On the Generalized Frequency Response Functions of Volterra Systems

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Xingjian Jing ◽  
Ziqiang Lang
Keyword(s):  
Frequency Response ◽  
Volterra Series ◽  
Mapping Function ◽  
Nonlinear Effects ◽  
Model Parameters ◽  
Linear Component ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Volterra Systems ◽  
System Frequency

The generalized frequency response function (GFRF) for Volterra systems described by the nonlinear autoregressive with exogenous input model is determined by a new mapping function based on its parametric characteristic. The nth-order GFRF can now be directly determined in terms of the first order GFRF, which represents the linear component of the system, and model parameters, which define system nonlinearities. Some new properties of the GFRFs are therefore developed. These results can analytically reveal the linear and nonlinear effects on system frequency response functions, and also demonstrate the relationship between convergence of system Volterra series expansion and model parameters.

Alternate Approach of Using Spectral Decomposition for the Identification of Structural Resonant Regions

2009 ◽  
Author(s):  
Steven M. Mankevich ◽  
Stephen Hambric
Keyword(s):  
Frequency Response ◽  
Spectral Decomposition ◽  
Impact Test ◽  
Spectral Characteristics ◽  
System Response ◽  
Acoustic Similarity ◽  
Response Functions ◽  
Frequency Response Functions ◽  
System Frequency ◽  
Similarity Laws

This paper investigates a method called spectral decomposition and is presented as an alternate approach to determine the system frequency response functions of turbomachinery. Spectral decomposition is a method that is based on the principals established by the acoustic similarity laws to determine the spectral characteristics of a source function. The decomposition process was originally implemented to investigate the isolated acoustic source spectra of fans specifically excluding structureborne sources; however, this paper focuses on using the method for the purpose of characterizing the system response functions associated with rotating machinery. During this investigation, static impact test data was acquired on a large industrial motor to characterize the frequency response functions of the motor/compressor system. Spectral decomposition results are then calculated using the motor operational structureborne data and compared to the results of the static impact test. This paper shows that the spectral decomposition is a viable option to use in place of the static impact test results where qualitative frequency response functions are desired.

Analysis of Locally Nonlinear MDOF Systems Using Nonlinear Output Frequency Response Functions

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Z. K. Peng ◽  
Z. Q. Lang ◽  
S. A. Billings
Keyword(s):  
Nonlinear Systems ◽  
Frequency Response ◽  
Nonlinear Effects ◽  
Response Analysis ◽  
Response Functions ◽  
Output Frequency ◽  
Engineering Structures ◽  
Frequency Response Functions ◽  
Linear Characteristic ◽  
Mdof Systems

The analysis of multidegree-of-freedom (MDOF) nonlinear systems is studied using the concept of nonlinear output frequency response functions (NOFRFs), which are a series of one-dimensional functions of frequency recently proposed by the authors to facilitate the analysis of nonlinear systems in the frequency domain. By inspecting the relationships between the NOFRFs of two consecutive masses in the locally nonlinear MDOF systems, a series of properties about the NOFRFs of the nonlinear systems are obtained. These properties clearly reveal how the system linear characteristic parameters govern the distribution of nonlinear effects induced by the system nonlinear component within the whole systems. The results obtained in the present work are of significance to the frequency response analysis for nonlinear systems. One important potential application of these results is the detection and location of damages in engineering structures, which make the structures behave nonlinearly.

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