Natural Frequency and Modes of the Longitudinal and Torsional Vibrations in the Bars with Variable Cross Section

I. S. Nikitin; Никитин И. С.; N. G. Burago; Бураго Н. Г.; A. D. Nikitin; Никитин А. Д.

doi:10.31857/S003282352302011X

Natural Frequency and Modes of the Longitudinal and Torsional Vibrations in the Bars with Variable Cross Section

作者: Nikitin I.¹, Burago N.¹^,2, Nikitin A.¹
隶属关系:
1. Institute for Computer Aided Design RAS
2. Ishlinsky Institute for Problems in Mechanics RAS
期: 卷 87, 编号 2 (2023)
页面: 327-336
栏目: Articles
URL: https://journals.rcsi.science/0032-8235/article/view/138861
DOI: https://doi.org/10.31857/S003282352302011X
EDN: https://elibrary.ru/UAJFFL
ID: 138861

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详细

The paper is focused on the problem of natural frequencies and modes determination based on perturbation theory for longitudinal and torsional vibrations in bars with variable cross section. The mechanical properties and cross section geometry of the bar are changing small from the average value with regard to longitudinal coordinate. Based on the theory of small perturbations the analytical solution is obtained for natural frequencies and modes of the stationary harmonic vibrations in bars. The efficiency of the proposed method is supported by comparison and good agreement of the obtain results with a sharp solution for a given cross section profiles. It was established that the approximate solution is working good up to the ratio 2.5–3 between maximum and minimum diameter of cross section. The results of numerical simulations are aimed to estimate the geometry and elastic behavior of the metallic specimens for very high cycle fatigue experimental investigation under axial tension-compression and torsion loadings. The piezoelectric fatigue testing system and procedure is based on stationary vibration excitation in the metallic specimen at the first mode natural frequency.

关键词

very high cycle fatigue, vibrations in bars, variable cross section, tension-compression, perturbation theory, analytical solution, high frequency tests, piezoelectric fatigue testing system

参考

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