Can this beam PDE problem be solve analytically?

  • Thread starter monkeyboy1
  • Start date
  • #1
A work problem, but more like a homework problem....

Homework Statement



Euler-Bernoulli beam with a lumped mass at x=L, simply supported at x=0 and x=L/2. The beam has a linear initial velocity profile v(x) = w*x.

Homework Equations



BCs
Y(0)=0
y''(0)=0
Y(L/2)=0
Y'''(L)+M/m*beta*Y(L)=0

The Attempt at a Solution



I can solve the simply supported case, and I can solve the cantilever with tip mass case by separation of variables and eigenfunction expansions. Can this problem be solved in a similar way? When I go at it in a straight forward manner, I only get a single eigenvalue at zero.

Homework Statement





Homework Equations





The Attempt at a Solution

 

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