Энергетический метод для решения волновых задач гибкой нити

Abstract

The paper considers the behavior of a flexible deformable thread when longitudinal and transverse waves pass through it. The processes occurring in a thread during the passage of a wave perturbation through it are analyzed under the assumption that the wave front zone is limited comparing with the length of the thread but not assuming this quantity to be of infinite smallness. In contrast to other similar works, no assumptions were made in advance about the shape of the thread in the zone of the wave perturbation passage (the fracture of the thread) and the dependence of the tension force on its elongation. The only requirement is the implementation of the general theorems of dynamics. Formulas for the relation of the thread speed before and after the passage of the wave with a change in the angle of thread inclination are obtained making possible solving wave propagation problems in a new way. The method is illustrated by new solutions to known problems, which allows comparing the obtained results with known solutions and verifying the advantages of the proposed method.