Nicolo

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11 years, 242 days

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star4fifth.mw

E(x) := 1+beta[1] x+beta[2] x^2+beta[3] x^3+beta[4] x^4:

W(x) := 26 x^2-14 x^3+x^4+x^5:

T(x) := -1/(2)*x^(2) - R*x + R + 1/(2):

E(x)*(diff(W(x), x, x, x, x))+2*(diff(E(x), x))*(diff(W(x), x, x, x))+(diff(E(x), x, x))*(diff(W(x), x, x))-L^4*m[0]*Omega^2*T(x)*(diff(W(x), x, x))/EI[0]-F*L^2*(diff(W(x), x, x))/EI[0]-L^4*m[0]*Omega^2*(diff(T(x), x))*(diff(W(x), x))/EI[0]-L^4*m[0]*omega^2*W(x)/EI[0]

(1+beta[1]*x+beta[2]*x^2+beta[3]*x^3+beta[4]*x^4)*(24+120*x)+2*(beta[1]+2*beta[2]*x+3*beta[3]*x^2+4*beta[4]*x^3)*(-84+24*x+60*x^2)+(2*beta[2]+6*beta[3]*x+12*beta[4]*x^2)*(52-84*x+12*x^2+20*x^3)-L^4*m[0]*Omega^2*(-(1/2)*x^2-R*x+R+1/2)*(52-84*x+12*x^2+20*x^3)/EI[0]-F*L^2*(52-84*x+12*x^2+20*x^3)/EI[0]-L^4*m[0]*Omega^2*(-x-R)*(52*x-42*x^2+4*x^3+5*x^4)/EI[0]-L^4*m[0]*omega^2*(26*x^2-14*x^3+x^4+x^5)/EI[0]

(1)

(->)

series(24-52*L^4*m[0]*Omega^2*(R+1/2)/EI[0]-168*beta[1]-52*F*L^2/EI[0]+104*beta[2]+(120+72*beta[1]+104*L^4*m[0]*Omega^2*R/EI[0]-504*beta[2]+312*beta[3]+84*L^4*m[0]*Omega^2*(R+1/2)/EI[0]+84*F*L^2/EI[0])*x+(240*beta[1]+144*beta[2]-1008*beta[3]+624*beta[4]-12*L^4*m[0]*Omega^2*(R+1/2)/EI[0]-126*L^4*m[0]*Omega^2*R/EI[0]+78*L^4*m[0]*Omega^2/EI[0]-12*F*L^2/EI[0]-26*L^4*m[0]*omega^2/EI[0])*x^2+(16*L^4*m[0]*Omega^2*R/EI[0]-84*L^4*m[0]*Omega^2/EI[0]+14*L^4*m[0]*omega^2/EI[0]+400*beta[2]+240*beta[3]-1680*beta[4]-20*F*L^2/EI[0]-20*L^4*m[0]*Omega^2*(R+1/2)/EI[0])*x^3+(600*beta[3]+360*beta[4]+25*L^4*m[0]*Omega^2*R/EI[0]+10*L^4*m[0]*Omega^2/EI[0]-L^4*m[0]*omega^2/EI[0])*x^4+(840*beta[4]+15*L^4*m[0]*Omega^2/EI[0]-L^4*m[0]*omega^2/EI[0])*x^5,x)

(2)

``

solve({24-52*L^4*m[0]*Omega^2*(R+1/2)/EI[0]-168*beta[1]-52*F*L^2/EI[0]+104*beta[2], 600*beta[3]+360*beta[4]+25*L^4*m[0]*Omega^2*R/EI[0]+10*L^4*m[0]*Omega^2/EI[0]-L^4*m[0]*omega^2/EI[0], 120+72*beta[1]+104*L^4*m[0]*Omega^2*R/EI[0]-504*beta[2]+312*beta[3]+84*L^4*m[0]*Omega^2*(R+1/2)/EI[0]+84*F*L^2/EI[0], 16*L^4*m[0]*Omega^2*R/EI[0]-84*L^4*m[0]*Omega^2/EI[0]+14*L^4*m[0]*omega^2/EI[0]+400*beta[2]+240*beta[3]-1680*beta[4]-20*F*L^2/EI[0]-20*L^4*m[0]*Omega^2*(R+1/2)/EI[0], 240*beta[1]+144*beta[2]-1008*beta[3]+624*beta[4]-12*L^4*m[0]*Omega^2*(R+1/2)/EI[0]-126*L^4*m[0]*Omega^2*R/EI[0]+78*L^4*m[0]*Omega^2/EI[0]-12*F*L^2/EI[0]-26*L^4*m[0]*omega^2/EI[0]}, {beta[1], beta[2], beta[3], beta[4], omega^2})



``

``

``


Download star4fifth.mw 

Is it this what I am supossed to do?

