thank you for your help, actually that is an old paperback in my university library , it doesn't have much explanations, it's a domestic paper...
now that i see your table, your results are the same as mine in maple when p,q≥1/8
exactly the same except that my c is up to max 1.675 to reach b<1...
thanks Mr Simpson for your help , but i get different results for solution of the system with Maple:
Even if i give positive range to p & q before solving , this way:
S := fsolve({F1 = 0, F2 = 0}, {p = 0 .. 10, q = 0 .. 10})
and supposing c=1/2 , i get {p = 7.991211001, q = 0.}
and also with...
thanks Mr Vickson ,
yes i saw those plots , it seems that this system has a lot solutions , [ i made a simple mistake in F1 , instead of (p^2 - q^2) we must have (q^2 - p^2) in first term , although this doesn't affect the whole problem and plots ]
so the correct F1 & F2 are:
$$...
^ I'm now considering only maple , what i want to know is a suitable range for fsolve and just for 1 value of c , say c=1 for example ,
in maple for a specific value of c :
> S := fsolve({F1 = 0, F2 = 0}, {p = 0 .. 20, q = 0 .. 20}); {p = 15.03019936, q = 0.}and if :
> S :=...
thanks but i am seeking for p,q , how can i plot them when don't have them in hand ?! i want to know a possible range for solution of p & q and then apply the range to fsolve command ...
no problem Mr Vickson; there is a contradiction here ! when i change the range of p and q i get different results :
for example ,if i set :
> S := fsolve({F1 = 0, F2 = 0}, {p = 0 .. 20, q = 0 .. 20}); {p = 15.03019936, q = 0.}and if :
> S := fsolve({F1 = 0, F2 = 0}, {p = 0 ...
what i have is F1=0 & F2=0 , i give some values to c in range of [0,2.5] and fsolve in maple is ok ,this way as you said :
fsolve({F1=0,F2=0},{p,q})
but as I'm not too much familiar to maple , i need the similar case for MATLAB to be able to write my code easier (matlab is easier for me...
thank you very much Ray , very helpful Notes , i used fsolve and it is ok now ,giving me good values for p&q ,you did a great job , it would be very nice to help me with MATLAB too in my next comment
Homework Statement
i'm trying to find a solution for these two equations, p & q are variables and c is known constant (it's given randomly) :
$$
\begin{align}...
Eigenvalue problem after galerkin
Homework Statement
i am working on vibration of cylindrical shell analysis, after solving the equations of motion by galerkin method , i reach to an eigenvalue problem this way :
{ p^2*C1+p*C2+C3 } * X=0
C1,C2,C3 are all square matrices of order n*n...
@aralbrec
thank you for your help, i get what you're saying , but please look at this red line I've drawn in this picture:
http://i45.fastpic.ru/big/2012/1027/2f/678839cd8c87271c8453274f1a30b72f.jpg
it is showing that there must be 4 different lambda for the solution and not repeated lambda's (...
thanks...this is some likely answer , but here in this article we need 4 different lambda's .
besides, as u see the four independent solutions are different from those u mentioned...that is exponential in the series form and 4 lambda's are included...
thanks for reply but i forgot to explain more, here it is:
we have 3 linear partial differential equations:
http://i45.fastpic.ru/big/2012/1027/8f/429c9d2a3bd454656212ed589156f38f.jpg
now for homogeneous solution we're going to substitute below Equation into Eqs. (11) and (12) at the above...