Natural vibration analysis of clear wooden beams: a theoretical review

Abstract

 In wood science, natural vibration analysis is being used to an increasing extent to characterise the longitudinal and the shear modulus of elacticity of various geometrical types of prismatic beams. A lateral or a axial percussion at one end of a beam set up on elastic support produces bending or longitudinal vibrations. Considering the hypothesis of the homogeneity of geometrical and mechanical properties of the beam, basic dynamics theorems can be applied to obtain the motion equations of longitudinal and transverse vibrations. The resolution of the differential equation for transverse motion leads to a search for solutions to the frequency equation. Because no exact analytical solution can be found, several approximate results are analysed. The application and validity range have to be defined to be able to achieve realistic results. The effects of the elastic support, the shear modulus and the height to length ratio are discussed. The conceptual bases help in understanding the analytical results and accuracy calculations can then be developed for practical applications. We present the most common theoretical models and define their validity range, application conditions, and accuracy levels with respect to measured values.