Нестационарные колебания пластины с дополнительной вязкоупругой опорой

Abstract

Mechanical system consists of hingedly supported medium-thickness rectangular plate with additional concentrated viscoelastic support. The nonstationary concentrated transversal load, which initiates vibration, is acting on the plate. The simulation of the plate deforming is based on S. P. Timoshenko’s refined theory. The calculations are reduced to the Volterra integral equations. The solving of such Volterra integral equations is ill-posed problem, which is solved numerically with using of Tikhonov's regularization method. Stable analytical and numerical solution of ill-posed problems for considered mechanical system is obtained without the use of iterative computational schemes. The unknown reaction between the plate and additional support vs. time are obtained consequently. The question concerned with the selection of Tikhonov’s regularization parameter is considered. The results of numerical calculation for plate with additional viscoelastic support are presented.