The paper deals with an approach to the analytical solution of the periodical vibration of mechanical systems with n DOF esspecially drives containing periodically varying parameters (e.g. stiffnesses). The model is described by means of the Fredholm’s matrix integral equation with degenerated kernel and a periodical Green’s function is used for the solution. The application can be shown e.g. on the Cardan’s mechanism and gear transmission having the time varying tooth stiffnesses. The result correctness is validated by means of Runge-Kutta integration method.

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