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

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.