Torsional vibrations of a cylindrical shell in a linear viscoelastic medium
Ismoil Safarov, M. Kh. Teshaev, Elyor Toshmatov, Zafar Ihterovich Boltaev, Farhod Homidov
Abstract
Abstract In this paper, we consider the natural vibrations of inhomogeneous mechanical systems, i.e., cylindrical bodies located in a deformable viscoelastic medium. The theory and methods for studying the natural vibrations of a cylindrical shell in a viscoelastic medium are constructed. The viscoelastic properties of the medium are taken into account using the hereditary Boltzmann-Walter theory. For the statement of the problem, the general equation of the theory of viscoelasticity in the potentials of displacements in a cylindrical coordinate system is used. An algorithm has been developed to solve the tasks posed on a computer using the Bessel, Hankel, and Mueller and Gauss methods. The considered problems were reduced to finding complex natural frequencies for the system of equations of motion of a cylindrical shell in an infinite viscoelastic medium using radiation conditions. It is shown that the problem has a discrete complex spectrum. The eigen frequencies of oscillations of a low-contrast heterogeneity are found. Revealed that the imaginary part of the eigen frequencies is comparable with the real one, which can lead to aperiodic movements of the systems considered.