I am very sorry since I am new in asking questions. and OMEGA^2 is to be assumed as a known. lowercase omega is the one that i want solve for. In the uploaded sheet you will find the variables I want to solve for. Also something I tried to do that did not work. I need to solve for the 5 unknowns but they have to satisfy every equation. Yes the x^0 term which would be the first also has to be zero

 

 

24-52*L^4*m[0]*Omega^2*(R+1/2)/EI[0]-168*beta[1]-52*F*L^2/EI[0]+104*beta[2]+(120+72*beta[1]+104*L^4*m[0]*Omega^2*R/EI[0]-504*beta[2]+312*beta[3]+84*L^4*m[0]*Omega^2*(R+1/2)/EI[0]+84*F*L^2/EI[0])*x+(240*beta[1]+144*beta[2]-1008*beta[3]+624*beta[4]-12*L^4*m[0]*Omega^2*(R+1/2)/EI[0]-126*L^4*m[0]*Omega^2*R/EI[0]+78*L^4*m[0]*Omega^2/EI[0]-12*F*L^2/EI[0]-26*L^4*m[0]*omega^2/EI[0])*x^2+(16*L^4*m[0]*Omega^2*R/EI[0]-84*L^4*m[0]*Omega^2/EI[0]+14*L^4*m[0]*omega^2/EI[0]+400*beta[2]+240*beta[3]-1680*beta[4]-20*F*L^2/EI[0]-20*L^4*m[0]*Omega^2*(R+1/2)/EI[0])*x^3+(600*beta[3]+360*beta[4]+25*L^4*m[0]*Omega^2*R/EI[0]+10*L^4*m[0]*Omega^2/EI[0]-L^4*m[0]*omega^2/EI[0])*x^4+(840*beta[4]+15*L^4*m[0]*Omega^2/EI[0]-L^4*m[0]*omega^2/EI[0])*x^5

I am sorry the zero.ta[2] is just a typo. what i tried to write was:

every coefficient in front of a x^n has to be zero for example {a1+a2}*x^3 whats inside the{} is treated as an equation and its used to solve for the desired unknowns. Now everything is treated as a known except:

beta[1], beta[2], beta[3], beta[4] and omega^2. since i have x^(n+5) i have 6 equations but only 5 unknowns.

{..}x^0,{..}x^1,{..}x^2......{..}x^5. Taking whatever is inside the {} as individual equations setting them to zero and using the 6 of them to solve for the 5 previously stated unknowns is what I am trying to achieve. 

I tried using the solve({},{}) function but I had no succes with this approach.

I hope now you can understand my question better,

and Thanks for your help!

I am sorry the zero.ta[2] is just a typo. what i tried to write was:

every coefficient in front of a x^n has to be zero for example {a1+a2}*x^3 whats inside the{} is treated as an equation and its used to solve for the desired unknowns. Now everything is treated as a known except:

beta[1], beta[2], beta[3], beta[4] and omega^2. since i have x^(n+5) i have 6 equations but only 5 unknowns.

{..}x^0,{..}x^1,{..}x^2......{..}x^5. Taking whatever is inside the {} as individual equations setting them to zero and using the 6 of them to solve for the 5 previously stated unknowns is what I am trying to achieve. 

I tried using the solve({},{}) function but I had no succes with this approach.

I hope now you can understand my question better,

and Thanks for your help!

> solve([w(0), w(1), (D(D(w)))(0), (D(D(w)))(1)]);
{a[0] = 0, a[1] = a[4], a[2] = 0, a[3] = -2 a[4], a[4] = a[4]}
> solve([w(1), (D(D(w)))(1)]);
{a[0] = -a[1] + 2 a[3] + 5 a[4], a[1] = a[1],

a[2] = -3 a[3] - 6 a[4], a[3] = a[3], a[4] = a[4]}
This is what i got. My question is how can I make maple remember that a[0] = 0 and a[2] = 0. so i can keep       solving my equation to get an answer in terms of w(x) and x with the constants being replaced. 
> solve([w(0), w(1), (D(D(w)))(0), (D(D(w)))(1)]);
{a[0] = 0, a[1] = a[4], a[2] = 0, a[3] = -2 a[4], a[4] = a[4]}
> solve([w(1), (D(D(w)))(1)]);
{a[0] = -a[1] + 2 a[3] + 5 a[4], a[1] = a[1],

a[2] = -3 a[3] - 6 a[4], a[3] = a[3], a[4] = a[4]}
This is what i got. My question is how can I make maple remember that a[0] = 0 and a[2] = 0. so i can keep       solving my equation to get an answer in terms of w(x) and x with the constants being replaced. 
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