MECHANICS

Plate vibrations with periodically changing parameters

N. V. Naumova, D. N. Ivanov, N. P. Dorofeev

St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

Abstract: Vibrations of square plate with periodically changing parameters are considered. The averaged fourth-order partial differential equation for the plate deflection w is offered. Solution of the problem is obtained by using the approximate theory. The approximate results are presented by analytical formulas. Asymptotic averaging (realized in Wolfram Mathematica) and Finite Elements Method (ANSYS) are used to get the values of vibrations frequencies. The comparison of numerical and asymptotic results is performed.

Keywords: plate, reinforced plate, heterogeneous plate, vibrations of plates, deformations of plates.

UDC: 539.3

MSC: 74K20, 74H45

Received: 22.03.2021
Revised: 02.05.2021
Accepted: 17.07.2021

DOI: 10.21638/spbu01.2021.412

 English version: Vestnik St. Petersburg University, Mathematics, 2021, 8:4, 411–417