Free vibrations of simply supported double plate on two models of elastic soils

In this paper the free vibrations of simply supported rectangular plates, resting on two different models of soils, are considered. The first model called Het´enyi, by the name of the deviser, assumes a continuous plate, embedded in a Winkler-type soil to realize the foundation partial continuity. The upper plate rests on a multiple layer characterized by a Winkler-type soil, a continuous plate and another Winkler-type soil in sequence. The two Winkler-type soils have different modules. In the second model, the plate will be embedded in two layers of soils, whose behavior is similar to that of the Pasternak–Kerr-type soil. The two models have been already used for the study of the double beam system. The free motions, in both cases, are described by a homogeneous set of partial differential equations, based on Kirchhoff–Love theory. Next, the homogeneous equations of motion are solved by using the classical Navier method. The free frequencies and associated vibration mode shapes of double plate system are found and numerical examples are illustrated to compare the two models.