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Re: nontrivial solution of Euler-beam problem?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg84657] Re: nontrivial solution of Euler-beam problem?
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Tue, 8 Jan 2008 01:35:00 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <flslfs$poc$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

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
> 
> Is it possible to obtain different modes 
> looks like 
> F_n[x]=A_n Sin[n Pi x] ?
> 
> This function simply satisfy euler==0 equation with above
> boundary conditions for om2=n^4
> 
> Regards, Olaf
> 
> 
> 


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