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 (E n) 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 E n. A free-free flexural vibration test was undertaken and E n 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 E n 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 E n did not decrease monotonically with n had a high density part because of indented rings, knots, or resin.
Article PDF
Similar content being viewed by others
References
Kubojima Y, Tonosaki M, Yoshihara H (2005) Effect of additional mass on Young’s modulus of a wooden beam. J Test Eval (in press)
Fukazawa K, Ohtani J (1984) Indented rings in sitka spruce. Proceedings of Pacific Regional Wood Anatomy Conference, Tsukuba, pp 28–30
Ohtani J, Fukazawa K, Fukumorita T (1987) SEM observations on indented rings. IAWA Bull 8:113–124
Larson PR (1994) The vascular cambium. Springer, Berlin Heidelberg New York, pp 422–423
Yang X, Ishimaru Y, Iida I (2002) Application of modal analysis by the transfer function to nondestructive testing of wood III. Detection of knots and estimation of elastic modulus distribution in wood by the curvature ratio of the flexural vibration wave shape. Mokuzai Gakkaishi 48:16–22
Kodama Y, Zhang Z (2000) Evaluation of wood quality by wavelet analysis I. Wavelet analysis of the tapping tone of wood with a knot (in Japanese). Mokuzai Gakkaishi 46:197–202
Kodama Y, Zhang Z, Kawabata H (2001) Evaluation of wood quality by wavelet analysis II. Estimation of knot size (in Japanese). Mokuzai Gakkaishi 47:473–478
Kodama Y, Zhang Z, Kawabata H (2004) Study on evaluation of wood quality using wavelet transform (in Japanese). T Jpn Soc Mech Eng 70:184–191
Kubojima Y, Yoshihara H, Ohta M, Okano T (1996) Examination of the method of measuring the shear modulus of wood based on the Timoshenko theory of bending. Mokuzai Gakkaishi 42:1170–1176
Kubojima Y, Yoshihara H, Ohta M, Okano T (1997) Accuracy of the shear modulus of wood obtained by Timoshenko’s theory of bending. Mokuzai Gakkaishi 43:439–443
Yoshihara H, Matsumoto S (1999) Examination of the proper span/depth ratio range in measuring the bending Young’s modulus of wood based on the elementary beam theory (in Japanese). Wood Ind 54:269–272
Yoshihara H, Kubojima Y, Nagaoka K, Ohta M (1998) Measurement of the shear modulus of wood by static bending tests. J Wood Sci 44:15–20
Goens E (1931) Über die Bestimmung des Elastizitätsmodulus von Stäben mit Hilfe von Biegungsschwingungen. Ann Phys 5F 11:649–678
Hearmon RFS (1958) The influence of shear and rotatory inertia on the free flexural vibration of wooden beams. Brit J Appl Phys 9:381–388
Timoshenko SP (1921) On the correction for shear of the differential equation for transverse vibrations of prismatic bars. Philos Mag 6th Ser 41:744–746
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Kubojima, Y., Tonosaki, M. & Yoshihara, H. Young’s modulus obtained by flexural vibration test of a wooden beam with inhomogeneity of density. J Wood Sci 52, 20–24 (2006). https://doi.org/10.1007/s10086-005-0732-9
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10086-005-0732-9