The modified couple stress model for bending of normal deformable viscoelastic nanobeams resting on visco-Pasternak foundations |
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Authors: | Mohammed Sobhy Ashraf M Zenkour |
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Affiliation: | 1. Department of Mathematics and Statistics, Faculty of Science, King Faisal University, Hofuf, Saudi Arabia;2. Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh, Egyptmsobhy@kfu.edu.sahttps://orcid.org/0000-0002-5999-2169;4. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;5. Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh, Egypthttps://orcid.org/0000-0002-0883-8073 |
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Abstract: | ABSTRACTThe modified couple stress theory (MCST) is utilized to investigate the bending of viscoelastic nanobeams laying on visco-Pasternak elastic foundations based on a new shear and normal deformations beam theory. This model consists of the material length scale coefficient that captures the size impact on small-scale beams. The simply supported beam is made of viscoelastic material, subjected to time harmonic transverse load. The nanobeam is presumed to be laying on double layers of foundations. The first layer is modeled as Kelvin–Voigt viscoelastic model and the second is taken as a shear layer. Based on the proposed beam theory and MCST, the differential motion equations are deduced using Hamilton’s principle. To check the validity of the obtained formulations, the predicted results are compared with those available in the open literature. In addition, the influences of various parameters such as the material length scale parameter, length-to-depth ratio, viscoelastic damping structure, the stiffness and damping coefficients of the viscoelastic substrate, and shear and normal strains on the deflection and stresses are illustrated. |
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Keywords: | Modified couple stress model viscoelastic nanobeams bending beam theory |
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