Transverse Vibration Analysis of an Axially-Loaded Euler-Bernoulli Beam (Continuous System)

[@moaqirahmad5948]

thank you very much.. very useful... keep it up

[@Lalallalala35]

Thank you kind sir

[@aminamiripour6583]

Thank you so much for your useful lectures. I just didn't understand 1 thing : Why didn't you put (p + dp)sin(theta).dx in the Momentum Equation? I mean, it is a force which you put it in the Newton's law Equation But you didn't consider its Momentum on point 0.

[@franzwurst6329]

I did ask myself the exact same thing. Does anybody know the answer?

[@pmanikantabalaji4476]

I guess, youll get that by truncating taylor series expansion for differential element

[@soroushasadian9100]

@@franzwurst6329 Axial forces cross from point O; therefore, there won't be any moment caused by force P and P+dP. The figure shown above might cause a misunderstanding.

[@franzwurst6329]

@@soroushasadian9100 i don't think so.... The figure shown should be fine

[@franzwurst6329]

@@pmanikantabalaji4476 thank's 👍 your suggestion lead me on the correct path. By taylor series expansion and neglecting higher order terms you'll see that the axial force does not contribute to the moment balance (limited to small displacements)

Man, thanks!!