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

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.

arXiv comment35 pages, 13 figures

References in corpus (5)

• Analytical formulation of 3D dynamic homogenization for periodic elastic systems
• Overall Dynamic Properties of 3-D periodic elastic composites
• Resonant and Non-Local Properties of Phononic Metasolids
• Realizing the Willis equations with pre-stresses
• The form-invariance of wave equations without requiring a priori relations between field variables

Cited by in corpus (4)

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• Understanding the First Order Inhomogeneous Linear Elasticity through Local Gauge Transformations
• Deeper understandings of the gauge theory for the first order inhomogeneous linear elasticity