Longitudinal Vibration Analysis of a Stepped Nonlocal Rod Embedded in Several Elastic Media

Tamer Elsayed; Moustafa S.  Taima; Said H.  Farghaly

doi:10.1007/s42417-022-00454-7

Longitudinal Vibration Analysis of a Stepped Nonlocal Rod Embedded in Several Elastic Media

Tamer Elsayed^* (Corresponding Author), Moustafa S. Taima, Said H. Farghaly

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

2 Downloads (Pure)

Abstract

Purpose
Mechanical properties of 1D nanostructures are of great importance in nanoelectromechanical systems (NEMS) applications. The free vibration analysis is a non-destructive technique for evaluating Young's modulus of nanorods and for detecting defects in nanorods. Therefore, this paper aims to study the longitudinal free vibration of a stepped nanorod embedded in several elastic media.

Methods
The analysis is based on Eringen’s nonlocal theory of elasticity. The governing equation is obtained using Hamilton’s principle and then transformed into the nonlocal analysis. The dynamic stiffness matrix (DSM) method is used to assemble the rod segments equations. The case of a two-segment nanorod embedded in two elastic media is then deeply investigated.

Results
The effect of changing the elastic media stiffness, the segments stiffness ratio, boundary conditions and the nonlocal parameter are examined. The nano-rod spectrum and dispersion relations are also investigated.

Conclusion
The results show that increasing the elastic media stiffness and the segment stiffness ratio increases the natural frequencies. Furthermore, increasing the nonlocal parameter reduces natural frequencies slightly at lower modes and significantly at higher modes.

Original language	English
Pages (from-to)	1399–1412
Number of pages	14
Journal	Journal of Vibration Engineering & Technologies
Volume	10
Issue number	4
Early online date	28 Mar 2022
DOIs	https://doi.org/10.1007/s42417-022-00454-7
Publication status	Published - 1 Jun 2022

Keywords

Nanorod
Stepped rod
Exact solution
Elastic media
Continuum mechanics
Dynamic stiffness matrix

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Cite this

@article{822c9fb02f0644b7814e0b065731aed5,

title = "Longitudinal Vibration Analysis of a Stepped Nonlocal Rod Embedded in Several Elastic Media",

abstract = "PurposeMechanical properties of 1D nanostructures are of great importance in nanoelectromechanical systems (NEMS) applications. The free vibration analysis is a non-destructive technique for evaluating Young's modulus of nanorods and for detecting defects in nanorods. Therefore, this paper aims to study the longitudinal free vibration of a stepped nanorod embedded in several elastic media.MethodsThe analysis is based on Eringen{\textquoteright}s nonlocal theory of elasticity. The governing equation is obtained using Hamilton{\textquoteright}s principle and then transformed into the nonlocal analysis. The dynamic stiffness matrix (DSM) method is used to assemble the rod segments equations. The case of a two-segment nanorod embedded in two elastic media is then deeply investigated.ResultsThe effect of changing the elastic media stiffness, the segments stiffness ratio, boundary conditions and the nonlocal parameter are examined. The nano-rod spectrum and dispersion relations are also investigated.ConclusionThe results show that increasing the elastic media stiffness and the segment stiffness ratio increases the natural frequencies. Furthermore, increasing the nonlocal parameter reduces natural frequencies slightly at lower modes and significantly at higher modes.",

keywords = "Nanorod, Stepped rod, Exact solution, Elastic media, Continuum mechanics, Dynamic stiffness matrix",

author = "Tamer Elsayed and Taima, {Moustafa S.} and Farghaly, {Said H.}",

year = "2022",

month = jun,

day = "1",

doi = "10.1007/s42417-022-00454-7",

language = "English",

volume = "10",

pages = "1399–1412",

journal = "Journal of Vibration Engineering & Technologies",

issn = "2523-3939",

publisher = "Springer ",

number = "4",

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TY - JOUR

T1 - Longitudinal Vibration Analysis of a Stepped Nonlocal Rod Embedded in Several Elastic Media

AU - Elsayed, Tamer

AU - Taima, Moustafa S.

AU - Farghaly, Said H.

PY - 2022/6/1

Y1 - 2022/6/1

N2 - PurposeMechanical properties of 1D nanostructures are of great importance in nanoelectromechanical systems (NEMS) applications. The free vibration analysis is a non-destructive technique for evaluating Young's modulus of nanorods and for detecting defects in nanorods. Therefore, this paper aims to study the longitudinal free vibration of a stepped nanorod embedded in several elastic media.MethodsThe analysis is based on Eringen’s nonlocal theory of elasticity. The governing equation is obtained using Hamilton’s principle and then transformed into the nonlocal analysis. The dynamic stiffness matrix (DSM) method is used to assemble the rod segments equations. The case of a two-segment nanorod embedded in two elastic media is then deeply investigated.ResultsThe effect of changing the elastic media stiffness, the segments stiffness ratio, boundary conditions and the nonlocal parameter are examined. The nano-rod spectrum and dispersion relations are also investigated.ConclusionThe results show that increasing the elastic media stiffness and the segment stiffness ratio increases the natural frequencies. Furthermore, increasing the nonlocal parameter reduces natural frequencies slightly at lower modes and significantly at higher modes.

AB - PurposeMechanical properties of 1D nanostructures are of great importance in nanoelectromechanical systems (NEMS) applications. The free vibration analysis is a non-destructive technique for evaluating Young's modulus of nanorods and for detecting defects in nanorods. Therefore, this paper aims to study the longitudinal free vibration of a stepped nanorod embedded in several elastic media.MethodsThe analysis is based on Eringen’s nonlocal theory of elasticity. The governing equation is obtained using Hamilton’s principle and then transformed into the nonlocal analysis. The dynamic stiffness matrix (DSM) method is used to assemble the rod segments equations. The case of a two-segment nanorod embedded in two elastic media is then deeply investigated.ResultsThe effect of changing the elastic media stiffness, the segments stiffness ratio, boundary conditions and the nonlocal parameter are examined. The nano-rod spectrum and dispersion relations are also investigated.ConclusionThe results show that increasing the elastic media stiffness and the segment stiffness ratio increases the natural frequencies. Furthermore, increasing the nonlocal parameter reduces natural frequencies slightly at lower modes and significantly at higher modes.

KW - Nanorod

KW - Stepped rod

KW - Exact solution

KW - Elastic media

KW - Continuum mechanics

KW - Dynamic stiffness matrix

U2 - 10.1007/s42417-022-00454-7

DO - 10.1007/s42417-022-00454-7

M3 - Article

SN - 2523-3939

VL - 10

SP - 1399

EP - 1412

JO - Journal of Vibration Engineering & Technologies

JF - Journal of Vibration Engineering & Technologies

IS - 4

ER -

Longitudinal Vibration Analysis of a Stepped Nonlocal Rod Embedded in Several Elastic Media

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Keywords

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