Rheological Interpretation of Rayleigh Damping

TL;DR

This paper links Rayleigh damping used in numerical models to a rheological generalized Maxwell model, clarifying its physical meaning and demonstrating its accuracy for moderate damping scenarios through analytical and finite element comparisons.

Contribution

It introduces a rheological interpretation of Rayleigh damping using a generalized Maxwell model with three parameters, enhancing understanding of its physical basis.

Findings

For damping below 25%, the model aligns with Rayleigh damping.

The model accurately captures internal friction effects.

Finite element and analytical results agree in simple cases.

Abstract

Damping is defined through various terms such as energy loss per cycle (for cyclic tests), logarithmic decrement (for vibration tests), complex modulus, rise-time or spectrum ratio (for wave propagation analysis), etc. For numerical modeling purposes, another type of damping is frequently used : it is called Rayleigh damping. It is a very convenient way of accounting for damping in numerical models, although the physical or rheological meaning of this approach is not clear. A rheological model is proposed to be related to classical Rayleigh damping : it is a generalized Maxwell model with three parameters. For moderate damping (<25%), this model perfectly coincide with Rayleigh damping approach since internal friction has the same expression in both cases and dispersive phenomena are negligible. This is illustrated by finite element (Rayleigh damping) and analytical (generalized Maxwell model) results in a simple one-dimensional case.