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Structural Engineering and Mechanics Volume 57, Number 2, January25 2016 , pages 239-63 DOI: https://doi.org/10.12989/sem.2016.57.2.239 |
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Natural vibration of the three-layered solid sphere with middle layer made of FGM: three-dimensional approach |
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Surkay D. Akbarov, Hatam H. Guliyev and Nazmiye Yahnioglu
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| Abstract | ||
| The paper studies the natural oscillation of the three-layered solid sphere with a middle layer made of Functionally Graded Material (FGM). It is assumed that the materials of the core and outer layer of the sphere are homogeneous and isotropic elastic. The three-dimensional exact equations and relations of linear elastodynamics are employed for the investigations. The discrete-analytical method proposed by the first author in his earlier works is applied for solution of the corresponding eigenvalue problem. It is assumed that the modulus of elasticity, Poisson\'s ratio and density of the middle-layer material vary continuously through the inward radial direction according to power law distribution. Numerical results on the natural frequencies related to the torsional and spheroidal oscillation modes are presented and discussed. In particular, it is established that the increase of the modulus of elasticity (mass density) in the inward radial direction causes an increase (a decrease) in the values of the natural frequencies. | ||
| Key Words | ||
| functionally graded material; three-layered solid sphere; natural vibration; natural frequencies; torsional oscillation; spheroidal oscillation | ||
| Address | ||
| Surkay D. Akbarov: Department of Mechanical Engineering, Yildiz Technical University, Yildiz Campus, 34349, Besiktas, Istanbul, Turkey; Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan, AZ1141, Baku, Azerbaijan Hatam H. Guliyev: Institute of Geology and Geophysics of the National Academy of Sciences of Azerbaijan, AZ1073, Baku, Azerbaijan Nazmiye Yahnioglu: Department of Mathematical Engineering, Yildiz Technical University, Davutpasa Campus, 34220, Esenler Istanbul, Turkey | ||