Analysis of Rectangular Plate Vibrations in a Fractional Derivative Viscous Medium
An original method for solving the problem on transient vibrations of rectangular plates in viscous medium, when the viscoelastic features are described by fractional derivatives, has been presented in this article. It is based on the assumption that each mode of vibrations has its own damping coefficient and its own retardation time. The Laplace integral transform method is employed as a method of solution, which is followed by the expansion of the desired functions in series with respect to eigenfunctions of the problem. As this takes place, during the transition from image to pre--image, the nonrationalized characteristic equation with fractional powers is solved by the method suggested by the authors. The solution is obtained in the form of the sum of two terms, one of which governs the drift of the system's equilibrium position
and is defined by the quasi--static processes of creep occurring in the system, and the other term describes damped vibrations around the equilibrium position and is determined by the systems's inertia and energy dissipation.