Unstationary interaction of a three-layer plate with a dying plane wave in elastic transient stress-strain | Mekhanika | kompozitsionnykh | materialov i konstruktsii

### Unstationary interaction of a three-layer plate with a dying plane wave in elastic transient stress-strain

#### Abstract:

A study of the interaction of a three-layer plate with a damped plane wave in the soil has been carried out. As a model of an obstacle in the soil, a three-layer plate is considered, described by the system of equations of V.N. Paimushin, placed in the soil and dividing it into two parts. A flat formulation of the problem is considered. The boundary conditions correspond to the hinge fixation of the obstacle, and the initial conditions are zero. A damped plane wave induced in one of the semi-media is considered as an external influence. To describe the motion of the soil, the equations of the theory of elasticity, the Cauchy relations and the physical law, or their equivalent displacements in potentials and the Lame equations, are used. The problem is solved in a related setting, where the movement of platinum and its surroundings is considered together. All components of the equations of motion of the plate and media are expanded into trigonometric series that satisfy the boundary conditions, and the Laplace transform is applied to them. To specify a plane damped incident wave, the scalar potentials of the displacement field are considered, to which the Laplace transform in time and the expansion into a trigonometric series in coordinate are also applied. The equality of normal displacements and stresses at the interface between the medium and the plate is taken as the conditions for contact between the plate and the soil. It is also considered that the pressure amplitudes and normal stresses coincide. After determining the constants from the contact conditions, the displacement values and the values of normal and tangential stresses are found, after which their originals are found. Since the analytical determination of the originals of functions is impossible, the Durbin method is applied.

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