Solid Mechanics Problems - Meshless Methods in Biomechanics - page 210

Fig. 5.58 Cantilever beam vibration modes [ 2 ]

Once again it is visible the good concordance between the distinct methods. In
Fig. 5.62 the first eight vibration modes of the shear wall obtained using the V2P1
NNRPIM formulation are presented.

5.4.4 Forced Vibration of a Cantilever Beam

In this example a cantilever beam, Fig. 5.63 , is subjected to a forced vibration. The
geometrical parameters are, L = 48 m, D = 12 m and thickness h = 1 m. The
material properties are Young's modulus E = 3.0 9 10 7 Pa, Poisson ratio t = 0.3
and mass density q = 1.0 kg/m 3 . The problem is analysed considering the 2D
plane stress deformation theory and the 3D deformation theory. As Fig. 5.63
indicates, the beam is discretized with 297 nodes for the 2D analysis and with 891
nodes for the 3D study. The beam is subjected to a parabolic load at the free end,
f ð t Þ ¼1,000 g ð t Þ N, where g(t) is a time functional.
The three distinct time-dependent loading conditions presented in Sect. 2.3.7
are considered. In this example, for the load case B it is considered: t i ¼ 0 : 5s.
The dynamic response of the complete beam is obtained, i.e., the complete
displacement field is obtained for each time step. However the most interesting