Mathematical Modeling of the Effect of Temperature on the Dynamic Characteristics of a Cantilever Beam with Flexible Root

This study presents the development of an analytical solution for the dynamic response of a cantilever beam with a flexible root taking into account the influence of temperature. The investigated cantilever beam has a uniform rectangular cross-section with finite lengths. The dynamic response of the...

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Main Authors: Samaher Mohammed Sarhan, Salah Al-Zubaidi
Format: Article
Language:English
Published: Wiley 2023-01-01
Series:The Scientific World Journal
Online Access:http://dx.doi.org/10.1155/2023/6568120
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author Samaher Mohammed Sarhan
Salah Al-Zubaidi
author_facet Samaher Mohammed Sarhan
Salah Al-Zubaidi
author_sort Samaher Mohammed Sarhan
collection DOAJ
description This study presents the development of an analytical solution for the dynamic response of a cantilever beam with a flexible root taking into account the influence of temperature. The investigated cantilever beam has a uniform rectangular cross-section with finite lengths. The dynamic response of the cantilever was investigated under three conditions, namely, rigid root, resilient root, and resilient root accompanied by different surrounding temperatures. The selected lengths for the beam were 0.3175, 0.1588, 0.1058, 0.0794, 0.0635, 0.0529, 0.0454, 0.0397, 0.0353, and 0.03175 m. The chosen linear spring coefficients were 0.01, 0.1, 100, and ∞ N/m while rotational spring coefficients were 0.01, 0.1, 100, and ∞ N·m/rad. The surrounding temperatures for the third condition were −100, 25, 100, and 200°C. A MATLAB code was developed to calculate the fundamental natural frequency under different surrounding temperatures and spring coefficients. The proposed mathematical solution was validated with real experimental data and the verification findings revealed a good match between them. For the rigid condition, the finding revealed good matching between the analytical model and experimental results, particularly at the length range of 0.3175−0.1058 m. For the resilient condition, the fundamental natural frequencies were found to be highly affected by decreasing beam length and increased at 100 N/m and 100 N·m/rad and higher coefficients. Finally, there was a reduction in the calculated natural frequencies with increasing temperature.
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spelling doaj-art-6d205c338c17403b8fd97bded264e07a2025-08-20T02:24:03ZengWileyThe Scientific World Journal1537-744X2023-01-01202310.1155/2023/6568120Mathematical Modeling of the Effect of Temperature on the Dynamic Characteristics of a Cantilever Beam with Flexible RootSamaher Mohammed Sarhan0Salah Al-Zubaidi1Department of Mechatronics EngineeringDepartment of Automated Manufacturing EngineeringThis study presents the development of an analytical solution for the dynamic response of a cantilever beam with a flexible root taking into account the influence of temperature. The investigated cantilever beam has a uniform rectangular cross-section with finite lengths. The dynamic response of the cantilever was investigated under three conditions, namely, rigid root, resilient root, and resilient root accompanied by different surrounding temperatures. The selected lengths for the beam were 0.3175, 0.1588, 0.1058, 0.0794, 0.0635, 0.0529, 0.0454, 0.0397, 0.0353, and 0.03175 m. The chosen linear spring coefficients were 0.01, 0.1, 100, and ∞ N/m while rotational spring coefficients were 0.01, 0.1, 100, and ∞ N·m/rad. The surrounding temperatures for the third condition were −100, 25, 100, and 200°C. A MATLAB code was developed to calculate the fundamental natural frequency under different surrounding temperatures and spring coefficients. The proposed mathematical solution was validated with real experimental data and the verification findings revealed a good match between them. For the rigid condition, the finding revealed good matching between the analytical model and experimental results, particularly at the length range of 0.3175−0.1058 m. For the resilient condition, the fundamental natural frequencies were found to be highly affected by decreasing beam length and increased at 100 N/m and 100 N·m/rad and higher coefficients. Finally, there was a reduction in the calculated natural frequencies with increasing temperature.http://dx.doi.org/10.1155/2023/6568120
spellingShingle Samaher Mohammed Sarhan
Salah Al-Zubaidi
Mathematical Modeling of the Effect of Temperature on the Dynamic Characteristics of a Cantilever Beam with Flexible Root
The Scientific World Journal
title Mathematical Modeling of the Effect of Temperature on the Dynamic Characteristics of a Cantilever Beam with Flexible Root
title_full Mathematical Modeling of the Effect of Temperature on the Dynamic Characteristics of a Cantilever Beam with Flexible Root
title_fullStr Mathematical Modeling of the Effect of Temperature on the Dynamic Characteristics of a Cantilever Beam with Flexible Root
title_full_unstemmed Mathematical Modeling of the Effect of Temperature on the Dynamic Characteristics of a Cantilever Beam with Flexible Root
title_short Mathematical Modeling of the Effect of Temperature on the Dynamic Characteristics of a Cantilever Beam with Flexible Root
title_sort mathematical modeling of the effect of temperature on the dynamic characteristics of a cantilever beam with flexible root
url http://dx.doi.org/10.1155/2023/6568120
work_keys_str_mv AT samahermohammedsarhan mathematicalmodelingoftheeffectoftemperatureonthedynamiccharacteristicsofacantileverbeamwithflexibleroot
AT salahalzubaidi mathematicalmodelingoftheeffectoftemperatureonthedynamiccharacteristicsofacantileverbeamwithflexibleroot