21.8 Internal Friction as Source of Mechanical Noise

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Chapter 20 claims that internal friction is responsible not only for damping but also for significant

mechanical noise of 1=f type. Figure 21.33 is provided in support of that claim.

The pendulum in these experiments (lead spheres near the ends of an aluminum tube with a pair of

steel-points for the axis) was operated in a high vacuum to eliminate the influence of air. The electronics

Illustration of Mode Mixing

Illustration of Mode Mixing

(sum case)

Normalized A1 · A2 Normalized A1 · A2

Normalized Am

Normalized Am

(difference case)

index of mix = 3.7%

y = 0.93x

R2 = 0.97

index of mix = 1.2%

y = 0.96 x

R2 = 0.96

1.2

0.8

0.6

0.4

0.2

1

0

1.2

0.8

0.6

0.4

0.2

1

0

0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1

FIGURE 21.32 Evidence in support of nonlinear mixing according to Equation 21.8.

FIGURE 21.33 Power spectrum and associated temporal record showing mechanical 1=f noise (right pair). For

reference, electronics noise is also provided (left pair).

21-28 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

noise was obtained by removing the top mass and measuring the motion after oscillation reached a

minimum (frequency approximately 1 Hz); some pendulous mode remains because of pump noise

transmitted through the vacuum hose. Similarly, the pump vibrations excite a vibratory mode in the

long-period pendulum (sharp spectral line at 3.5 Hz, right spectrum). In this vibratory mode the lead

masses move in the same direction relative to the stationary axis (similar to the bending mode of the

carbon dioxide molecule). It is interesting to note that there is no coherent oscillation to be seen above

noise corresponding to the period of 5.7 sec. The mechanical noise is seen to include bistability, which is

not uncommon for this type of system before hardening, following a significant force disturbance. The

data in Figure 21.33 were collected after replacing the upper mass, which had been removed to measure

the electronics noise, and after pumping to the operating pressure (below 5 mm Hg).

The mechanical noise is seen to be 1=f for f , 1:5 Hz; which is where electronics begins to contribute

noticeably. Everywhere below 1 Hz, the electronics noise is an order of magnitude smaller than the

mechanical noise.

After the pendulum had stabilized overnight and been allowed to oscillate through a number of freedecays

(initialization by tilting the chamber), the data shown in Figure 21.34 was collected.

It can be seen that the mechanical noise has mostly settled out, leaving the remnant electronics

noise.

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