Cargando…
Solution for Determining Modulus of Elasticity of Natural Materials Using Vibrations of Non-Uniform Circular Cross-Section Cantilevers
The article presents an original method for determining the modulus of elasticity of natural materials. A studied solution was based on vibrations of non-uniform circular cross-section cantilevers solved using Bessel functions. The derived equations, together with experimental tests, allowed for cal...
Autores principales: | , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2023
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10224203/ https://www.ncbi.nlm.nih.gov/pubmed/37241495 http://dx.doi.org/10.3390/ma16103868 |
_version_ | 1785050121115795456 |
---|---|
author | Podgórski, Jerzy Kawecki, Bartosz |
author_facet | Podgórski, Jerzy Kawecki, Bartosz |
author_sort | Podgórski, Jerzy |
collection | PubMed |
description | The article presents an original method for determining the modulus of elasticity of natural materials. A studied solution was based on vibrations of non-uniform circular cross-section cantilevers solved using Bessel functions. The derived equations, together with experimental tests, allowed for calculating the material’s properties. Assessments were based on the measurement of the free-end oscillations in time using the Digital Image Correlation (DIC) method. They were induced manually and positioned at the end of a cantilever and monitored in time using a fast Vision Research Phantom v12.1 Camera with 1000 fps. GOM Correlate software tools were then used to find increments of deflection on a free end in every frame. It provided us with the ability to make diagrams containing a displacement–time relation. To find natural vibration frequencies, fast Fourier transform (FFT) analyses were conducted. The correctness of the proposed method was compared with a three-point bending test performed on a Zwick/Roell Z2.5 testing machine. The presented solution generates trustworthy results and can provide a method to confirm the elastic properties of natural materials obtained in various experimental tests. |
format | Online Article Text |
id | pubmed-10224203 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-102242032023-05-28 Solution for Determining Modulus of Elasticity of Natural Materials Using Vibrations of Non-Uniform Circular Cross-Section Cantilevers Podgórski, Jerzy Kawecki, Bartosz Materials (Basel) Article The article presents an original method for determining the modulus of elasticity of natural materials. A studied solution was based on vibrations of non-uniform circular cross-section cantilevers solved using Bessel functions. The derived equations, together with experimental tests, allowed for calculating the material’s properties. Assessments were based on the measurement of the free-end oscillations in time using the Digital Image Correlation (DIC) method. They were induced manually and positioned at the end of a cantilever and monitored in time using a fast Vision Research Phantom v12.1 Camera with 1000 fps. GOM Correlate software tools were then used to find increments of deflection on a free end in every frame. It provided us with the ability to make diagrams containing a displacement–time relation. To find natural vibration frequencies, fast Fourier transform (FFT) analyses were conducted. The correctness of the proposed method was compared with a three-point bending test performed on a Zwick/Roell Z2.5 testing machine. The presented solution generates trustworthy results and can provide a method to confirm the elastic properties of natural materials obtained in various experimental tests. MDPI 2023-05-21 /pmc/articles/PMC10224203/ /pubmed/37241495 http://dx.doi.org/10.3390/ma16103868 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Podgórski, Jerzy Kawecki, Bartosz Solution for Determining Modulus of Elasticity of Natural Materials Using Vibrations of Non-Uniform Circular Cross-Section Cantilevers |
title | Solution for Determining Modulus of Elasticity of Natural Materials Using Vibrations of Non-Uniform Circular Cross-Section Cantilevers |
title_full | Solution for Determining Modulus of Elasticity of Natural Materials Using Vibrations of Non-Uniform Circular Cross-Section Cantilevers |
title_fullStr | Solution for Determining Modulus of Elasticity of Natural Materials Using Vibrations of Non-Uniform Circular Cross-Section Cantilevers |
title_full_unstemmed | Solution for Determining Modulus of Elasticity of Natural Materials Using Vibrations of Non-Uniform Circular Cross-Section Cantilevers |
title_short | Solution for Determining Modulus of Elasticity of Natural Materials Using Vibrations of Non-Uniform Circular Cross-Section Cantilevers |
title_sort | solution for determining modulus of elasticity of natural materials using vibrations of non-uniform circular cross-section cantilevers |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10224203/ https://www.ncbi.nlm.nih.gov/pubmed/37241495 http://dx.doi.org/10.3390/ma16103868 |
work_keys_str_mv | AT podgorskijerzy solutionfordeterminingmodulusofelasticityofnaturalmaterialsusingvibrationsofnonuniformcircularcrosssectioncantilevers AT kaweckibartosz solutionfordeterminingmodulusofelasticityofnaturalmaterialsusingvibrationsofnonuniformcircularcrosssectioncantilevers |