5.8 Free Vibration of Damped Two Degrees of Freedom System
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5.20 A cantilever beam is modelled by lumping the mass as shown. The density
of the material of the beam is ρ and E is the modulus of elasticity. Determine
the natural frequencies and mode shapes of this model.
Prob. 5.20.
5.21 Determine the steady-state vibration of the system shown in figure, assuming
that F 1 (t ) = F 1 cos ω t and F 2 ( t ) = F 2 cos ω t.
Prob. 5.21.
5.22 In a refrigeration plant, a section of the pipe carrying the refrigerant vibrated
violently at a compressor speed of 200 rpm. To eliminate this problem, spring–
mass system is clamped to the pipe to act as an absorber. In the trial test, the
4 kg absorber turned to 250 cpm resulted in two natural frequencies of 190
and 250 cpm. If the absorber system is to be designed so that the natural
frequencies lie outside the region 170 and 300 cycles/m, what must be the
weight and spring stiffness?
References
1. W. Weaver, S.P. Timoshenko and D.H. Young, Vibration Problems in Engineering, Fifth Edition,
Wiley Interscience, 1990.
2. H. Benaroya, Mechanical Vibration, Practice Hall, New Jersey, 1998.