This paper presents a simulation of the vibrations of a membrane in the form of a rhombus. Partial solutions of the problem of free vibrations of a membrane with different initial conditions are obtained and the natural frequencies of vibrations are found. The result obtained can be used to strengthen the structural elements of aircraft with a cellular diamond-shaped structure, as well as in the design of unmanned drones of the flying wing type.

Keywords: free vibrations of a membrane, a membrane in the shape of a rhombus, natural frequencies of vibrations

This work presents a simulation of a hexagonal membrane. Some partial solutions for the problem of free vibrations of a membrane of regular hexagonal shape with a different initial bending of the surface are obtained and the natural frequencies of vibrations are found. The result obtained can be used in modeling wing structures in the form of a hexagon of such aircraft as a paraglider.

Keywords: Modeling of a hexagonal wing, free vibrations of a membrane, a membrane of a regular hexagonal shape, natural frequencies of vibrations

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