Прямая задача для нестационарных колебаний системы трех струн

Abstract

Non-stationary vibrations of a three-string system are studied. The system vibrations are caused by an external concentrated load applied at a certain point of one of the strings. The displacements of the points of the strings are described by a one-dimensional wave equation. The reactions of the strings are simulated by additional concentrated loads applied at the contact points. The Laplace integral transform is used for solving the differential equations. The problem is reduced to a system of two Volterr's integral equations. The system of integral equations is solved using quadrature formulas and Tikhonov's regularization method. A computational example is given. The dependences of contact forces on time and displacements of each of the strings are obtained. The graphs of changes of contact forces and displacements in time are shown.