Abstract
In this paper, the natural frequencies of the radial vibrations of a hollow cylinder and hollow sphere with different boundary conditions under influences of rotation and non-homogeneity have been studied. The radial vibrations of orthotropic material as affected by the angular velocity are investigated on the basis of the linear theory of elasticity. The of elastodynamic equations have been solved in analytical form. Numerical results are given and illustrated graphically for each case. Comparisons are made with previous results which given in the absence of rotation and non-homogeneity. The results indicate that the effect of rotation and non-homogeneity is very pronounced.
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This paper was recommended for publication in revised form by Associate Editor Kyeongsik Woo
Samy. R. Mahmoud was born in Sohag, Egypt, in 1971. He received his B. Sc. Degree from Assiut University, in 1994 with honors degree. He received his M. Sc. and Ph.D. degree in mathematics from Sohag University, in 2004. Now he is working as an Assistant professor of Mathematics, in faculty of Science, King Abdul Aziz University, Saudi Arabia. His research interests include theory of elasticity, vibration, thermoelasticity and fluid mechanics. He is the author or co-author of over 30 scientific publications, reviewer of many international journals in solid mechanics and applied mathematics. His research papers have been cited in many articles and textbooks. He authored many books in mathematics.
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Abd-Alla, A.M., Mahmoud, S.R. Analytical solution of wave propagation in a non-homogeneous orthotropic rotating elastic media. J Mech Sci Technol 26, 917–926 (2012). https://doi.org/10.1007/s12206-011-1241-y
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DOI: https://doi.org/10.1007/s12206-011-1241-y