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The paper is focused on the solution of a vibrating system with one-degree-of-freedom with the objective to deal with the method for periodical response calculation (if exists) reminding Harmonic Balance Method of linear systems having time dependent parameters of mass, damping and stiffness under arbitrary periodical excitation. As a starting point of the investigation, a periodic Green’s function (PGF) construction of the stationary part of the original differential equation is used. The PGF then enables a transformation of the differential equation to the integro-differential one whose analytical solution is given in this paper. Such solution exists only in the case that the investigated system is stable and can be expressed in exact form. The second goal of the paper is to assess the stability and solution existence. For this purpose, a methodology of (in)stable parametric domain border determination is developed. c © 2020 University of West Bohemia. All rights reserved.

Existence of analytical solution, stability assessment and periodic response of vibrating systems with time varying parameters