A rigid mass of \(1 \mathrm{~kg}\) drops from a height of \(1 \mathrm{~m}\) onto a simply supported aluminum beam at the center (figure 8.14). Use Newmark time integration to calculate the maximum impact force and impact duration. Plot the center deflection of the beam as a function of time. The dimensions of the beam are: \(1 \times 1 \times 30 \mathrm{~cm} ; E=70 \mathrm{GPa}\), and density \(ho=2,700 \mathrm{~kg} / \mathrm{m}^{3}\).

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P 1 Figure 8.14 (Top) Impact of a mass on a simply supported beam; (bottom) oneelement FE model of one half of the beam. 2