*(diff(v[Theta0](r, theta), theta, r))*V[R(n)](r)+I*r^2*S*(diff(V[R(n)](r), r, r))+V[R(n)](r)*(diff(v[Theta0](r, theta), r))*n+r*V[R(n)](r)*(diff(v[Theta0](r, theta), r, r))*n-v[Theta0](r, theta)*n*(diff(V[R(n)](r), r))-v[Theta0](r, theta)*n*r*(diff(V[R(n)](r), r, r))+I*r^2*(diff(v[R0](r, theta), r))*(diff(V[R(n)](r), r, r))+I*(diff(v[Theta0](r, theta), theta))*r*(diff(V[R(n)](r), r, r))+2*Omega*V[R(n)](r)*n+2*Omega*r*(diff(V[R(n)](r), r))*n+(4*I)*v[R0](r, theta)*(diff(V[R(n)](r), r))+(3*I)*r*S*(diff(V[R(n)](r), r))+(3*I)*r*(diff(v[R0](r, theta), r))*(diff(V[R(n)](r), r))+I*r^2*v[R0](r, theta)*(diff(V[R(n)](r), r, r, r))+(5*I)*r*v[R0](r, theta)*(diff(V[R(n)](r), r, r))+(2*I)*(diff(v[Theta0](r, theta), theta))*(diff(V[R(n)](r), r))+I*(diff(v[Theta0](r, theta), theta, r))*r*(diff(V[R(n)](r), r))+I*(diff(v[R0](r, theta), r))*V[R(n)](r))/n^2

-(-S*V[R(n)](r)*r*n+(2*I)*Omega*r*V[R(n)](r)+(2*I)*Omega*r^2*(diff(V[R(n)](r), r))-r*U*(1-a^2/r^2)*cos(theta)*(diff(V[R(n)](r), r))*n-2*V[R(n)](r)*U*a^2*cos(theta)*n/r^2-I*(-U*(1+a^2/r^2)*sin(theta)-(1/2)*Omega/(Pi*r)-Omega*r)*V[R(n)](r)*n^2+I*U*(1-a^2/r^2)*sin(theta)*V[R(n)](r)+I*U*(1-a^2/r^2)*sin(theta)*r*(diff(V[R(n)](r), r))+(2*I)*(-U*(1+a^2/r^2)*sin(theta)-(1/2)*Omega/(Pi*r)-Omega*r)*V[R(n)](r)+(2*I)*(-U*(1+a^2/r^2)*sin(theta)-(1/2)*Omega/(Pi*r)-Omega*r)*r*(diff(V[R(n)](r), r)))/(n*r) = -I*(I*r^2*U*(1-a^2/r^2)*cos(theta)*(diff(diff(diff(V[R(n)](r), r), r), r))-I*U*(1+a^2/r^2)*cos(theta)*r*(diff(diff(V[R(n)](r), r), r))+(4*I)*U*(1-a^2/r^2)*cos(theta)*(diff(V[R(n)](r), r))+V[R(n)](r)*(2*U*a^2*sin(theta)/r^3+(1/2)*Omega/(Pi*r^2)-Omega)*n+r*V[R(n)](r)*(-6*U*a^2*sin(theta)/r^4-Omega/(Pi*r^3))*n-(-U*(1+a^2/r^2)*sin(theta)-(1/2)*Omega/(Pi*r)-Omega*r)*n*(diff(V[R(n)](r), r))-(-U*(1+a^2/r^2)*sin(theta)-(1/2)*Omega/(Pi*r)-Omega*r)*n*r*(diff(diff(V[R(n)](r), r), r))-(2*I)*U*(1+a^2/r^2)*cos(theta)*(diff(V[R(n)](r), r))+(4*I)*U*a^2*cos(theta)*V[R(n)](r)/r^3+2*Omega*V[R(n)](r)*n+2*Omega*r*(diff(V[R(n)](r), r))*n+I*S*V[R(n)](r)+(8*I)*U*a^2*cos(theta)*(diff(V[R(n)](r), r))/r^2+I*r^2*S*(diff(diff(V[R(n)](r), r), r))+(5*I)*r*U*(1-a^2/r^2)*cos(theta)*(diff(diff(V[R(n)](r), r), r))+(3*I)*r*S*(diff(V[R(n)](r), r))+(2*I)*U*a^2*cos(theta)*(diff(diff(V[R(n)](r), r), r))/r)/n^2

