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

Guadalupe Leon,Hung-Liang Chen

doi:10.3390/vibration2010010

Abstract

In this paper, the exact solution of the Timoshenko circular beam vibration frequency equation under free-free boundary conditions was determined with an accurate shear shape factor. The exact solution was compared with a 3-D finite element calculation using the ABAQUS program, and the difference between the exact solution and the 3-D finite element method (FEM) was within 0.15% for both the transverse and torsional modes. Furthermore, relationships between the resonance frequencies and Poisson’s ratio were proposed that can directly determine the elastic constants. The frequency ratio between the 1st bending mode and the 1st torsional mode, or the frequency ratio between the 1st bending mode and the 2nd bending mode for any rod with a length-to-diameter ratio, L/D ≥ 2 can be directly estimated. The proposed equations were used to verify the elastic constants of a steel rod with less than 0.36% error percentage. The transverse and torsional frequencies of concrete, aluminum, and steel rods were tested. Results show that using the equations proposed in this study, the Young’s modulus and Poisson’s ratio of a rod can be determined from the measured frequency ratio quickly and efficiently.

Highlights

Non-destructive testing (NDT) methods are often used to estimate the elastic properties of a material such as the dynamic elastic modulus and Poisson’s ratio
The proposed methods do not require any iterations to solve for the material constants
This paper presents a method to calculate Poisson’s ratio and dynamic elastic modulus using experimentally measured transverse and torsional modes

Summary

Introduction

Non-destructive testing (NDT) methods are often used to estimate the elastic properties of a material such as the dynamic elastic modulus and Poisson’s ratio. Nieves et al estimated the shear modulus and Poisson’s ratio for short cylinders using the two lowest axisymmetric natural frequencies [5]. Wang et al proposed a method to evaluate Poisson’s ratio of a rod with only two experimental impact-echo values (fundamental longitudinal and cross-sectional resonant frequencies). Their methods require an L/D ≥ 25υ for the dynamic Poisson’s ratio to be valid [6]

Methods

Findings

Discussion

Conclusion