Energy Spectrum Evolution of a Diffuse Field in Elastic Body Caused by Weak Nonlinearity

TL;DR

This paper investigates how weak nonlinearity affects the energy spectrum evolution in diffuse elastic fields, providing a convolution-based model and quantitative estimates for materials like aluminum and fused silica.

Contribution

It introduces a convolution-based model for the spectral energy evolution due to weak nonlinearity in elastic bodies, supported by quantitative estimates for specific materials.

Findings

The energy spectrum evolves according to a convolution of linear energy at different frequencies.

Quantitative estimates are provided for aluminum and fused silica.

Weak nonlinearity significantly influences the spectral energy distribution.

Abstract

We study the evolution of diffuse elastodynamic spectral energy density under the influence of weak nonlinearity. It is shown that the rate of change of this quantity is given by a convolution of the linear energy at two frequencies. Quantitative estimates are given for sample aluminum and fused silica blocks of experimental interest.