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GATE 2021 ME (ME2) – Question 43

Vibrations · Vibration isolation and transmissibility ratio · 2 marks · Multiple choice

A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness ($K$) and damper (damping factor, $\zeta$) in parallel. The designer has the following four isolators:

1) $K=640$ kN/m, $\zeta=0.70$
2) $K=640$ kN/m, $\zeta=0.07$
3) $K=22.5$ kN/m, $\zeta=0.70$
4) $K=22.5$ kN/m, $\zeta=0.07$

Arrange the isolators in the ascending order of the force transmitted to the foundation.

  1. 1-3-4-2
  2. 1-3-2-4
  3. 4-3-1-2
  4. 3-1-2-4

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Show answer and explanation

Correct answer: (C) 4-3-1-2

Explanation

For each isolator use $r=\omega/\sqrt{K/m}$ and force transmissibility $T_F=\sqrt{[1+(2\zeta r)^2]/[(1-r^2)^2+(2\zeta r)^2]}$.

The values for 1–4 are 1.1898,1.3308,0.5397,0.1743. Sorting gives **4–3–1–2 (C)**. Lower damping helps isolation above the isolation threshold.