Modeling of triangular-shaped membrane vibrations

Abstract

Modeling of triangular-shaped membrane vibrations

Сhernyshov N.A.

Incoming article date: 07.02.2020

In many modern engineering designs are applied membranes of various shapes. This can be electroacoustic devices, medical equipment, and the skin of the aircraft body with triangular cells. Solutions for free vibrations of rectangular and circular membranes are known by the Fourier method. There are also quite a few solutions to the problems of vibrations of membranes of various shapes by the finite element method. Analytical solutions for membranes of more complex shapes are of great interest due to the complex geometry of the contour and the difficulty of obtaining the solution itself. In this paper, we obtained partial solutions for the problem of free vibrations of a regular triangular membrane with different initial surface bending and found eigenfrequencies of vibrations.

Keywords: Free vibrations of the membrane, the membrane of the correct triangular shape, natural frequencies of vibrations