Analysis of Damped Vibrations of a Cylindrical Shell Embedded into a Fractional Derivative Viscoelastic Medium

摘要

Damped vibrations of elastic circular cylindrical shells embedded into a viscoelastic medium, the rheological features of which are described by fractional derivatives, are considered in the present paper. Besides the forces of viscous friction, the shell is subjected to the action of external forces dependent on the coordinates of the middle surface and time. The boundary conditions are proposed in such a way that the governing equations allow the Navier-type solution. The Laplace integral transform method of expansion of all functions entering into the set of governing equations in terms of the eigen-functions of the given problem are used as the methods of solution. It is shown that as a result of such a procedure the systems of equations in the generalized coordinates could be reduced to infinite sets of uncoupled equations, each of which describes damped vibrations of a mechanical oscillator based on the fractional derivative Kelvin-Voigt model.