Application of special nonsmooth temporal transformations to linear and nonlinear systems under discontinuous and impulsive excitation

Linear and nonlinear mechanical systems under periodic impulsive excitation are considered. Solutions of the differential equations of motion are repr esented in a special form which contains a standard pair of nonsmooth perio dic functions and possesses a convenient structure. This form is also suita ble in the case of excitation with a periodic series of discontinuities of the first kind (a stepwise excitation). The transformations are illustrated in a series of examples. An explicit form of analytical solutions has been obtained for periodic regimes. In the case of parametric impulsive excitat ion, it is shown that a nonequidistant distribution of the impulses with di pole-like temporal shifts may significantly effect the qualitative characte ristics of the response. For example, the sequence of instability zones los es its different subsequences depending on the parameter of the shifts. It is shown that the method's applicability can be extended for nonperiodic re gimes by involving the idea of averaging.