Effect of Additional Mass on the Apparent Young’s Modulus of a Wooden Bar by Longitudinal Vibration

Abstract

We investigated the influence of an additional mass bonded on a wooden bar on its apparent Young’s modulus based on a longitudinal vibration theory. Rectangular bars of Sitka spruce (Picea sitchensis Carr.) were used as experimental materials. After bonding an iron piece on a bar, a free-free longitudinal vibration test was performed to obtain the Young’s modulus. Modal analysis was also performed to examine the effect of a knot on the measured Young’s modulus. The Young’s modulus decreased with an increase in mass of iron pieces bonded on the specimen and that in a size of the knot, since the constants required for the frequency equation of longitudinal vibration changed due to the additional mass and the knot. An equation was developed which contains the effects of the mass and position of the iron piece on the constants. The Young’s moduli calculated by this equation resembled the values without an iron piece and the knot. Assuming a knot to be the additional mass, the estimation method used to examine the effect of a knot on the apparent Young’s modulus was proposed. The analysis showed that the higher the resonance mode and the nearer the position to an end, the more effective efforts to reduce the effect of the additional mass will be.