Cantilever clamping rigidity impact on dynamic modulus of elasticity calculation

Miran Merhar and Bojan Bučar (2006) Cantilever clamping rigidity impact on dynamic modulus of elasticity calculation. Zbornik gozdarstva in lesarstva (79). pp. 85-92. ISSN 0351-3114

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Abstract

The paper presents the impact of the clamping ratio of a clamped beech (Fagus sylvatica) cantilever specimen on the calculation of a dynamic modulus of elasticity. First we measured the specimen's frequency of the first mode of damped transverse free vibrations of a specimen with free ends. In accordance with the Bernoulli-Euler theory, we then calculated the modulus of elasticity for the mentioned conditions, which we subsequently used as a reference. The specimen was then clamped as a cantilever beam several times, from a clamping ratio of 18 to 105, and each time the frequency of the first damped transverse free vibrations was measured. The modulus of elasticity was calculated according to the theory for rigid cantilever clamping, and compared to the reference module. In the case of small clamping ratios, the error was around 20 %, whereas in the case of large clamping ratios the error decreased to 5 %. The cause of the major error is insufficient specimen clamping rigidity, which is due - despite a sufficient rigidity of the clamping system - to the specimen compressibility in the transverse radial or tangential directions where the modulus of elasticity is more than ten times smaller than the modulus along the tissue.

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