The paper is devoted to problem of analysis, identification and prediction of the presence of damages, which above a certain level may present a serious threat to the engineering (vibrating) structures such as different technical systems (hydrotechnical equipment, hydroelectrical station engines, atomic reactors ones etc). Usually change of structural dynamic properties due to environmental, operational and other effects allows to determine the existence, location and size of damages.
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.