Title:	Existence of analytical solution, stability assessment and periodic response of vibrating systems with time varying parameters
Authors:	Dupal, Jan Zajíček, Martin
Citation:	Applied and Computational Mechanics. 2020, vol. 14, no. 2, p. 123-144.
Issue Date:	2020
Publisher:	University of West Bohemia
Document type:	článek article
URI:	http://hdl.handle.net/11025/42272
ISSN:	1802-680X (Print) 2336-1182 (Online)
Keywords:	vibrace;periodická odezva;stabilita;integro-diferenciální rovnice;periodická Greenova funkce
Keywords in different language:	vibration;periodic response;stability;integro-differential equation;periodic Green’s function
Abstract in different language:	The paper is focused on a solution of a vibrating system with one-degree-of-freedom (1 DOF). The goal of this presentation is to deal with the method for periodical response calculation (if exists) reminding Harmonic Balance Method (HBM) 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 case that the investigated system is stable and can be expressed in exact form. The second goal of the paper is stability and solution existence assessment. For this reason a methodology of (in)stable parametric domain border determination has been accurately developed.
Rights:	© University of West Bohemia
Appears in Collections:	Články / Articles (NTIS) Volume 14, Number 2 (2020) Volume 14, Number 2 (2020)

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