- STRUCTURAL MECHANICS
- The Frequency Of Natural Vibrations Of A Plate Located On An Inhomogeneous Base
- UDC 624.04

doi: 10.33622/0869-7019.2023.01.69-74

**Andrey N. LEONTIEV**, an_leontiev@mail.ru

**Ksenia V. BALANDINA**, ksuuu-balandina@yandex.ru

Moscow State University of Civil Engineering (National Research University), 26, Yaroslavskoe shosse, Moscow, 129337, Russian Federation

**Abstract**. Currently, the problems of calculating structures on an elastic base are very relevant. In this connection, the influence of the inhomogeneity of the base on the frequencies of natural vibrations of thin plates is investigated. The plates located on the elastic base of the Winkler and having hinge supports along the contour are considered. It is assumed that the value of the coefficient of the base bed has a symmetrical character of change relative to the middle of the plate, and within its limits is described by a quadratic law. The Bubnov-Galerkin variational method was used to determine the fundamental frequency of natural oscillations. The calculation was performed in an Excel environment, while trigonometric functions were taken as approximating ones. Plates with different relative lengths are presented - short, medium length and long. It is shown that the influence of the inhomogeneity of the base on the fundamental frequency of natural oscillations is most noticeable for long plates.

**Keywords**: thin plates, elastic inhomogeneous base, Winkler model, Bubnov-Galerkin method, natural oscillation frequency, bed coefficient - REFERENCES

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