The nonlinear mathematical model of the impulse pile driver

A mathematical model of the operation of a pile-driving vibration loader, which is based on the impact on the submerged element in the form of a Maxwell — Feyer pulse, is described. This pulse has a number of properties, the main of which is optimality in the sense of the asymmetry coefficient. The solvability of the resulting model, which is a nonlinear differential equation of the second order, is investigated. The representation of the solution corresponds to the well-known principle of dividing into the sum of slow and fast movements. We write out eigenfunctions, on the basis of which we can construct approximate solutions using the Galerkin approximations. This algorithm allows us to conduct numerical experiments to determine the optimal parameters and characteristics of the devices under study.