Abstract
Linear mechanical systems with periodic impulse excitation are related to the classical area of dynamical analysis. The exact solutions obtained played an important role in mathematics and had numerous applications in vibration analysis and machine dynamics. The introduction of non-linear factors into the excited models makes integration impossible and generally involves the use of various difficult estimated approximations. However, it is shown here that for one important class of strongly non-linear mechanical systems, vibro-impact systems, it is possible to produce an exact steady state solution of the problem of periodic impulse excitation by the use of the periodic Green function method. These solutions can be applied to the analysis of impulse transformations in percussion machines, non-linear mechanical structures and in systems of vibration protection.
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