20.8 Failure of the Common Theory

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Many mechanical oscillator studies in decades past, mainly by engineers, have shown that the so-called

decay constant b is proportional to v21 instead of being constant (e.g., Bert, 1973). The damping for

these cases came to be called “material”, “structural”, or “hysteretic.” A common way to obtain the correct

frequency dependence was to divide the velocity by frequency and call the result an “equivalent viscous”

form of damping. The adjective “equivalent” draws attention to the fact that internal friction in a solid

cannot really result from fluid effects. Moreover, elsewhere in this document, there is plenty of support

for the position that the linear equations of viscous damping type cannot produce truly meaningful

(predictive) models when doing modal analysis on multibody systems.

An important early work by Kimball and Lovell (1927) is evidently the first experiment to show that

internal friction (“force”) of many solids is virtually independent of frequency. In other words, their

elegant technique, in which a rotating rod is deflected by a transverse force, was the first to demonstrate

the “universality” of hysteretic damping. Although both researchers were physicists at General Electric in

the time of Steinmetz, few physicists of the 21st century know of this important work. As with the

important contributions of Portevin and LeChatelier, their study of systems influenced by “dirty physics”

was evidently ignored in favor of the “clean” new quantum mechanics of that era.

FIGURE 20.8 Free-decay of a seismometer due to hysteretic damping.

Damping Theory 20-29

© 2005 by Taylor & Francis Group, LLC

It is interesting that a bell made of lead does not tinkle at room temperature, but it can be made to do

so at 77 K, by immersion in liquid nitrogen. This demonstration, which is often employed in physics

“circuses,” shows clearly that the internal friction of lead at audio frequencies can be reduced substantially

by lowering the temperature. An important lesson to be learned from these observations is that damping,

in general, is a complex function of temperature, frequency, conductivity, …(who knows where to

terminate this list). Not only is a multitude of state variables necessary for a complete description of

dissipation, but the previous history of stress – strain cycling may also be critical. Such is the nature of

defect structures responsible for damping.

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