Eigenfrequencies and eigenforms of regular chain oscillatory systems

Хорошев, К. Г., Кикоть, С. В. (2021). Eigenfrequencies and eigenforms of regular chain oscillatory systems. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics(4), 88–93. https://doi.org/10.17721/1812-5409.2021/4.14

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