ДИНАМИЧЕСКОЕ ДОГРУЖЕНИЕ СТЕРЖНЯ ПРИ ВНЕЗАПНОМ ИЗМЕНЕНИИ СТРУКТУРЫ УПРУГОГО ОСНОВАНИЯ

Abstract

A mathematical model of the dynamic process in the structurally nonlinear system «beam – two-parameter foundation», which arises as a result of a sudden change in the physical and mechanical properties of the foundation, leading to zeroing of its shear stiffness, is constructed in a structurally-nonlinear system «beam – two-parameter foundation» The solution of the static problem of bending of a beam supported on a Pasternak base serves as the initial condition for the problem of forced vibrations of a beam on a Winkler base that arose after the sudden formation of a defect. Solutions to static and dynamic problems are constructed by the method of initial parameters with the use of vectors of states of beam sections and matrices of the influence of initial parameters on the state of arbitrary sections. In the analysis of forced vibrations, the decomposition of the load and deflections of the initial static state into rows according to the forms of natural vibrations of the new state is used.