Analysis of fast-sampled non-linear systems: Generalised frequency response functions for -operator models

2006 ◽  
Vol 86 (11) ◽  
pp. 3246-3257 ◽  
Author(s):  
M.A. Chadwick ◽  
V. Kadirkamanathan ◽  
S.A. Billings
Keyword(s):  
Frequency Response ◽  
Linear Systems ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Non Linear ◽  
Non Linear Systems

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.

Non-Linear Characteristics in the Dynamic Responses of Seated Subjects Exposed to Vertical Whole-Body Vibration

2002 ◽  
Vol 124 (5) ◽  
pp. 527-532 ◽  
Author(s):  
Yasunao Matsumoto ◽  
Michael J. Griffin
Keyword(s):  
Frequency Response ◽  
The Body ◽  
Dynamic Responses ◽  
Whole Body ◽  
Apparent Mass ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Resonance Frequencies ◽  
Non Linear ◽  
Vibration Magnitude

The effect of the magnitude of vertical vibration on the dynamic response of the seated human body has been investigated. Eight male subjects were exposed to random vibration in the 0.5 to 20 Hz frequency range at five magnitudes: 0.125, 0.25, 0.5, 1.0 and 2.0 ms−2 r.m.s. The dynamic responses of the body were measured at eight locations: at the first, fifth, and tenth thoracic vertebrae (T1, T5, T10), at the first, third, and fifth lumbar vertebrae (L1, L3, L5) and at the pelvis (the posterior-superior iliac spine). At each location, the motions on the body surface were measured in the three orthogonal axes within the sagittal plane (i.e., the vertical, fore-and-aft, and pitch axes). The force at the seat surface was also measured. Frequency response functions (i.e., transmissibilities and apparent mass) were used to represent the responses of the body. Non-linear characteristics were observed in the apparent mass and in the transmissibilities to most measurement locations. Resonance frequencies in the frequency response functions decreased with increases in the vibration magnitude (e.g. for the vertical transmissibility to L3, a reduction from 6.25 to 4.75 Hz when the vibration magnitude increased from 0.125 to 2.0 ms−2 r.m.s.). The transmission of vibration within the spine also showed some evidence of a non-linear characteristic. It can be concluded from this study that the dynamic responses of seated subjects are clearly non-linear with respect to vibration magnitude, whereas previous studies have reported inconsistent conclusions. More understanding of the dependence on vibration magnitude of both the dynamic responses of the soft tissues of the body and the muscle activity (voluntary and involuntary) is required to identify the causes of the non-linear characteristics observed in this study.

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