Vibrations of a solid sphere or shell of Functionally Graded Materials |
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| Affiliation: | 1. Department of Computer Science, The University of Calgary, Calgary, Alberta, Canada T2N-1N4;2. Department of Mathematics and Statistics, The University of Calgary, Calgary, Alberta, Canada T2N-1N4;1. State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China;2. College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, China;1. Department of Engineering, Aarhus University, Denmark;2. Department of Civil Engineering, Technical University of Denmark, Denmark;1. Department of Chemical, Materials and Production Engineering, University of Naples Federico II, Piazzale Tecchio 80, 80125 Naples, Italy;2. Istituto Motori, National Research Council of Italy, Viale Marconi 4, 80125 Naples, Italy |
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| Abstract: | We have solved the equation of equilibrium for torsional vibrations of a sphere in which the density and rigidity are functions of the radial distance and co-latitude. Making use of the particular forms of heterogeneity the exact frequency equations are derived. The work is motivated by the recent research activity on functionally graded materials (FGM), i.e. materials with spatially varying properties tailored to satisfy particular engineering applications. |
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