| Abstrakt: |
The paper considers a homogeneous isotropic Timoshenko beam of finite length. Hinged support conditions are used as boundary conditions. The initial conditions are assumed to be zero. At the initial moment of time, an arbitrary non-stationary distributed load is applied to the beam. At the right end, a sensor (sensors) is installed, which, in the course of the corresponding experiment, take readings of the beam deflection at points. The methodology for solving the direct problem is based on the principle of superposition, in which displacements and contact stresses are connected by means of integral operators in the space variable and time. At the same time, the cores of the latter are the so-called influence functions. These functions are fundamental solutions to systems of differential equations of motion of the beam under study. Their construction is a separate task. The influence functions are found using the Laplace transform in time and expansions in Fourier series in terms of the system of eigenfunctions. In the inverse problem, it is assumed that the dependence of the load on time is known; it is required to restore the law of its distribution over the beam. As a result, the task of identifying a non-stationary load is reduced to solving one integral equation of the Voltaire type, which is incorrect for J. Hadamaru [1]. In this paper, the problem in solving the integral equation is eliminated using numerical methods together with regularization according to Tikhonov [2], [3]. The results of calculations obtained in the work testify to the effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR] |
