Open AccessFree oscillations of a beam with installation (1st part)
Author(s) -
Kh P. Kulterbaev,
В. А. Водахова,
L. A. Baragunova,
M. M. Shogenova,
A. Kh Tsipinova
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/1083/1/012043
Subject(s) - boundary value problem , eigenvalues and eigenvectors , beam (structure) , mathematical analysis , matlab , partial differential equation , oscillation (cell signaling) , separation of variables , mathematics , timoshenko beam theory , physics , computer science , quantum mechanics , biology , optics , genetics , operating system
The transverse oscillations of a beam carrying a discrete mass in a span are studied. The mathematical model of oscillations is presented as a boundary value problem from the main partial differential equation of the fourth order hyperbolic type in the spatial coordinate, of the second order in time, the boundary conditions and the conditions for the sections‘ conjugation. The technical theory of the rods bending oscillations, based on Bernoulli‘s hypothesis, is used. The spectral problem of determining the eigenvalues and eigenmodes of oscillations (the Sturm-Liouville problem), necessary for analyzing the problems of forced oscillations, is considered. It is argued that the solution by analytical methods is impractical due to the large volume of transformations and cumbersome calculations. Methods of separation of variables and finite differences are used. An algorithm for solving the problem, implemented in the Matlab software environment in the form of high-precision graphic-analytical calculations, is developed. The conclusions for practical applications of the results are made.