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Assignment The bending vibration of a shaft shown in the figure is investigated. The shaft is prismatic, its density is denoted by p and its Young's modulus is E. A disk of mass m and mass moment of inertia ész is attached to the shaft that is also connected to the environment through a spring of stiffness k. KA HA A-A VA m.es Data p = 7800 kg/m E = 210 GPa a = 20 mm b = 2 mm 11 = 95 mm 12 = 110 mm m = 0.18 kg Osz = 0.05 gm? k = 113 kN/m oa 11 ll! 12 Figure: Mechanical model Tasks 1. Estimate the first natural frequency of the shaft with the help of Rayleigh’s Principle! Use an approximated mode shape that satisfies the boundary conditions while the disk and the spring are neglected! Sketch the applied approximating first mode shape function!