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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Semnan University
2023-11-01
|
| Series: | Mechanics of Advanced Composite Structures |
| Subjects: | |
| Online Access: | https://macs.semnan.ac.ir/article_7282_7f582411eb455271b977091219b08a3b.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850116665721749504 |
|---|---|
| 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. |
| format | Article |
| id | doaj-art-d8eabe3ab92a458ca4382ee648ecf708 |
| institution | OA Journals |
| issn | 2423-4826 2423-7043 |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Semnan University |
| record_format | Article |
| series | Mechanics of Advanced Composite Structures |
| 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 |