Example 12.1:
Figure 12.9: A simply supported beam
The following data are given: the diameter of the beam d = 10 mm, the density of the beam material 
=
7800 Kg/m3,
, the Young's modulus of the beam material E = 2.1x10 11 N/m2 ,the length of the beam l = 3m. Obtain natural frequencies of a continuous beam system as shown in Figure 12.9. by finite element method