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Research Article

Exact radial free vibration frequencies of a thick-walled sphere made of an isotropic and homogeneous material – A case study with a carbon nanofiller reinforced aluminum hollow sphere

Vebil Yıldırım

Çukurova University Department of Mechanical Engineering, Adana, Turkey

Keywords

Abstract


Exact free vibration, 

Natural frequency, 

Thick-walled sphere, 

Spherical Bessel’s,

 Metal-matrix composites (MMCs)

In this study exact free vibration analysis is performed for thick-walled hollow spheres made of an isotropic and homogeneous linear elastic material. Equation of motion in terms of Lame constants is derived from the field equations of elasticity, and then solved analytically with the help of spherical Bessel’s functions. This existing solution technique is extended to several boundary conditions. For each classical boundary condition, the characteristic free vibration equation is presented in closed forms. After verifying the present results with the available literature, variation of the dimensionless natural frequencies with respect to the boundary conditions and the sphere aspect ratio (outer radius/inner radius) are examined. To show the direct use of the present results, some of which are originals, a case study for a metal-matrix composite is originally studied. This composite material is formed by a perfect dispersion of either single-walled carbon-nanotubes (SWCNT) or multi-walled carbon-nanotubes (MWCNT) within an Aluminum (AL) metal matrix so that the resulting composite is still to have both isotropy and homogeneity properties. Elastic properties of the composite are computed by using the simple mixture rule and Halpin–Tsai equations.

 © 2018 MIM Research Group. All rights reserved.

DOI: http://dx.doi.org/10.17515/resm2017.24me0608                          Full Text

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22/02/2021 Indexed by InfoBase Index: We are informed that our journal is accepted to be included in the InfoBase Index. 


11/02/2021 Collaboration for ULIBTK 2021: Editorial Board of our journal and Organizing Committee of the 23. Congress on Thermal Science and Technology (ULIBTK 2021) have agreed to collaborate. Extended versions of the selected papers from the conference will be published in our journal. For more see Events.


31/12/2020 Most Cited Award: 

According to the Editorial Board evaluation, the paper authored by Nelson Batista, Rui Melicio, Victor Mendes entitled as “Darrieus vertical axis wind turbines: methodology to study the self-start capabilities considering symmetric and asymmetric airfoils" is awarded the 2020 Most Cited Paper Award of Research on Engineering Structures and Materials (RESM).


31/12/2020 Best Paper Award:

According to the Advisory Board decision, the paper authored by Marcelo Mesquita do Amaral, Matheus Wanglon Ferreira and Mauro de Vasconcellos Real entitled as “A simplified method for analysis of reinforced concrete beams exposed to fire situation” is awarded the 2020 Best Paper Award of Research on Engineering Structures and Materials (RESM).


02/11/2020 Indexed by SCOPUS: We are informed that our journal is accepted to be included in the SCOPUS Index. See news for more info.


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LATEST AWARDS


2020 Most Cited Paper Award:

The paper authored by Nelson Batista, Rui Melicio, Victor Mendes entitled as “Darrieus vertical axis wind turbines: methodology to study the self-start capabilities considering symmetric and asymmetric airfoils" is awarded the


2020 Best Paper Award:

The paper authored by Ahsen Ünal, Işıl Özer, Melek Erol Taygun, Sadriye Küçükbayrak entitled as “Fabrication and in-vitro evaluation of copper doped bioactive glass/polymer composite scaffolds for bone tissue engineering” is awarded the 


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Last Update:

27.02.2021

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