Question 13.3.1: A certain machine with supports has a measured natural frequ......
A certain machine with supports has a measured natural frequency of 5 Hz. The machine will be subjected to a rotating unbalance force having an amplitude of 2 lb and a frequency of 4 Hz. Design a dynamic vibration absorber for this machine. The available clearance for the absorber’s motion is 0.5 in.
Step-by-Step
The frequency of the applied force is ω = 2π(4) = 8π rad/sec. The absorber’s design requires that ω_{n_2} = ω = 8π. Thus
\omega_{n_2}=\sqrt{\frac{k_2}{m_2}}=8 \piSolve for the mass:
m_2=\frac{k_2}{64 \pi^2}The maximum allowable clearance is 0.5 in. = 1/24 ft. Using (13.3.12), we obtain
X_2=\left|X_2(j \omega)\right|=\frac{1}{k_2} F (13.3.12)
\frac{1}{24}=\frac{F}{k_2}=\frac{2}{k_2}or k_2 = 48 lb/ft. Thus, the absorber’s mass must be
m_2=\frac{k_2}{64 \pi^2}=\frac{48}{64 \pi^2}=0.076 \text { slug }Related Answered Questions
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