Open AccessExamining Beam Oscillations in the Space of Technogenic and Seismic Impact Parameters (Part I)
Author(s) -
Kh P Kulterbayev,
M. M. Oshkhunov,
L. A. Baragunova,
A A Kabzhikhov,
S. G. Bulanov
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/1079/3/032057
Subject(s) - boundary value problem , eigenvalues and eigenvectors , beam (structure) , matlab , mathematical analysis , timoshenko beam theory , space (punctuation) , connection (principal bundle) , mathematics , bending , computer science , physics , geometry , structural engineering , engineering , quantum mechanics , operating system
Free transverse oscillations of a compressed beam carrying two evenly distributed loads and two discrete masses in the span are studied. The mathematical model of oscillations is presented as a boundary value problem from the basic equation in hyperbolic partial derivatives of the fourth order in spatial coordinates, of second order in time, boundary conditions and block connection conditions. The technical theory of bending oscillations of rods based on Bernoulli’s hypothesis is used. We consider the spectral problem on the determination of eigenvalues, eigenmodes (Sturm-Liouville problem), which is necessary for the analysis of forced oscillations. It is argued that the solution by analytical methods is inexpedient in view of the large amount of transformations and calculations. The methods of separation of variables and finite differences are used. An algorithm of task solution has been developed and implemented in the Matlab software environment in the form of high precision graphoanalytic calculations. Practical conclusions have been made.