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Question: Euler-Bernoulli beam Guided/sliding at both ends

Question:Euler-Bernoulli beam Guided/sliding at both ends

Cavemaann 5 Maple
homework pde pdsolve boundary-conditions
November 29 2018
1

Hello, i am trying to solve the PDE

 (E*I) d4/dx4 [w(x,t)] + (rho*A) d2/dt2 [w(x,t)]=0

where w(x,t) = W(x) * cos (ω *t)

W(x) is the amplitude of the beam, the PDE is solved for W(x) by seperation of variables.

my first question is how to simplify the equations by replacing the e^ terms with alpha as done in the lecture, so that things look cleaner. And the next question is how do i proceed to input the Boundary conditions to solve the problem? I have looked in quite a lot of places but there is no example of a second or third order boundary condition(if that makes sense)

 beam_vibration_displacement.mwMech_vibrations.pdf
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