The influence of imperfect contact conditions on the natural frequencies of a three-layer hollow sphere for high-order harmonics (pp.480-494)
Yu.M. Sevdimaliyev¹
https://doi.org/10.30546/1683-6154.22.4.2023.480

¹Department of Theoretical and Continuum Mechanics, Faculty of Mechanics and Mathematics, Baku State University, Baku, Z. Khalilov Str., 33, AZ 1148, Azerbaijan, e-mail: yusifsev@bsu.edu.az

Abstract. This work investigates the effects of imperfect contact conditions on the interface of the layers of a three-layer hollow sphere on their natural frequencies of higher-order spherical harmonics. 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 imperfect contact conditions between the layers of the sphere are described by the “shear-spring” type model. To solve the problem, an analytic-numerical method is used, and the expressions of the required quantities are determined analytically using the Helmholtz representations. The resulting transcendental equation for determining natural frequencies from the contact and boundary conditions is solved numerically using the algorithm developed by the author with the aid of PC programs. Numerical results on the effect of imperfection parameters on the natural frequencies of the higher harmonics of the sphere are discussed, and it is established that the indicated effect on higher harmonics is not only quantitative, but also qualitative.

Keywords: Natural Frequencies of Higher Modes, Hollow Three-Layer Sphere, Imperfect Contact, Spheroidal Oscillations Mode.

AMS Subject Classification: 74F10.