Jompa
Feb12-09, 03:35 PM
Hello smarties!
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=\int0.5*\rhoA(w(x,t)^2)dx from 0 to L
Stating U: U=L/6EI *[(-\intq(x,t)xdx+M(t))^2 +M(t)(-\intq(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=\overline{W}=L/6EI*[M_{A}M_{B}+M_{A}^2+M_{B}^] where M_{A} and M_{B} 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 ^{}_{S_t}\intF*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
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=\int0.5*\rhoA(w(x,t)^2)dx from 0 to L
Stating U: U=L/6EI *[(-\intq(x,t)xdx+M(t))^2 +M(t)(-\intq(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=\overline{W}=L/6EI*[M_{A}M_{B}+M_{A}^2+M_{B}^] where M_{A} and M_{B} 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 ^{}_{S_t}\intF*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