Open AccessForced oscillations of beams with installation (Part II)
Author(s) -
Kh P. Kulterbaev,
В. А. Водахова,
L. A. Baragunova,
M. M. Shogenova,
A Kh Tsypinova
Publication year - 2021
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/1083/1/012044
Subject(s) - beam (structure) , boundary value problem , continuation , partial differential equation , harmonic , matlab , harmonic balance , computer science , plane (geometry) , mathematical analysis , mathematics , physics , geometry , acoustics , optics , nonlinear system , quantum mechanics , programming language , operating system
This article (Part II) is a continuation of Part I, published in the same edition, where the spectral problem is considered. Part II examines two types of transverse beam oscillations: forced harmonic and forced random. The beam carries its own distributed mass and discrete mass. The source of oscillations is operating equipment with an element moving during technological operations. The mathematical model of oscillations is presented as a boundary value problem from the main partial differential equation of the hyperbolic type of the fourth order in the spatial coordinate, the second order in time, the boundary conditions and the conditions of the beam sections‘ conjugation. The technical theory of the rods‘ bending oscillations is used, based on Bernoulli‘s hypothesis about the beam plane cross-sections‘ invariability. The methods of variables separation and finite differences are applied. The algorithms for solving the problems have been developed, implemented in the Matlab software environment. Verification of the proposed mathematical models is demonstrated using the specific examples. The particular examples have been carried out and the practical conclusions have been outlined.