Direct Determination of Dynamic Elastic Modulus and Poisson’s Ratio of Rectangular Timoshenko Prisms

Abstract

In this paper, the exact solution of the Timoshenko beam vibration frequency equation under free-free boundary conditions is determined with an accurate shear shape factor. The exact solution is compared with a three-dimensional (3D) finite element calculation using ABAQUS, and the difference between the exact solution and the 3D finite-element model are within 0.05% for both the transverse and torsional modes. Furthermore, a relationship between the resonance frequencies and Poisson’s ratio was proposed that can directly determine the elastic modulus and Poisson’s ratio simultaneously, without the need for iteration, unlike the equations provided by an industry standard. The frequency ratio between the first bending and torsional mode for any combination of specimen dimensions can be directly estimated. Rectangular concrete beam specimens with three different mix designs were produced, and the transverse and torsional frequencies of these beams were tested. Results show that using the equations proposed in this study, the Young’s modulus and Poisson’s ratio of the concrete beams can be determined more directly than those obtained from the industry standard and with excellent accuracy.