Volterra-series-based equivalent nonlinear system method for subharmonic vibration systems

ABSTRACT

Subharmonics generation in the nonlinear system, directly using the traditional finite Volterra series, cannot generally represent the aimed system. In this paper, a new approach is presented, which is an extension of single finite Volterra series for representation and analysis of the subharmonic vibration system based on equivalent nonlinear system. The equivalent nonlinear system, which is constructed by pre-compensating the subharmonic vibration system with the super-harmonic nonlinear model, yields the input–output relation between the virtual source and the response of the aimed nonlinear system. Orthogonal least square method is employed to identify the truncated order of Volterra series and predominant Volterra kernels of the equivalent nonlinear system. The MGFRFs (modified generalised frequency response functions) of the equivalent nonlinear system is obtained from the data of the virtual source and response, and verified by comparing the response estimated by the MGFRFs with its true value. Therefore, the aimed subharmonic vibration system can be analysed by taking advantage of a truncated Volterra series based on the equivalent nonlinear system. Numerical simulations were carried out, whose results have shown that the proposed method is valid and feasible, and suitable to apply on representation and analysis of subharmonic vibration systems.

KEYWORDS:

• The subharmonic vibration
• the MGFRFs
• the equivalent nonlinear system method
• the Volterra series

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Bin Xiao http://orcid.org/0000-0002-0233-5176

Additional information

Funding

This work was supported by National Natural Science Foundation of China: [Grant Number 51475088,51705071]; Natural Science Foundation of Jilin Province: [Grant Number 20140101065JC, 20190201109JC]; Research Foundation of Education Department of Jilin Province of China: [Grant Number 2015-244].