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The bendings of plates on an elastic base with variable susceptibility coefficient

Consideration is given to rectangular plates of two opposite borders, freely supported, and with the others having arbitrary boundary conditions resting on a single parameter Winkler type base with variable susceptibility coefficient. The problem was investigated to an infinite set of integral equations indicating certain particular cases for which this set leads to an infinite set or to finite sets of operating equations. The solution obtained is characterized by a considerable degree of generality. This was achieved by the application of Mikusiński's operators. To emphasize this fact, the continuous plates are considered as special cases of plates on an elastic base, yielding very simple solutions in the form of finite sets (systems) of algebraic equations.