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nonlinear system problem (DSolve syntax)

diana giarola

Posted 10 years ago

I need to resolve this system of equation v1[x_]''''=q/B v2[x_]''''+t2^2v2[x_]''=0 v3[x_]''''+t3^2v3[x_]''=0 then: v1[x_] := A1 + B1x + C1x^2 + D1x^3 + qx^4/(24B) v2[x_] := A2 + B2x + C2Cos[t2x] + D2Sin[t2x] v3[x_] := A3 + B3x + C3Cos[t3x] + D3Sin[t3*x] with B>0 and p2 and p3 are in function of q t2 = Sqrt[p2/B] t3 = Sqrt[p3/B] I have 14 boundary condition eq1 := v1[0] == 0 eq2 := v1''[0] == 0 eq3 := v3[0] == 0 eq4 := v3''[0] == 0 eq5 := v2'[l/2] == 0 eq6 := - v2'''[l/2] - t2^2 v2'[l/2] == 0 eq7 := v1'[l/2] - v3'[l] == 0 eq8 := v2'[0] - v3'[l] == 0 eq9 := - v1''[l/2] + v2''[0] - v3''[l] == 0 eq10 := v1[l/2] == 0 eq11 := v2[0] == 0 eq12 := v3[l] == 0 eq13 := -t2^2 - (- v3'''[l] - t3^2 v3'[l]) == 0 eq14 := -v1'''[l/2] - (-v2'''[0] - t2^2 v2'[0]) + t3^2 == 0 for the 14 unknowns constant (A1,B1,C1,D1,A2,B2,C2,D2,A3,B3,C3,D3,p2,p3). I need to resolve the nonlinear system, find p2 and p3, put them into the system to find q by doing the determinant of the matrix of coefficient=0. my problem is that i don't know how to resolve the nonlinear system

I need to resolve this system of equation

v1[x_]''''=q/B
v2[x_]''''+t2^2*v2[x_]''=0
v3[x_]''''+t3^2*v3[x_]''=0

then:

 v1[x_] := A1 + B1*x + C1*x^2 + D1*x^3 + q*x^4/(24*B)
 v2[x_] := A2 + B2*x + C2*Cos[t2*x] + D2*Sin[t2*x] 
 v3[x_] := A3 + B3*x + C3*Cos[t3*x] + D3*Sin[t3*x]

with B>0 and p2 and p3 are in function of q

t2 = Sqrt[p2/B]
t3 = Sqrt[p3/B]

I have 14 boundary condition

eq1 := v1[0] == 0
eq2 := v1''[0] == 0
eq3 := v3[0] == 0
eq4 := v3''[0] == 0
eq5 := v2'[l/2] == 0
eq6 := - v2'''[l/2] - t2^2 v2'[l/2] == 0
eq7 := v1'[l/2] - v3'[l] == 0
eq8 := v2'[0] - v3'[l] == 0
eq9 := - v1''[l/2] + v2''[0] - v3''[l] == 0
eq10 := v1[l/2] == 0
eq11 := v2[0] == 0
eq12 := v3[l] == 0
eq13 := -t2^2 - (- v3'''[l] - t3^2 v3'[l]) == 0
eq14 := -v1'''[l/2] - (-v2'''[0] - t2^2 v2'[0]) + t3^2 == 0

for the 14 unknowns constant (A1,B1,C1,D1,A2,B2,C2,D2,A3,B3,C3,D3,p2,p3). I need to resolve the nonlinear system, find p2 and p3, put them into the system to find q by doing the determinant of the matrix of coefficient=0.

my problem is that i don't know how to resolve the nonlinear system

POSTED BY: diana giarola

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diana giarola

Posted 10 years ago

oh yes, sorry, I'm wrong, today I've worked on and I found this nonlinear system > sys:={D2 t2 Cos[(l t2)/2] == C2 t2 Sin[(l t2)/2], B1 + (3 D1 l^2)/4 + (l^3 q)/(48 B) == B3 + D3 t3 Cos[l t3], D2 t2 == B3 + D3 t3 Cos[l t3], t3^2 D3 Sin[l t3] == 3 D1 l + (l^2 q)/(8 B) + C2 t2^2, 48 l (4 B1 + l (D1 l)) + (l^4 q)/B == 0, A2 + C2 == 0, B3 l + D3 Sin[l t3] == 0, t2^2 == B3 t3^2, 12 D1 + (l q)/B == 2 t3^2} I tried to do Solve[sys,{B1, D1, A2, C2, D2, B3, D3, t2, t3}] DSolve[sys,{B1, D1, A2, C2, D2, B3, D3, t2, t3}] but it doesn't work....how can I solve it?

oh yes, sorry, I'm wrong, today I've worked on and I found this nonlinear system

> sys:={D2 t2 Cos[(l t2)/2] == C2 t2 Sin[(l t2)/2], 
         B1 + (3 D1 l^2)/4 + (l^3 q)/(48 B) == B3 + D3 t3 Cos[l t3], 
         D2 t2 == B3 + D3 t3 Cos[l t3], 
         t3^2 D3 Sin[l t3] == 3 D1 l + (l^2 q)/(8 B) + C2 t2^2, 
         48 l (4 B1 + l (D1 l)) + (l^4 q)/B == 0, 
         A2 + C2 == 0, 
         B3 l + D3 Sin[l t3] == 0, 
         t2^2 == B3 t3^2, 
         12 D1 + (l q)/B == 2 t3^2}

I tried to do

 Solve[sys,{B1, D1, A2, C2, D2, B3, D3, t2, t3}]
    DSolve[sys,{B1, D1, A2, C2, D2, B3, D3, t2, t3}]

but it doesn't work....how can I solve it?

POSTED BY: diana giarola

David Keith

Posted 10 years ago

Sorry Diana-- I didn't recognize the syntax. If these are differential equations the Mathematica syntax is v1''''[x] == q/B v2''''[x] + t2^2v2''[x] == 0 v3''''[x] + t3^2v3[x] == 0 Note the double equal for equality rather than assignment.. You might have a look at this: How to work with differential equations Kind regards, David

POSTED BY: David Keith

diana giarola

Posted 10 years ago

I have to resolve a frame composed by 3 beams. these 3 differential equations are the elastic lines of the 3 beams. v2 and v3 are the elastic lines using a second order analysis. I need to find the critical load q.

POSTED BY: diana giarola

David Keith

Posted 10 years ago

What does this mean? v1[x_]''''=q/B v2[x_]''''+t2^2v2[x_]''=0 v3[x_]''''+t3^2v3[x_]''=0

POSTED BY: David Keith

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