On the frequency dependence of the modulus of elasticity of wood

Abstract

 This short note reviews the reasons for the frequency dependence of the Modulus of Elasticity, MOE, of wood. It has in fact been reported in several publications on wood that depending on the technique used in the test experiment, the value of the MOE depends to some degree on the frequency at which it is evaluated. The frequency ranges used are namely zero frequency in the case of static bending, audio frequencies when using mechanical vibrations or sound radiation and finally ultrasonics. The results from implementing these three different techniques show that the lowest value that may be obtained for the MOE occurs when using the static mode, and thereafter increases with increasing frequency. This property of increasing dynamic MOE with frequency is shared by all solid materials, and finds its theoretical explanation in the Kramers-Kronig relations. Dispersion in conjunction with the notion of complex MOE permit to establish the relation between the real and the imaginary components of the MOE, i.e. respectively the dynamic and loss moduli. Due to the mathematical difficulties encountered in using the exact expressions, approximations are necessary for applications in practical situations. Hence, an improved version of the Zener model for viscoelasticity, which has lately been proposed by Pritz (1999), is presented. With some assumptions, and under which excellent agreement has been obtained with the exact theory, this model is used for predicting the viscoelastic properties of wood.