On Influence of Imperfect Contact Conditions on Natural Frequencies of Three-Layer Hollow Sphere for Torsional Vibration

Abstract

This work investigates the effects of imperfect contact conditions on the interface of the layers of a three-layer hollow sphere on its natural frequencies under torsional vibrations. This study is carried out within the framework of the piecewise homogeneous body model by using the three-dimensional exact equations and relations of elastodynamics. The shear-spring type model describes the imperfect contact conditions between the layers of the sphere. Analytic-numeric method is used for solving the problem, and the expressions of the required quantities are determined analytically using the Helmholtz representations. The resulting transcendental equation for determining the natural frequencies from the contact and boundary conditions is solved numerically using the algorithm and PC programs developed by the authors. Numerical results on the effect of imperfection parameters on the natural frequencies of the sphere are discussed, and it is established that the indicated effect on the natural frequencies of the torsional vibration is quantitative and qualitative.