# Generalized formula for estimating the oscillation frequency response of a cantilever bar with point masses

• O. Khabidolda Karaganda University named after Academician E.A. Buketov
• S. K. Akhmediyev Karaganda Technical University
• N. Vatin Peter the Great St.Petersburg Polytechnic University
• R. Muratkhan Karaganda University named after Academician E.A. Buketo
• N. Medeubaev Karaganda University named after Academician E.A. Buketo

### Abstract

This paper presents a study of natural oscillations of a cantilever bar with ﬁve point masses with variable geometric and stiﬀness parameters (distances between locations of the masses, coeﬃcients of variability of the bending stiﬀness of the bar sections). Using the exact method of forces based on the Mohr formula, there have been obtained expressions in general form for calculating the main unit coeﬃcients of the secular equation, which makes it possible to perform calculations and to determine the oscillation frequency response of natural oscillations with a wide range of changes in the initial parameters of the physical and geometric state of cantilever bars. A numerical example has been given to illustrate the proposed theoretical approaches. The results have been compared with the results based on calculating a similar can tilever bar with one( reduced by masses) degree of freedom. A graphical dependence of the oscillation frequency response value on changing the value of the bending stiﬀness along the length of the cantilever bar gas been obtained. The theoretical provisions and applied results presented in the work will be widely used both in the practical design of bar systems and in scientiﬁc research in the ﬁeld of mechanics of a deformable solid body.

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How to Cite
KHABIDOLDA, O. et al. Generalized formula for estimating the oscillation frequency response of a cantilever bar with point masses. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 116, n. 4, dec. 2022. ISSN 2617-4871. Available at: <https://bm.kaznu.kz/index.php/kaznu/article/view/1163>. Date accessed: 28 jan. 2023. doi: https://doi.org/10.26577/JMMCS.2022.v116.i4.03.
Citation Formats
Section
Mechanics
Keywords cantilever bar, variable bending stiffness, main unit coefficients, oscillations frequency response for natural oscillations, graphical dependence of the oscillation frequency response,, reduced mass, calculation reliability, calculation nomogram