Analysis of bilinear oscillators under harmonic loading using nonlinear output frequency response functions

Abstract

In this paper, the new concept of Nonlinear Output Frequency ResponseFunctions (NOFRFs) is extended to the harmonic input case, an input-independent relationship is found between the NOFRFs and the Generalized Frequency Response Functions (GFRFs). This relationship can greatly simplify the application of the NOFRFs.Then, beginning with the demonstration that a bilinear oscillator can be approximated using a polynomial type nonlinear oscillator, the NOFRFs are used to analyze the energy transfer phenomenon of bilinear oscillators in the frequency domain. The analysis provides insight into how new frequency generation can occur using bilinear oscillators and how the sub-resonances occur for the bilinear oscillators, and reveals that it is the resonant frequencies of the NOFRFs that dominate the occurrence of this well-known nonlinear behaviour. The results are of significance for the design and fault diagnosis of mechanical systems and structures which can be described by a bilinear oscillator model.

Design of Nonlinear Systems in the Frequency Domain: An Output Frequency Response Function-Based Approach

“…In order to demonstrate how to follow the five step procedure in Section III-D to carry out a design, consider the design of the simple nonlinear system (33). The design objective is to achieve a specified force   out ft for the system.…”

“…In (11a), the n th order GFRFs' coefficient vector n can be calculated by using the algorithm discussed in Peng et al [33]: Substituting (13) into (C1), 2 can be obtained satisfying Proposition 3. Moreover, by using the mathematical induction and assuming Proposition 3 holds for n , it can be obtained that…”

A novel approach for nonlinearity detection in vibrating systems

“…Equations (12) to (14) show the relationships between the NOFRFs associated with two consecutive masses in system (3,4) and indicate that These properties are a very important development for the recently proposed theories and methods of the NOFRF based nonlinear system frequency domain analysis [15][16][17][18][19][20] and are especially useful for the location of the nonlinear component in MDOF systems. The properties have been rigorously proved and used for nonlinear MDOF system analysis [7,8].…”

Vibrational behavior of MDOF oscillators subjected to multiple contact constraints

“…Peng et al [10] studied the energy transfer phenomenon of a bilinear oscillator in the frequency domain by means of the nonlinear output frequency response functions. They modeled a bilinear oscillator with a fourth-order polynomial type of nonlinearity.…”