Torsional vibrations of a cylindrical shell in a linear viscoelastic medium

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.

Relative speed and temperature effect investigation of the of the drying agent on the moisture content of cotton

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Natural Vibrations of the Reinforced Tapered Shell with Taking Into Account the Viscoelastic Properties of the Material

“…The values of the rheological parameters of the shell are taken as = 0,048; = 0,05; = 0,1. Table 1 shows the complex values of the low frequencies of a reinforced (with four rods) truncated conical shell at different shell thicknesses in the limit of the Kirchhoff -Love hypothesis [26][27][28]. It is necessary to determine the values of the complex natural frequency and the corresponding oscillation forms when both ends of the shell contour are pivotally supported ( 1 = 1 = = = = 0).…”

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