Question

A shaft carrying two rotating disks of masses m Figure Q5(a). Assume that the deflections of the bearings and gyroscopic effect of the disks are negligible. Take E 209 x 109 N/m2. 20 kg and m2 35 kg as shown in Find the flexibility influence coefficients of the system. i) (5 marks) Determine the natural frequency of the system using Dunkerley's method. ii) (5 marks) 20 mm dia 35 kg 20 kg 150 mm 150 mm 600 mm DIK DK

*Vibration

Answer 1

Consider the given diagram. 35 kg 20 kg 20 mm dia. 7 150 mm 150 mm 600 mm Calculate the flexibility influence coefficient considering the first mass. 0113EIL 3EIL 48EI Substitute the given values.

(0.600) 911 =- 5=2.74x10 m/N 48(209x10°) (64«(0.02074) Calculate the flexibility influence coefficient considering the second mass. 422 3EIL 3EIL 2 56 EI Substitute the given values. 3(0.600) 022 = 1.54x10m/N 256(209x109) m <(0.020) Write the equation for frequency due to the first mass. 012 48E1 Write the equation for frequency considering the second mass. 1 3m, 0, 256 EI

Calculate the natural frequency of the system using Dunkerley's method. m, 3m [ * 48E1 + 256E1 ľm3m = Substitute the given values. (0.600) (20) 3(35) [1 16(209x 10°) (0.020) 3 * 16 =95.87 rad/s - 687 -13 258H: