An experimental verification of the one-dimensional static Willis-form equations

TL;DR

This study experimentally verifies that the one-dimensional static Willis-form equations accurately describe the behavior of inhomogeneous springs under steady circular motion, providing insights into stress effects and material indifference principles.

Contribution

It provides the first experimental validation of the Willis-form equations for inhomogeneous springs in steady motion, confirming their predictive accuracy.

Findings

The Willis-form equations match experimental results very well.

They explain stress-stiffening and spin-softening effects.

The equations offer accurate linear approximations of finite deformations.

Abstract

This paper investigates the behavior of a heavy soft spring in steady circular motion. Since the spring is inhomogeneous due to centrifugal force, one can rigorously prove that it follows the one-dimensional static Willis-form equations. The theoretical predictions agree very well with experimental results. It further demonstrates that these equations can give a clear understanding of the stress-stiffening and spin-softening effect. These findings reveal that the Willis-form equations can give very accurate linear approximations of finite deformation problems and are also helpful to clarify the classical concept of the principle of material frame indifference.