Effect of Initial Stress on Wave Frequencies of Elastic Solid with Rotation

G. A. Yahya^1,2*, S. H. Elhag³, M. F. Sanaa^1,2, A. M. A. Amry^1,4, A. M. Abd-Alla^3,5

¹Physics Department, Faculty of Science, Taif University, Taif, KSA.
²Physics Department, Faculty of Science, Aswan University, Aswan, Egypt.
³Mathematics Department, Faculty of Science, Taif University, Taif, KSA.
⁴Physics Department, Faculty of Science, Assiut University, Assiut, Egypt.
⁵Mathematics Department, Faculty of Science, Sohag University, Sohag, Egypt.

DOI: 10.4236/jmp.2014.518197                

Abstract

In this paper, the effect of initial stress on the radial vibrations of elastic hollow cylinder with rotation is discussed. The one-dimensional equation of elastodynamic is solved in terms of radial displacement. The frequency equation is obtained when the boundaries are free; fixed and mixed boundary condition is examined numerically. The determination is concerned with the eigenvalues of the natural frequency of the radial vibrations in the case of harmonic vibrations. The effect of rotation and initial stress on the natural frequencies was examined. It was shown that the dispersion curves of guided waves were significantly influenced by the rotation and initial stress of the elastic cylinder. Numerical results are given and illustrated graphically for each case considered. The results indicate that the effect of rotation and initial stress are very pronounced.

Keywords

Ealstodynamics, Radial Vibrations, Isotropic Material, Rotation, Elastic Hollow Cylinder, Initial Stress

Conflicts of Interest

The authors declare no conflicts of interest.

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