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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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25/12/2019 Most Cited Paper Award: The paper authored by Manoj Sahni and Sanjeev Sharma entitled as “Elastic-plastic deformation of a thin rotating solid disk of exponentially varying density" is awarded the 2019 Most Cited Paper Award of Research on Engineering Structures and Materials (RESM).

25/12/2019 Best Paper Award: 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 2019 Best Paper Award of Research on Engineering Structures and Materials (RESM).


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LATEST AWARDS


2019 Most Cited Paper Award:

The paper authored by Manoj Sahni and Sanjeev Sharma entitled as “Elastic-plastic deformation of a thin rotating solid disk of exponentially varying density" is awarded the


2019 Best Paper Award:

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 


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Last Update:

15.02.2020

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