The Volterra series and higher-order frequency response functions

2019 ◽  
pp. 377-476
Author(s):  
K Worden ◽  
G R Tomlinson
Keyword(s):  
Frequency Response ◽  
Volterra Series ◽  
Higher Order ◽  
Response Functions ◽  
Frequency Response Functions

Characterization of automotive dampers using higher order frequency response functions

1997 ◽  
Vol 211 (3) ◽  
pp. 181-203 ◽  
Author(s):  
S Cafferty ◽  
G. R. Tomlinson
Keyword(s):  
Energy Transfer ◽  
Frequency Response ◽  
Ride Comfort ◽  
Higher Order ◽  
Suspension System ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Damping Coefficients ◽  
Non Linear ◽  
Linear Behaviour

Automotive dampers are an important element of a vehicle's suspension system for controlling road handling and passenger ride comfort. Many automotive dampers have non-linear asymmetric characteristics to accommodate the incompatible requirements between ride comfort and road handling, thus the ride comfort engineer requires techniques that can characterize this non-linear behaviour and provide models of the dampers for use in ride performance simulations of the full suspension system. The work presented in this paper is concerned with developing a frequency domain technique using higher order frequency response functions (HFRFs) to characterize a Monroe automotive damper. The principal diagonals and multidimensional surfaces of the HFRFs up to third order are obtained. Non-linear damping coefficients for the damper are derived from the HFRFs and the energy transfer properties are investigated. The results show that the majority of the HFRFs contain no peaks or resonances, indicating that the damper has no preferred frequencies for energy transfer. The accuracy of the damping coefficients determined from the HFRFs is poor. This is due to the inability of the technique to measure the pure HFRFs and separate the effects of non-linearities in the input actuator from those in the damper. It is concluded that these constraints currently impose some limit on the use of the methodology.

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.

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