Hello smarties!(adsbygoogle = window.adsbygoogle || []).push({});

Anyone who can help me out here?

The problem statement is in the attachment, problem.jpg

My attempt:

Lagrangian: L=T-U where T kin. energy and U elastic potential.

Stating T: T=[tex]\int[/tex]0.5*[tex]\rho[/tex]A(w(x,t)^2)dx from 0 to L

Stating U: U=L/6EI *[(-[tex]\int[/tex]q(x,t)xdx+M(t))^2 +M(t)(-[tex]\int[/tex]q(x,t)xdx+M(t)) +M(t)^2]- what?

(the integrals from 0 to L, sorry couldn't get the hang of how to get the limits to look nice with latex)

The get the expression for W (the expression before "what") comes from W=[tex]\overline{W}[/tex]=L/6EI*[M[tex]_{A}[/tex]M[tex]_{B}[/tex]+M[tex]_{A}[/tex]^2+M[tex]_{B}[/tex]^] where M[tex]_{A}[/tex] and M[tex]_{B}[/tex] are the moments at the ends of the beam. They are determined with help of moment equilibrium.

How should the "what" term look like? Should it look someting like this [tex]^{}_{S_t}[/tex][tex]\int[/tex]F*w(L,t)dS

Does my elastic energy come out right?

Thanks for helping!

Most grateful for all comments.

/J

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: How to formulate the Lagrangian for a cantileverbeam

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**