Methods for Research of Nonconservative Systems States

International Multi-Conference on Industrial Engineering and Modern technologies

Burtseva, O.A.^1 ; Abuladze, N.R.^1 ; Chipko, S.A.^1

Platov South-Russian State Polytechnic University, Novocherkassk Polytechnic Institute, Prosveshcheniya str. 132, Novocheskarsk

346428, Russia^1

关键词: Equivalent linearization;    High-rise construction;    Linearized equations;    Mixed boundary condition;    Non conservative systems;    Nonconservative loadings;    Systems of ordinary differential equations;    Variable coefficients;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/463/4/042035/pdf
DOI  :  10.1088/1757-899X/463/4/042035

来源: IOP

【 摘 要 】

Mechanic equations of viscoelastic solid body are used for formulation of research problem of deformable constructions. These equations are considered together with mixed boundary conditions. Nonconservative loadings are deter-mined at one part of body surface, and at the other part of the body surface displacements are determined. Partial differential equations are transformed with variation methods into systems of ordinary differential equations that may have variable coefficients. Research of stability is performed on the base of joint solving of the main state equations and spectrum problem for linearized equations of disturbed motion. Lyapunov-Shmidt method and method of equivalent linearization are used for research of periodical regimes that branch themselves off the main states. Problem of oscillations of high-rise constructions under wind influence are solved.