## Asymptotic method and wave theory of motion in studying the effect of periodic impulse forces on systems characterized by longitudinal motion velocity

A methodology for researching dynamic processes of one-dimensional systems with distributed parameters that are characterized by longitudinal component of motion velocity and are under the effect of periodic impulse forces has been developed. The boundary problem for the generalized non-linear differential Klein–Gordon equation is the mathematical model of dynamics of the systems under study in Euler variables. Its specific feature is that the unexcited analogue does not allow applying the known classical Fourier and D'Alembert methods for building a solution. Non-r