On vibrations of a class of linear time-varying systems

A class of dynamic multi-degree-of-freedom systems with time-varying parameters has been studied. The systems have been assumed to vary during a limited time interval and to remain invariant outside of this interval. The exciting forces have been assumed to be periodic. Several analytical interpretations of the system responses have been considered. Applications to machine condition monitoring have been discussed. Methods of identification of the shape of the functions, describing the parameter variation as well as methods of identification of the relative intensity of the changes of individual parameters, have been developed. The identification techniques have been based on a realistic assumption that the exciting forces are unknown and that the responses of the system are available.