Non-linear system vibration analysis using Hilbert transform--I. Free vibration analysis method 'Freevib'

1994 ◽  
Vol 8 (2) ◽  
pp. 119-127 ◽  
Author(s):  
Michael Feldman
Keyword(s):  
Linear System ◽  
Free Vibration ◽  
Hilbert Transform ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Analysis Method ◽  
Non Linear ◽  
System Vibration ◽  
Non Linear System

scholarly journals Two Species Commensalism Model with Harvesting by Homotopy Analysis Method

2019 ◽  
Vol 8 (2S11) ◽  
pp. 3584-3588
Keyword(s):  
Linear System ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Analytical Study ◽  
Analysis Method ◽  
Linear Ordinary Differential Equations ◽  
Commensal Species ◽  
Non Linear ◽  
Homotopy Analysis ◽  
Non Linear System

In the present investigation a two species commensalism model was taken up for detailed analytical study in which commensal species was harvested at a rate proportional to its strength. The system under investigation was represented by a coupled non linear ordinary differential equations. The series solution of the non-linear system was approximated by Homotopy Analysis Method.

Non-Linear Spring and Damping Forces Estimation During Free Vibration

1995 ◽  
Author(s):  
Michael Feldman ◽  
Simon Braun
Keyword(s):  
Free Vibration ◽  
Hilbert Transform ◽  
Time Domain ◽  
Free Vibration Analysis ◽  
Single Degree Of Freedom ◽  
Non Linear ◽  
Linear Spring ◽  
The Time Domain ◽  
The Hilbert Transform ◽  
Vibrating Systems

Abstract A method for dynamic analysis of sophisticated nonlinear single-degree-of-freedom systems, based on the Hilbert transform in the time domain is described. Using the Hilbert transform together with the proposed method for system identification, we obtain both instantaneous modal parameters together with non-linear force characteristics during free vibration analysis under impulse excitation without long resonance testing. Using the Hilbert transform in the time domain is a new method of studying linear and non-linear vibrating systems exposed to impulse or shock inputs.

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