vibrationstransversales.py

Created on October 19, 2023

580 Bytes

Equation Type : 
  drond^4 Psi / drond x^4 + 1/a2 drond2 Psi /drond t2 =0
  avec a2 = v2r2 où v=E/ro et r2 = I/S
Les solutions stationnaires sont de la forme :
  Psi(x,t)=Phi(x)Z(t)
avec Phi(x)=:
  C1 cos sigma x + C2 sin sigma x + C3 ch sigma x + C4 sh sigma x 
ou ( avec s = sigma ):
  K1(cos sx + ch s x ) + K2 (cos s x - ch s x) + K3 (sin s x + sh s x) + K4 (sin s x - sh s x)
CLE :
  Extremité libre :
    Phi " = 0 & Phi ''' = 0
  Extremite appuyé :
    Phi = 0 & Phi" =0
  Extremite encastré :
    Phi = 0 Phi' = 0
Puis analyse graphique

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vibrationstransversales.py