A new mathematical procedure for simultaneous identification of the nonlinear damping and restoring characteristics based on acceleration measurements

Abstract

A new nonlinear inverse method of nonparametric identification is proposed for both recovering the full nonlinear damping and restoring functions in a harmonic forced nonlinear oscillator. For that, a proper inverse problem and its mathematical formalism are developed by introducing the intersection and zero-crossing times with respect to motion response, based on the acceleration response measurements. We have found that the present inverse study is well-posed in the sense of stability, i.e., it has stability properties. This implies that the identification does not depend on the usual regularisations, which, however, is generally essential to the usual (ill-posed) inverse problems arising in mathematical science and engineering. As a model equation, a highly nonlinear system is examined for the workability of the inverse method proposed here through numerical experiments.

Keywords:

• simultaneous identification
• nonparametric identification
• full nonlinear damping
• full nonlinear restoring
• well-conditioned

Acknowledgement

The author would like to thank Mr. Jinsoo Park, in the Department of Naval Architecture and Ocean Engineering, Pusan National University for his assistance.

Additional information

Funding

The present paper was supported by Basic Science Research Programme through the National Research Foundation of Korea (NRF) funded by the Ministry of Education [grant number NRF-2011-0010090].