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Particular Solution of 4th degree differential equation (column buckling)

Luis Valarinho

Luis Valarinho, IST - Tecnico Lisboa

Posted 10 years ago

I'm trying to use Mathematica to solve the Euler Column buckling problem (http://www.continuummechanics.org/cm/columnbuckling.html), but its not working out. Mathematica only shows me the zero solution. Is there any way of getting the no zero displacements solutions? For now, what I have is basically this: equation = EIy''[x] + Py[x] == 0 DSolve[{equation, y[0] == 0, y[L] == 0}, y[x], x] Out[143]= {{y[x] -> 0}} Thanks, Luís Valarinho

POSTED BY: Luis Valarinho

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Luis Valarinho

Luis Valarinho, IST - Tecnico Lisboa

Posted 10 years ago

Hello Kay! Thanks for the suggestion. What I did actually was using the nomenclature that we use in Civil Engineering But you're right, it can lead to mistakes. Thanks for the other suggestions too. I was actually wondering if it is possible to do it in one step. We cannot ask Mathematica to give all the possible solutions? Or adding an assumption that C[2] should be different than zero? (something that is not necessarily truth). Thanks, Luís Valarinho

POSTED BY: Luis Valarinho

Kay Herbert

Kay Herbert, Chief scientist, Sloan Valve Co.

Posted 10 years ago

I recommend not using capital letters for your constants (or at least give them unique names) because for example I is the symbol for Sqrt[-1] and E is the euler number Here is how I would solve it: In[13]:= Clear["Global`*"] In[14]:= sol = DSolve[{y''[x] + ps/(es is) y[x] == 0, y[0] == 0}, y[x], x] Out[14]= {{y[x] -> C[2] Sin[(Sqrt[ps] x)/(Sqrt[es] Sqrt[is])]}} In[15]:= Solve[Sqrt[ps] l/Sqrt[es is] == n Pi, ps] Out[15]= {{ps -> (es is n^2 \[Pi]^2)/l^2}}

I recommend not using capital letters for your constants (or at least give them unique names) because for example I is the symbol for Sqrt[-1] and E is the euler number Here is how I would solve it:

In[13]:= Clear["Global`*"]

In[14]:= sol = 
 DSolve[{y''[x] + ps/(es is) y[x] == 0, y[0] == 0}, y[x], x]

Out[14]= {{y[x] -> C[2] Sin[(Sqrt[ps] x)/(Sqrt[es] Sqrt[is])]}}

In[15]:= Solve[Sqrt[ps] l/Sqrt[es is] == n Pi, ps]

Out[15]= {{ps -> (es is n^2 \[Pi]^2)/l^2}}

POSTED BY: Kay Herbert