Young’s modulus obtained by flexural vibration test of a wooden beam with inhomogeneity of density

Abstract

The object of this study was to investigate the inhomogeneity of density within a beam from a relationship between the dynamic Young’s moduli from the Euler-Bernoulli elementary theory of bending (En) and resonance mode numbers (n), which is plotted as the “E-n” diagram in this article. Rectangular beams with dimensions of 300 (L) × 25 (R) × 5mm (T) of Sakhalin spruce (Picea glehnii Mast.), Sitka spruce (Picea sitchensis Carr.), Japanese red pine (Pinus densiflora Zieb. et Zucc.) and white oak (Cyclobalanopsis myrsinaefolia Oerst.) were used for specimens. Small parts of beams were replaced with a small portion of another species to examine the influence of the inhomogeneity of density on En. A free-free flexural vibration test was undertaken and En was calculated by the Euler-Bernoulli theory. The resonance frequency of a specimen with inhomogeneity of density was simulated by modal analysis. The density distribution in the longitudinal direction of the specimen for which En did not decrease monotonically with n was obtained. From the modal analysis, the inhomogeneity of density was equivalent to a concentrated mass attached to a uniform beam. The pattern of the E-n diagram was changed by replacing a part of the specimen with another species. Specimens for which En did not decrease monotonically with n had a high density part because of indented rings, knots, or resin.