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Linear Vibration of a Beam

A hinged-hinged beam of length 4 m, width 0.15 m and thickness 0.20 m with clamped edges is subjected to a suddenly applied load of 5000 N at the middle of the beam. The beam material has a Young's modulus of $1\times10^{12}$ N/ $\mbox{m}^2$ and mass density of 100 kg/m. Two different models for the beam are tested: 18 two-noded degenerated shell elements model and $4\times 10$ four-noded isoparametric solid elements in which four elements are used across the thickness. The central deflection time history is plotted and compared to the analytical solution in Figure (2.13).

Figure 2.13: Linear Vibration of a Beam

A. Zeiny