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

Chen, Hung-Liang; Leon, Guadalupe

doi:10.1061/(asce)em.1943-7889.0001643

Cited by 2 publications

(1 citation statement)

References 13 publications

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“…The ratio between the 2nd and 1st longitudinal resonance frequencies was used to determine the Poisson's ratio for a variety of length-to-diameter ratios (L/D) and afterward the elastic modulus was estimated. Similarly, Chen and Leon proposed a method to find the two elastic constants using the 1st bending mode and the 1st torsional for rectangular prisms [4]. Nieves et al also estimated the shear modulus and Poisson's ratio for short cylinders using the two lowest axisymmetric natural frequencies [5].…”

Section: Introductionmentioning

confidence: 99%

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

Leon

Chen

2019

Vibration

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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.

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Section: Introductionmentioning

confidence: 99%

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

Leon

Chen

2019

Vibration

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Simplified Calculation of Shear Rotations for First-Order Shear Deformation Theory in Deep Bridge Beams

Emadi

Galant

et al. 2023

Applied Sciences

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Nodal rotations are produced by bending and shear effects and bending rotations can be easily calculated using Euler–Bernoulli’s stiffness matrix method. Nevertheless, shear rotations are traditionally neglected, as their effects are practically negligible in most structures. This assumption might lead to significant errors in the simulation of the rotations in some structures, as well as the wrong identification of the mechanical properties in inverse analysis. Despite its important role, no other works studying the calculation of shear rotations in deep beams were found in the literature. To fill this gap, after illustrating the errors of commercial software regarding calculating the rotations in deep beams, this study proposed a simple and intuitive method to calculate shear rotations in both isostatic and statically redundant beams. The new method calculates the shear rotation for all segments separately and introduces the result to the total rotation of the structure. This method can be applied to find the shear rotation in a redundant structure as well. A parametric study was carried out to calculate slenderness ratios to determine in what structural systems the shear rotations can be neglected. In addition, the errors in the inverse analysis of deep beams were parametrically studied to determine the role of shear rotation in different structural systems. Finally, to validate the application of the method in actual structures, a construction stage of a composite bridge was analyzed.

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

Cited by 2 publications

References 13 publications

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

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

Simplified Calculation of Shear Rotations for First-Order Shear Deformation Theory in Deep Bridge Beams

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