Обратная задача при нестационарном деформировании прямоугольной 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 formulation and the solution of one inverse non-stationary problem for the mechanical system are given. The identification problem of unknown non-stationary load causing the deformation of the plate with additional support is considered. The simulation of the plate deforming is based on S. P. Timoshenko’s refined theory. The researches are reduced to the system of Volterra integral equations. The solving of such Volterra integral equations is ill-posed problem, which is solved numerically with using of Tikhonov's regularization algorithm. Stable analytical and numerical solution of ill-posed problems for considered mechanical system is obtained without the use of iterative computational schemes. The unknown external load and reaction between the plate and additional support vs. time are obtained consequently. Special attention paid to the regularization parameter choosing. The results of numerical calculation for inverse problem are presented.