180
5 Vibration of Two Degrees of Freedom System
Prob. 5.17.
5.17 A hoisting drum is mounted on a platform supported by two cantilever beams
at their two ends. Values of E and I of the beams are 205×10
2 N/m
2 , and
2672 × 10
4 mm
4 respectively. The beams are 3.2 m long. Neglecting the mass
of the beam, the weight concentrated at its top is 4550 N and the suspended
load is 18 kN. The hoist rope is a 12 mm stranded steel wire rope, having
a net cross-sectional area of 0.65 cm
2 . Calculate the natural frequencies and
amplitude ratios for vertical vibration, if the suspended length L of the rope
is 30 m.
5.18 Consider a two-storeyed structure shown in the figure. Determine the
displacement of the masses as a function of time for free vibration, if the
top storey is given an initial displacement of 50 mm.
Prob. 5.18.
Prob. 5.19.
5.19 A structure linked together by spring element is shown. Determine the
displacement of the masses for free vibration, if an initial displacement of 50
mm, 180° out of phase is given for both the masses.