A novel approach for nonlinearity detection in vibrating systems

This paper proposes a novel approach for nonlinearity detection in vibrating systems. The approach is developed based on a new concept recently proposed by the author known as nonlinear output frequency response functions (NOFRFs) and the properties of the NOFRFs for nonlinear systems with multiple degrees of freedom (mdof). The results of numerical simulation studies verify the effectiveness of the approach. Nonlinear components often represent faults in practical mdof systems including beams. The proposed approach therefore has significant potential in the fault diagnosis of practical mdof engineering systems and structures

Nonlinear output frequency response functions for multi-input nonlinear volterra systems

The concept of Nonlinear Output Frequency Response Functions (NOFRFs) is extended to the nonlinear systems that can be described by a multi-input Volterra series model. A new algorithm is also developed to determine the output frequency range of nonlinear systems from the frequency range of the inputs. These results allow the concept of NOFRFs to be applied to a wide range of engineering systems. The phenomenon of the energy transfer in a two degree of freedom nonlinear system is studied using the new concepts to demonstrate the significance of the new results

Relationships between the nonlinear output frequency response functions of multi- degree-of-freedom nonlinear systems

Nonlinear Output Frequency Response Functions (NOFRFs) are a new concept proposed by the authors for the analysis of nonlinear systems in the frequency domain. The present study is concerned with investigating inherent relationships between the NOFRFs of two masses in nonlinear MDOF systems. The results reveal very important properties of a class of nonlinear systems, and have considerable significance for the application of the NOFRF concept in engineering practices

Linear parameter estimation for multi-degree-of-freedom nonlinear systems using nonlinear output frequency-response functions

The Volterra series approach has been widely used for the analysis of nonlinear systems. Based on the Volterra series, a novel concept named Nonlinear Output Frequency Response Functions (NOFRFs) was proposed by the authors. This concept can be considered as an alternative extension of the classical frequency response function for linear systems to the nonlinear case. In this study, based on the NOFRFs, a novel algorithm is developed to estimate the linear stiffness and damping parameters of multi-degree-of-freedom (MDOF) nonlinear systems. The validity of this NOFRF based parameter estimation algorithm is demonstrated by numerical studies

Resonances and resonant frequencies for a class of nonlinear systems

Resonant phenomena for a class of nonlinear systems, which can be described by a SDOF model with a polynomial type nonlinear stiffness, are investigated using Nonlinear Output Frequency Response Functions (NOFRFs). The concepts of resonance and resonant frequencies are proposed for the first time for a class of nonlinear systems. The effects of damping on the resonances and resonant frequencies are also analyzed. These results produce a novel interpretation of energy transfer phenomena in this class of nonlinear systems and show how the damping effect influences the system resonant frequencies and amplitudes. The results are important for the design and fault diagnosis of mechanical systems and structures which can be described by the SDOF nonlinear model

A novel method for detecting the position of nonlinear components in multi-degree-of-freedom nonlinear systems

Based on the Nonlinear Output Frequency Response Functions (NOFRFs), a novel method is developed to detect the position of nonlinear components in MDOF nonlinear systems. The validity of this method is demonstrated by numerical studies. Although the method assumes that the linear stiffness and damping for MDOF systems under study are known a priori, the results of the numerical studies indicate that, even if only approximate values of the linear stiffness and damping parameters are used, the method can still correctly detect the position of the nonlinear component. Since the position of a nonlinear component often corresponds to the location of a defect in a MDOF system, this new method is of practical great significance for fault diagnosis in mechanical and structural systems

Crack detection using nonlinear output frequency response functions - an experimental study

The new concept of Nonlinear Output Frequency Response Functions (NOFRFs) is introduced in this paper to detect cracks in beams using frequency domain information. The results show that the NOFRFs are a sensitive indicator of the presence of cracks providing the excitation is of an appropriate strength. The new results provide a novel and effective method for the detection of cracks in beams, with applications in structural fault diagnosis

Analysis of multi-degree-of-freedom nonlinear systems using nonlinear output frequency response functions

The analysis of multi-degree-of-freedom (MDOF) nonlinear systems is studied using the concept of Nonlinear Output Frequency Response Functions (NOFRFs). The results reveal very important properties of MDOF systems, which are of significant importance for the analysis of nonlinear structures. One important application of the results obtained in this study is the detection and location of faults in engineering structures which make the structures behave nonlinearly

Nonlinear output frequency response functions of MDOF systems with multiple nonlinear components

In engineering practice, most mechanical and structural systems are modeled as Multi-Degree-of-Freedom (MDOF) systems. When some components within the systems have nonlinear characteristics, the whole system will behave nonlinearly. The concept of Nonlinear Output Frequency Response Functions (NOFRFs) was proposed by the authors recently and provides a simple way to investigate nonlinear systems in the frequency domain. The present study is concerned with investigating the inherent relationships between the NOFRFs for any two masses of nonlinear MDOF systems with multiple nonlinear components. The results reveal very important properties of the nonlinear systems. One significant application of the results is to detect and locate faults in engineering structures which make the structures behave nonlinearly

Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis

By using the Duffing oscillator as a case study, this paper shows that the harmonic components in the nonlinear system response to a sinusoidal input calculated using the Nonlinear Output Frequency Response Functions (NOFRFs) are one of the solutions obtained using the Harmonic Balance Method (HBM). A comparison of the performances of the two methods shows that the HBM can capture the well-known jump phenomenon, but is restricted by computational limits for some strongly nonlinear systems and can fail to provide accurate predictions for some harmonic components. Although the NOFRFs cannot capture the jump phenomenon, the method has few computational restrictions. For the nonlinear damping systems, the NOFRFs can give better predictions for all the harmonic components in the system response than the HBM even when the damping system is strongly nonlinear