Logarithmiccreepandhysteresis.docVIP

Are Hysteresis, Creep, and Damping of Mechanical Oscillators consequences of the same mechanism of internal friction? E. Wielandt, November 2006 (e.wielandt@t-online.de) unfinished manuscript The internal friction of metallic alloys used for elastic springs and hinges may limit the sensitivity and precision of inertial seismic sensors, especially those not stabilized by electronic feedback. It expresses itself in different observations that seem to be unrelated at first sight: The purely mechanical damping of a LaCoste pendulum, when expressed as a fraction of critical damping, increases with the square of its free period, in contrast to the classical oscillator with viscous damping for which theory predicts a linear increase (G. Streckeisen 1974, our fig. 1). Since the free period of a LaCoste pendulum is adjusted by tilting the whole instrument, without any other mechanical modification, this must be a property of the spring material. Similar observations have recently been made by R. Peters (2005) with an inverted pendulum. The restoring force of a spring or flexural hinge decreases with the (negative) logarithm of time after a step-like deflection. This was clearly observed by E. Wielandt and J. Otero in commercial Bendix-type flexural hinges at a time scale from a few seconds to one day (fig. 2). The creep is approximately proportional to the magnitude of the step. In Materials Science, logarithmic creep is well known. It is common in the low-temperature, low-stress regime, also in plastics, and is explained by the statistics of thermal activation of pre-existing dislocations. Measurements of mechanical hysteresis are insensitive to the time scale at which they are conducted. I have not investigated this myself but the general absence of timing information from experimental results conveys a clear message. Kimball and Lovell (1927) demonstrated with their ingenious rotating-cantilever method that hysteresis is the same at all frequencies from 0.03 to 50 Hz.