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</o:shapelayout></xml><![endif]--></head><body lang=FR link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span lang=EN-US>Deal All<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>I take the liberty in asking to Scilab community some advices, especially to mechanical specialists.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>In an optimization process, I would like to model with Scilab the natural frequencies of a beam following 2 configurations (see sketch hereafter) using either Euler-Bernoulli or Timoshenko theory.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>We can found in the literature (Blevins book and Timoshenko one among others) some particular cases, I’ve not found any solution for that configuration: does somebody hear something about it ?<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><i><u><span lang=EN-US>NB</span></u></i><span lang=EN-US>:<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US><span style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span lang=EN-US>An analytical solution will be great ; indeed solving by hand the 4<sup>th</sup> order derivative seems to be quite difficult<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US><span style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span lang=EN-US>If not, the numerical approach using Scilab will be the only one solution <o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US><span style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span lang=EN-US>Ultimately, I can use Finite Elements method (or even code it directly in Scilab), but it’s not the goal … and it’s much less elegant<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US><span style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span lang=EN-US>I’m currently working on test cases based on “basic” boundary conditions as described in the literature to validate the methodology<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-18.0pt;mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US><span style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span lang=EN-US>I’m sure such method could be extended to industrial (simplified but accurate) studies<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>a)<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US>/| P<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US>/| ||||||||||||||| <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US>/|--------------------------------------------------- where P is a linear force or pressure (not along all the beam)<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US>/|<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US>/|<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>Or <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>b)<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US>/| sliding<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US>/|---------------------===------------------------- bean can slide following its axis<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US>/|<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>Have a good WE<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US>Paul<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>