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Vibration Isolation: Onset at T = 1

A hidden base-excited isolator. Sweep the frequency ratio, watch T = X/Y, and report the r where isolation begins (T drops through 1).

University / research· 22 min·Related simulator: EngineeringVibration Isolation Transmissibility

Goal

Determine r_* as the frequency ratio where displacement transmissibility T = X/Y equals 1. Theory: r_* = √2.

Equipment

  • Base-excited isolator (unknown ζ)
  • Variable drive
  • Amplitude meters X and Y

Experiment

Theory

For a base-excited SDOF, T(r,ζ) = √(1+(2ζr)²) / √((1−r²)²+(2ζr)²). Setting T = 1 gives r = √2 for any ζ. Isolation (T < 1) is the region r > √2. The bench hides ζ, the analytic T(r) curve and any √2 marker. A live T = X/Y meter is the instrument.

Procedure

  1. Damping and the natural frequency are hidden. You only change the frequency ratio r = ω/ωn.
  2. Watch the live T = X/Y. Find the r where T crosses 1 (isolation begins). The bench does not mark √2.
  3. Record that r. Repeat the hunt at least 6 times (you may start from different r).
  4. Take the mean of the r column and compare with the reference.

Conclusion

The mean onset ratio agrees with √2. Main uncertainties: discrete r steps and judging T = 1 by eye. Isolation is the region r > √2.