(3)

a2 := isolate(a1, V[R(n)](r))

(8*I)*n*U*sin(theta)*r*(diff(V[R(n)](r), r))*Pi*a^2+(2*I)*n*r^2*(diff(diff(V[R(n)](r), r), r))*U*sin(theta)*Pi*a^2-2*r^5*S*(diff(diff(V[R(n)](r), r), r))*Pi-6*r^4*S*(diff(V[R(n)](r), r))*Pi-2*S*V[R(n)](r)*r^3*Pi-2*r*U*cos(theta)*(diff(V[R(n)](r), r))*n^2*Pi*a^2+(4*I)*n*U*sin(theta)*r^3*(diff(V[R(n)](r), r))*Pi+(2*I)*n*r^4*(diff(diff(V[R(n)](r), r), r))*U*sin(theta)*Pi-(2*I)*V[R(n)](r)*n^3*U*sin(theta)*Pi*r^2-(2*I)*V[R(n)](r)*n^3*U*sin(theta)*Pi*a^2+(2*I)*n*U*sin(theta)*V[R(n)](r)*Pi*r^2-(2*I)*n*U*sin(theta)*V[R(n)](r)*Pi*a^2-4*U*cos(theta)*(diff(V[R(n)](r), r))*r^3*Pi-8*r^4*U*cos(theta)*(diff(diff(V[R(n)](r), r), r))*Pi-2*r^5*U*cos(theta)*(diff(diff(diff(V[R(n)](r), r), r), r))*Pi+I*n*r^3*(diff(diff(V[R(n)](r), r), r))*Omega+(3*I)*n*Omega*r^2*(diff(V[R(n)](r), r))+2*S*V[R(n)](r)*r^3*n^2*Pi+I*n*Omega*r*V[R(n)](r)-8*U*a^2*cos(theta)*V[R(n)](r)*Pi-I*V[R(n)](r)*n^3*Omega*r+2*r^3*U*cos(theta)*(diff(V[R(n)](r), r))*n^2*Pi-4*U*a^2*cos(theta)*(diff(V[R(n)](r), r))*r*Pi+8*U*a^2*cos(theta)*(diff(diff(V[R(n)](r), r), r))*r^2*Pi+2*r^3*U*cos(theta)*(diff(diff(diff(V[R(n)](r), r), r), r))*Pi*a^2+(6*I)*Omega*r^4*(diff(V[R(n)](r), r))*n*Pi+(2*I)*n*r^5*(diff(diff(V[R(n)](r), r), r))*Omega*Pi+4*V[R(n)](r)*U*a^2*cos(theta)*n^2*Pi-(2*I)*V[R(n)](r)*n^3*Omega*r^3*Pi+(2*I)*Omega*V[R(n)](r)*n*r^3*Pi = 0

(4)

a3 := simplify(a2, 'size')

2*U*r^3*Pi*cos(theta)*(a-r)*(a+r)*(diff(diff(diff(V[R(n)](r), r), r), r))+2*(4*U*Pi*(a-r)*(a+r)*cos(theta)+I*n*(r^2+a^2)*U*Pi*sin(theta)+r*((I*n*Omega-S)*r^2*Pi+((1/2)*I)*n*Omega))*r^2*(diff(diff(V[R(n)](r), r), r))+8*r*(-(1/4)*((2-n^2)*r^2+a^2*(n^2+2))*U*Pi*cos(theta)+I*n*((1/2)*r^2+a^2)*U*Pi*sin(theta)+(3/4)*r*((I*n*Omega-S)*r^2*Pi+((1/2)*I)*n*Omega))*(diff(V[R(n)](r), r))-2*V[R(n)](r)*(-2*U*a^2*Pi*(-2+n^2)*cos(theta)+I*n*((-1+n^2)*r^2+a^2*(n^2+1))*U*Pi*sin(theta)+(n+1)*(-1+n)*r*((I*n*Omega-S)*r^2*Pi+((1/2)*I)*n*Omega)) = 0

(5)

dsolve(a3, {V[R(n)](r)})

Error, (in gcd/NoExpandDegreeCheck) inputs must be polynomials over all variables

 

``

``


thanks alot

Download ode.mw

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