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.
Highlights
The analysis of the dynamic problems of elastic bodies is an important and interesting research field for engineers and scientists
Abd-Alla, et al [6] studied the effect of non-homogeneity on the composite infinite cylinder of isotropic material
The rotation of a non-homogeneous composite infinite cylinder of orthotropic and isotropic material, and the thermal stresses in a rotating non-homogeneous orthotropic hollow cylinder has been investigated by El-Naggar, et al [8]-[10]
Summary
The analysis of the dynamic problems of elastic bodies is an important and interesting research field for engineers and scientists. Abd-Alla, et al [6] studied the effect of non-homogeneity on the composite infinite cylinder of isotropic material. In [11], Abd-Alla et al investigated the effect of the rotation on a non-homogeneous infinite cylinder of orthotropic material. Abd-Alla et al [12] studied the propagation of S-wave in a non-homogeneous anisotropic incompressible and initially stressed medium under influence of gravity field. Abd-Alla, et al [15] [16] investigated the effect of the non-homogeneity on the composite infinite cylinder of isotropic and orthotropic materials. We study the effect of initial stress on the radial vibrations of elastic hollow cylinder with rotation of a cylindrical region hollow of radius a, b with different boundary conditions (free-fixed-mixed). The numerical results of the frequency equation are discussed and plotted graphically
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