7TH INTERNATIONAL EURASIAN CONFERENCE ON MATHEMATICAL SCIENCES AND APPLICATIONS KYIV - UKRAINE, Kiev, Ukraine, 28 August 2018, vol.1, pp.1
In the present study, the influence of material constants on the torsional vibration
of a hollow sphere with non-homogeneous initial stresses is studied within the exact equations of three dimensional linearized theory of elastic waves in initially stressed bodies .The material of the sphere is assumed homogeneous and isotropic and the uniform radial forces act on the inner or outer surfaces of the sphere that cause inhomogeneous initial stresses in this sphere. Solutions of the corresponding eigenvalue problems for the inhomogeneous initial stressed hollow sphere require to solution of the system of three partial di erential equations with variable coecients. So, the solution of this system is achieved by using the discrete-analytical solution method proposed in [2, 3]. The influence of some material parameters as well as initial stresses
on the natural frequencies of the torsional vibration of this sphere are analyzed and discussed. Analyzing the numerical results show that material constants and initial stresses in the sphere are signi cantly a ected on the fundamental frequency of the torsional vibration of the considered sphere.