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Saraa12
• A shape function is carefully selected. 
• Equations of Motion are derived
Equations of Motion 
• System is in equilibrium: 
– Internal resisting bending moments and fictitious 
inertial forces 
– 푓퐼 푥, 푡 = −푚 푥 푢 푡 푥, 푡 
– 푓퐼 푥, 푡 = −푚 푥 푢 푡 푥, 푡 + 푢 푔 푡
• @ Ea. Time instant system is in equilibrium 
under action of internal 
• System in equilibrium subjected to virtual 
displacement 
퐿 
• 훿푢 푥 
0 
퐿 
푚 푥 휓 푥 2푑푥 
• 훿푊퐸 = −훿푧 푧 0
Saraa12

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Saraa12

  • 2. • A shape function is carefully selected. • Equations of Motion are derived
  • 3. Equations of Motion • System is in equilibrium: – Internal resisting bending moments and fictitious inertial forces – 푓퐼 푥, 푡 = −푚 푥 푢 푡 푥, 푡 – 푓퐼 푥, 푡 = −푚 푥 푢 푡 푥, 푡 + 푢 푔 푡
  • 4. • @ Ea. Time instant system is in equilibrium under action of internal • System in equilibrium subjected to virtual displacement 퐿 • 훿푢 푥 0 퐿 푚 푥 휓 푥 2푑푥 • 훿푊퐸 = −훿푧 푧 0