Özhan, BBPakdemirli, M2024-07-182024-07-180022-460X1095-8568http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/3378A general vibrational model of a continuous system with arbitrary linear and cubic operators is considered. Approximate analytical solutions are found using the method of multiple scales. The primary resonances of the external excitation and three-to-one internal resonances between two arbitrary natural frequencies are treated. The amplitude and phase modulation equations are derived. The steady-state solutions and their stability are discussed. The solution algorithm is applied to two specific problems: (1) axially moving Euler-Bernoulli beam, and (2) axially moving viscoelastic beam. (C) 2010 Elsevier Ltd. All rights reserved.EnglishSPATIALLY CONTINUOUS SYSTEMSMOVING VISCOELASTIC BEAMSPERTURBATION-METHODSSTABILITYCONTINUAMODELSSPEEDArticle