Task 4 TBM250 The element method
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a. Calculate the first two (lowest) natural frequencies for the geometry i
practice task 3.3.
Mass density, steel: rho = 7850. kg/m^3
Hint:
- The mass matrix of the beam element:
M = [ [ 140., 0., 0., 70., 0., 0. ],
[ 0., 156. , 22.*L , 0., 54., -13.*L ],
[ 0., 22.*L, 4.*L**2, 0., 13.*L, -3.*L**2],
[ 70th, 0th, 0th, 140th, 0th, 0th ],
[ 0., 54., 13.*L, 0., 156., -22.*L ],
[ 0., -13.*L, -3.*L**2, 0., -22.*L, 4.*L**2 ] ])*rho*A*L/420.
- This must also be transformed into a global system and "mapped" to
the mass matrix for the system, in the same way as the stiffness matrix
- Boundary conditions must also be introduced in the mass matrix
- Solve the eigenvalue problem with e.g. numpy.linalg.own
- Remember that the solution to the eigenvalue problem is lambda (which is omega
squared). It is to be solved in Python. In the PDF you have the question 3.3.