A uniform simply supported beam of length \(2.5 \mathrm{~m}\) with a hollow rectangular section is shown in Fig. 7.16. Assuming a deflection shape of

\[y(x)=C \sin \frac{\pi x}{l}\]

find the natural frequency of transverse vibration of the beam. The material of the beam has a Young's modulus of \(E=200 \mathrm{GPa}\) and a density of \(8000 \mathrm{~kg} / \mathrm{m}^{3}\).

Transcribed Image Text:

y(x) x A [I 150 mm 1125 mm 90 mm- FIGURE 7.16 Beam with hollow rectangular section. -100 mm- Section A-A