## Nonlinear analysis in synthesis of the resonant vibro-impact systems

The paper considers differential equation of the vibro-impact resonance system with an asymmetric piecewise linear elastic characteristic. The time-instant of switching of elastic characteristic is determined on the basis of equality of oscillation period to average value of the corresponding eigenfrequencies. Then, expansion of the asymmetric piecewise linear elastic characteristic into Fourier series was made. The initial differential equation was reduced to a kind of parametric equations of Hill’s andMathieu’s type with taking into account the time of elastic characteristic change.