The use of generalized functions in the problem of elastic oscillations of a composite rod

Abstract

The motion of a multicomponent anthropomorphic model is described by the equation of degenerate transverse oscillations of a one-dimensional system of rods with distributed mass and bending stiffness parameters and with concentrated inclusions into these parameters. The concentrated inclusions can be introduced into the analytic expression for the distributed parameters using impulse functions of the first and higher orders (the delta-function and its derivatives). The solution of the equation is found by the operational method. Krylov's generalized functions make it possible to obtain an analytic solution of the equation, which can be realized on a computer, and is written for the whole multicomponent structure at once in the framework of the direct and inverse problems of mechanics. Some optimization problems for a model of the motion of a sportsman are solved in the framework of the direct problem of mechanics.