Modeling of Constructions’ Structurally Nonlinear Oscillations Using Chebyshev's Polynomials

Abstract

A numerical algorithm for solving initial-boundary value problems with nonlinear boundary conditions was developed and implemented. The algorithm is constructed with reference to modeling of oscillations of an elastically supported deformable rod with limit stops at the ends under the action of a moving variable force. Such a rod is the design scheme of a number of building structures, including the span structure of a floating bridge of continuous system with limiting rigid supports at the ends. Chebyshev's polynomials were used to improve the computational schemes for realizing the practical problems of modeling constructive-nonlinear oscillations of building structures. The solution does not lose stability for large values of the elasticity coefficients of elastic couplings. Using the developed approach, it is possible to perform virtual computing experiments to skip a variety of movable loads on the floating bridge to analyze its deformed state and to make well-grounded design decisions.