Answer Happy

Question 4 A uniform cantilever beam of length 1.2 m and density of 7,800 kg/m is fixed at one end as illustrated in Figure Q4. The beam, which has a square cross-section, is manufactured from a steel with a Young's modulus of 234 GPa. A mass m of 2000 kg is applied at the free end. (a) (b) Using Rayleigh's energy method, derive an expression for the natural frequency of the system. [14] Determine a suitable depth for the beam such that the system can be operated at a maximum frequency of 60 Hz with a factor of safety of 2 over the natural frequency of the system 161 Note: The deflection at the end of the cantilever beam is: mg/3 Xi = ЗЕТ where m is the applied mass, E is Young's modulus and I is the second moment of area. The deflection at any point c along the cantilever beam is: mg (lc2 Xc = ΕΙ 2 The second moment of area for a rectangular cross section is: bd3 I= 12 where b and d are the breadth and depth, respectively. 1 m x X1 m dc Figure Q4: Cantilever beam geometry.