THE INFLUENCE OF MASS AND INERTIAL CHARACTERISTICS OF AN ADDITIONAL VISCOELASTIC SUPPORT IN THE NONSTATIONARY DEFORMING OF A RECTANGULAR PLATE

The nonstationary loading of a mechanical system consisting of a rectangular elastic isotropic plate and an additional viscoelastic support is investigated. The main attention is devoted to taking into account the mass and inertial characteristics of the additional viscoelastic support during modeling. As the main object, to which an additional support is attached, a plate of medium thickness within the framework of Timoshenko's hypotheses is considered. Since the focus of the paper is on the influence of the additional support, the plate itself is assumed to be hinged for simplicity of its model. We point out that the results presented are applicable to other objects that have additional supports (beams, plates and shells, which can have different supports along the contour and different shapes in plan). Nonstationary deformation is caused by the application of an external transverse disturbing load to the plate. The influence of the additional support on the deformation of the plate is replaced by the application of an unknown additional variable concentrated force, which, in fact, is the reaction of interaction between the plate and the additional support. The determination of this unknown reaction is reduced to solving the first kind Volterra integral equation. In this work, the main analytical relations for obtaining integral equations or their systems are derived, and an algorithm for their solving is presented. The results of calculations for specific numerical values are described. Moreover, the effect of an additional viscoelastic support on the plate is considered, both with and without taking into account the mass and inertial characteristics of the support. It is shown that for small masses the effect is practically absent, which can serve as an indirect proof of the correctness of the model obtained. As the main conclusion, it can be pointed out that the mass and inertial characteristics of the additional viscoelastic support have a noticeable effect on the vibration process, on both the amplitude and phase characteristics.

Using the method of integral Fourier transform to solve the problem of nonstationary deformation of an elastic medium

For the first time, for solving the wave equation, the method of the integral Fourier transform for an elastic medium under the action of variable internal pressure was used. This equation contains singularities of the second kind, which were excluded from the calculation by the half division method. The main parameters of the process of non-stationary deformation affecting the magnitude of stresses and displacements for the case of plane deformation are established.