Re: nontrivial solution of Euler-beam problem?
- To: mathgroup at smc.vnet.net
- Subject: [mg84661] Re: nontrivial solution of Euler-beam problem?
- From: bar at ANTYSPAM.ap.krakow.pl
- Date: Tue, 8 Jan 2008 03:38:18 -0500 (EST)
- References: <flslfs$poc$1@smc.vnet.net> <flv63i$2eo$1@smc.vnet.net>
Jens-Peer Kuska <kuska at informatik.uni-leipzig.de> wrote:
> Hi,
> you try to solve an eigenvalue problem. An eigenvalue
> problem has only the trivial solution or an infinite number
> of solution but never a unique of a finite number of
> solutions that DSolve[] can find.
> Regards
> Jens
> bar at ANTYSPAM.ap.krakow.pl wrote:
> > Hello,
> >
> > When I try solve Euler beam ( without time, with nondimensional coordinate)
> > ---
> > euler = F''''[x] + Pi^4 om2 F[x];
> > sol = DSolve[{euler == 0, F[0] == 0, F[1] == 0, F''[0] == 0, F''[1] == 0.0},
> > F[x], x];
> > ---
> > Mathematica calculated only trivial (F=0) solution, for any om2
> >
Yes , I know,
Have I need to reduced equation to four first-order equations and
applied eigenvalue method manually ?
Can Mathematica. help me ?
PS.
I tried to solve full partial Euler-beam equations and
Mathematica. sometimes can's solve this:
----------
Clear["`*"];
tmax = .3;
n = 2;
soln = NDSolve[{Pi^4 D[u[x, t], t, t] == -D[u[x, t], x, x, x, x],
u[x, 0] == Sin[n* Pi*x], Derivative[0, 1][u][x, 0] == 0, u[0, t] == 0,
u[1, t] == 0, Derivative[2, 0][u][0, t] == 0,
Derivative[2, 0][u][1, t] == 0}, u, {x, 0, 1}, {t, 0, tmax}
, WorkingPrecision -> 16, PrecisionGoal -> 8]
Plot3D[Evaluate[u[x, t] /. First[soln]], {x, 0, 1}, {t, 0, tmax},
PlotPoints -> 30]
ContourPlot[Evaluate[u[x, t] /. First[soln]], {x, 0, 1}, {t, 0, tmax},
PlotPoints -> 30, Contours -> 30, ContourLines -> False,
ColorFunction -> Hue, PlotRange -> All]
---------------
It's look like very simple problem , but in this case
for time t=0.3 caculate never ended.
After some test with different WorkingPrecision and PrecisionGoal
sometimes I obtained solution, sometimes not
A can't use repeated way to obtain solution for different n (modes) ?