Eigenfrequencies and eigenforms of regular chain oscillatory systems

Authors

DOI:

https://doi.org/10.17721/1812-5409.2021/4.14

Keywords:

regular chain oscillating systems, eigenfrequencies, eigenforms

Abstract

The classical approach in the investigation of natural oscillations of discrete mechanical oscillatingsystems is the solution of the secular equation for finding the eigenfrequencies and the system of algebraic equations for determining the amplitude coefficients (eigenforms). However, the analytical solution of the secular equation is possible only for a limited class of discrete systems, especially with a finite degree of freedom. This class includes regular chain oscillating systems in which the same oscillators are connected in series. Regular systems are divided into systems with rigidly fixed ends, with one or both free ends, which significantly affects the search for eigenfrequencies and eigenforms. This paper shows how, having a solution for the secular equation of a regular system with rigidly fixed ends, it is possible to determine the eigenfrequencies and eigenforms of regular systems with one or both free ends.

Pages of the article in the issue: 88 - 93

Language of the article: Ukrainian

References

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GERADIN M., RIXEN D. (2015) Mechanical vibrations: theory and application to structural dynamics. 3rd Ed. Chichester: John Wiley & Sons Ltd.

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Published

2021-12-21

How to Cite

Khoroshev, K. G., & Kykot, S. V. (2021). Eigenfrequencies and eigenforms of regular chain oscillatory systems. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (4), 88–93. https://doi.org/10.17721/1812-5409.2021/4.14

Issue

Section

Differential equations, mathematical physics and mechanics