Anelasticity in Flexure Strips Revisited

TL;DR

This paper revisits and corrects previous analyses of damping due to anelasticity in flexure elements, providing a clearer derivation and extending the methodology to smaller suspended objects.

Contribution

It offers a corrected calculation of flexure anelasticity, clarifies previous errors, and extends the analysis to smaller objects relative to the flexure length.

Findings

Corrected the calculation of anelastic damping in flexure strips.

Identified and rectified errors in earlier models.

Extended methodology to smaller suspended objects.

Abstract

This note reviews previous analyses by the author of the damping produced by the anelasticity of a simple flexure element that is loaded in tension by an extended object such as a beam balance. The correct calculation of the anelasticity of a simple flexure appeared in an appendix in Quinn et al (1995) where the change in the gravitational potential energy due to the shortening of the flexure was calculated enabling expressions for the elastic energy and its associated losses to be derived. Publications prior to this paper did not include this lossless term which led to incorrect predictions of the anelastic losses in flexure pivots in Quinn et al (1987). In this current paper the derivation of the result is given in such a way that it can be easily contrasted with the expressions in these earlier papers. I also extend the methodology to calculate the elastic and gravitational energy associated with the motion of a suspended object whose dimensions are significantly smaller than the length of the flexure.