Mode Shapes of Hysteresis Type Elastic Dissipative Characteristic Plate Protected from Vibrations

Abstract

In this study, hysteresis type elastic dissipative characteristic plate under the influence of kinematic excitations is devoted to reducing the values of low frequency transverse mode shapes in conjunction with a liquid section dynamic absorber. A mathematical model and a solution method were developed to estimate the mode shapes of an elastic dissipative characteristic plate of the hysteresis type, which is protected from vibrations under the influence of kinematic motions. In the differential equations of motion, the elastic dissipative characteristics of the plate material of the hysteresis type are taken into account by means of harmonic linearity coefficients based on the Pisarenko-Boginich hypothesis. The efficiency of the liquid section dynamic absorber in the reduction of harmful vibrations of the plate at low frequencies is evaluated on the basis of the results of numerical calculations, and it is shown that the mode shapes can achieve minimum values. In this case, the boundary conditions are taken for the plate where the two opposite sides are fixed and the other two sides are free. As a dynamic condition, the force exerted on the plate by a liquid section dynamic absorber is equal to the shear force at the point where the plate is connected to the liquid section dynamic absorber. Numerical calculations were performed and conclusions were made for the case where the liquid section dynamic absorber was mounted in the geometric center of the plate. Optimal values of elastic and damping elements of the liquid section dynamic absorber, where the mode shapes reach the minimum values, have been determined.