Longitudinal Vibration of Nanobeams by Two-Phase Local/Nonlocal Elasticity, Rayleigh Theory, and Generalized Differential Quadrature Method

To solve a differential equation of motion via more reliable procedures, it is essential to realize their efficiency. Whether Rayleigh's theory can be a compatible platform with two-phase local/nonlocal elasticity to render more reliable results compared to other theories or not is the main que...

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Main Authors: Reza Nazemnezhad, Roozbeh Ashrafian
Format: Article
Language:English
Published: Semnan University 2023-11-01
Series:Mechanics of Advanced Composite Structures
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Online Access:https://macs.semnan.ac.ir/article_7282_7f582411eb455271b977091219b08a3b.pdf
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author Reza Nazemnezhad
Roozbeh Ashrafian
author_facet Reza Nazemnezhad
Roozbeh Ashrafian
author_sort Reza Nazemnezhad
collection DOAJ
description To solve a differential equation of motion via more reliable procedures, it is essential to realize their efficiency. Whether Rayleigh's theory can be a compatible platform with two-phase local/nonlocal elasticity to render more reliable results compared to other theories or not is the main question that will be answered by this paper. Thus, nanobeam modeled by Rayleigh beam theory is analyzed by two-phase local/nonlocal elasticity. Governing equation in presence of the axial and transverse displacements is derived by means of Hamilton’s principle and differential law of two-phase elasticity. Next, fourth-order Generalized Differential Quadrature Method (GDQM) is utilized to attain the discretized two-phase formulation. In order to confirm, the method and the results are compared with the exact solution prepared and presented in the literature. Moreover, the effects of various parameters such as geometrical properties like thickness, mode shape number, Local phase fraction coefficient, and nonlocal factor on the natural frequency are investigated to clarify that utilizing these theories with a common goal how ends with more accurate results, and how affects the natural frequencies.
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spelling doaj-art-d8eabe3ab92a458ca4382ee648ecf7082025-08-20T02:36:16ZengSemnan UniversityMechanics of Advanced Composite Structures2423-48262423-70432023-11-0110222123210.22075/macs.2023.25701.13747282Longitudinal Vibration of Nanobeams by Two-Phase Local/Nonlocal Elasticity, Rayleigh Theory, and Generalized Differential Quadrature MethodReza Nazemnezhad0Roozbeh Ashrafian1School of Engineering, Damghan University, Damghan, IranSchool of Engineering, Damghan University, Damghan, IranTo solve a differential equation of motion via more reliable procedures, it is essential to realize their efficiency. Whether Rayleigh's theory can be a compatible platform with two-phase local/nonlocal elasticity to render more reliable results compared to other theories or not is the main question that will be answered by this paper. Thus, nanobeam modeled by Rayleigh beam theory is analyzed by two-phase local/nonlocal elasticity. Governing equation in presence of the axial and transverse displacements is derived by means of Hamilton’s principle and differential law of two-phase elasticity. Next, fourth-order Generalized Differential Quadrature Method (GDQM) is utilized to attain the discretized two-phase formulation. In order to confirm, the method and the results are compared with the exact solution prepared and presented in the literature. Moreover, the effects of various parameters such as geometrical properties like thickness, mode shape number, Local phase fraction coefficient, and nonlocal factor on the natural frequency are investigated to clarify that utilizing these theories with a common goal how ends with more accurate results, and how affects the natural frequencies.https://macs.semnan.ac.ir/article_7282_7f582411eb455271b977091219b08a3b.pdflongitudinal vibrationnanobeamtwo-phase elasticity
spellingShingle Reza Nazemnezhad
Roozbeh Ashrafian
Longitudinal Vibration of Nanobeams by Two-Phase Local/Nonlocal Elasticity, Rayleigh Theory, and Generalized Differential Quadrature Method
Mechanics of Advanced Composite Structures
longitudinal vibration
nanobeam
two-phase elasticity
title Longitudinal Vibration of Nanobeams by Two-Phase Local/Nonlocal Elasticity, Rayleigh Theory, and Generalized Differential Quadrature Method
title_full Longitudinal Vibration of Nanobeams by Two-Phase Local/Nonlocal Elasticity, Rayleigh Theory, and Generalized Differential Quadrature Method
title_fullStr Longitudinal Vibration of Nanobeams by Two-Phase Local/Nonlocal Elasticity, Rayleigh Theory, and Generalized Differential Quadrature Method
title_full_unstemmed Longitudinal Vibration of Nanobeams by Two-Phase Local/Nonlocal Elasticity, Rayleigh Theory, and Generalized Differential Quadrature Method
title_short Longitudinal Vibration of Nanobeams by Two-Phase Local/Nonlocal Elasticity, Rayleigh Theory, and Generalized Differential Quadrature Method
title_sort longitudinal vibration of nanobeams by two phase local nonlocal elasticity rayleigh theory and generalized differential quadrature method
topic longitudinal vibration
nanobeam
two-phase elasticity
url https://macs.semnan.ac.ir/article_7282_7f582411eb455271b977091219b08a3b.pdf
work_keys_str_mv AT rezanazemnezhad longitudinalvibrationofnanobeamsbytwophaselocalnonlocalelasticityrayleightheoryandgeneralizeddifferentialquadraturemethod
AT roozbehashrafian longitudinalvibrationofnanobeamsbytwophaselocalnonlocalelasticityrayleightheoryandgeneralizeddifferentialquadraturemethod