Significant improvement in estimation of the Young's modulus of the metal foam based on the Timoshenko's bend theory

TL;DR

This paper presents a combined computational and experimental method to accurately estimate the Young's modulus of metal foams using Timoshenko's bend theory, accounting for skin effects and density variations.

Contribution

It introduces a new rule relating Young's modulus to foam density and demonstrates improved estimation accuracy through vibration analysis and numerical validation.

Findings

Skin presence increases transverse stiffness by about 50%.

Frequency dependence of Young's modulus explained by density distribution.

Excellent agreement between experimental and numerical data.

Abstract

A computational and experimental approach based on a natural vibration of a free prismatic thick beam with square cross-section is suggested. Three variants of the beam sample were used (one with skin and two without skin). From 13 to 16 lowest resonant frequencies of longitudinal, torsional and flexural vibration of each beam were analyzed. A rule for dependence of Young's modulus on the average foam density was derived from the sample without skin. It is shown that the skin presence causes known anisotropy that the stiffness in transverse direction is about 50% greater than that in the longitudinal direction. It has also been shown that the seeming frequency dependence of the Young's module can be explained by non-uniform distribution of mass density in the sample. Agreement among experimental and numerical data is excellent in most cases. The rule is also verified on solution of two lowest resonant frequencies of the free foam plates with various mass densities (from 400 to 1350 kg/m3). Agreement among experimental and numerical frequencies is acceptable.