Response during Acceleration through Resonance of Duffing Type Non-linear Systems

Abstract

Response during a uniform acceleration through resonance of the non-linear systems with a hardening spring is analyzed by using the asymptotic method. The equations to estimate the characteristic points in the response, which are the maximum amplitude point and the frequency jumping point, are derived by the analysis. The more simple approximate formula is obtained to estimate the maximum amplitude value. The estimated value showed good agreement with that obtained by a numerical integration under a certain condition.