2013/12/16 by Rousselet, Bernard, Brahim, Nadia Ben
#Classical Analysis and ODEs (math.CA) #Classical Physics (physics.class-ph) #FOS: Mathematics #FOS: Physical sciences
paper · doi:10.48550/arxiv.1312.4492
We consider \it small solutions of a vibrating mechanical system with smooth non-linearities for which we provide an approximate solution by using a triple scale analysis; a rigorous proof of convergence of the triple scale method is included; for the forced response, a stability result is needed in order to prove convergence in a neighbourhood of a primary resonance. The amplitude of the response with respect to the frequency forcing is described and it is related to the frequency of a free periodic vibration.