Investigation of waves in the strengthened net

Abstract

The movements of a reinforced net are considered. Mesh systems are used in various areas of modern technology, aviation, fishing, and construction. In recent years, much attention has been drawn to the complete equations that describe the motion of a deformable thread. In accordance with the studied task, the reinforcement of the net is carried out by adding terms in the equations of motion. In the planar case, the static behavior of the structure is investigated, and equations of motion are derived that allow the study of motion. The problem of wave propagation in deformable filament systems, taking into account a significant deviation of the filament shape from the original rectilinear one, is mathematically very difficult, since the equations of motion are a system of nonlinear differential equations in partial derivatives. To solve the problem, the method of characteristics is used. As well the method of characteristics solves the problem of the propagation of unloading waves (in the case of a load, shock waves arise). Depending on the velocity distribution at the boundary, the distribution of the strain constant on the characteristics is determined. The results are constructed by numerical integration of the integrals of the characteristics found by the method. The solution using the characteristic equations shows the occurrence of traveling waves.