Response of Parametrically Excited One Degree of Freedom System With Non-linear Damping and Stiffness

2002 ◽  
Vol 66 (6) ◽  
pp. 410-416 ◽  
Author(s):  
M M Kamel ◽  
Y A Amer
Keyword(s):  
Degree Of Freedom ◽  
Parametrically Excited ◽  
Non Linear ◽  
Linear Damping

Numerical Investigations of Parametrically Excited Non-Linear Multi Degree of Freedom Micro-Electromechanical Systems

2016 ◽  
Author(s):  
Till J. Kniffka ◽  
Horst Ecker ◽  
Brian R. Mace ◽  
Roger Halkyard
Keyword(s):  
Limit Cycles ◽  
Basins Of Attraction ◽  
Degree Of Freedom ◽  
User Friendliness ◽  
Electromechanical Systems ◽  
Parameter Spaces ◽  
Parametrically Excited ◽  
Rest Position ◽  
Phase Parameter ◽  
Non Linear

More and more systems exploit parametric excitation (PE) to improve their performance compared to conventional system. Especially in the field of micro-electromechanical systems (MEMS) such technologies rapidly gain in importance. Different to conventional resonance cases PE may destabilise the system’s rest position when parametrically excited time-periodically with a certain PE frequency. At such parametric resonances vibrations are only limited due to non-linearities. The system is repelled by the unstable rest position and enters a bifurcated limit cycle. Finding these limit cycles has become more easy in recent years. Advances have been made in numerical path following tools regarding both their power and their user friendliness. As a result, designing such systems has become more common. Indeed, the focus of studies has been on 1DOF systems mostly. However, for multi degree of freedom systems choosing a meaningful phase space to discuss the results is a task on its own. Quasi-modally transforming the equations of motion, the vibrations are decomposed allowing one to focus on the predominant modes. By concentrating on these predominant modes, continuation results can be displayed in meaningfully reduced phase-parameter spaces. Basins of attraction can be found in Poincaré sections of these phase-parameter spaces. Employing these approaches, it is demonstrated how to investigate a non-linear 2DOF PE MEMS, how to change the characteristics of the limit cycles and how this affects their basins of attraction.

scholarly journals A Decrement Method for Quantifying Nonlinear and Linear Damping in Multi-Degree of Freedom Systems

2006 ◽  
Author(s):  
Craig Meskell
Keyword(s):  
Natural Frequencies ◽  
Degree Of Freedom ◽  
Pass Band ◽  
Response Measurement ◽  
Free Decay ◽  
Decay Test ◽  
Non Linear ◽  
Linear Damping ◽  
The Time Domain ◽  
Single Response

A method is presented which can estimate the linear and non-linear damping parameters in a lightly damped multi-degree of freedom system. This in effect allows the system to be decomposed into a set of single degree of freedom nonlinear systems. Only a single response measurement from a free decay test is required as input. This ensures that the magnitude of the damping parameters is not compromised by phase distortion between measurements. The response is band-pass filtered in the time domain, with the pass band centered on each of the natural frequencies. This provides a set of free response measurements, one for each mode. However, it does introduce a restriction in that the natural frequencies must be distinct and separated somewhat. The instantaneous energy of each trace is used to describe the long-term evolution of the mode. Practically this is achieved by using only the peak amplitudes in each period. In this way the stiffness and inertial forces are effectively ignored, and only the damping forces are considered. For this reason, the method is not unlike the familiar decrement method, which can be used to estimate the viscous damping in linear systems. The method is developed in the context of a weakly non-linear, lightly damping two degree-of-freedom system, with both linear and Coulomb damping. Simulated response data is used to demonstrate the accuracy of the technique.

scholarly journals Non-linear damping for scattering-passive systems in the Maxwell class

2020 ◽  
Vol 53 (2) ◽  
pp. 7458-7465
Author(s):  
Shantanu Singh ◽  
George Weiss ◽  
Marius Tucsnak
Keyword(s):  
Passive Systems ◽  
Non Linear ◽  
Linear Damping

Non-linear torsional oscillation of a two-degree-of-freedom system incorporating a Hooke joint

1964 ◽  
Vol 277 (1368) ◽  
pp. 92-106 ◽  
Keyword(s):  
Large Amplitude ◽  
Critical Speed ◽  
Torsional Oscillation ◽  
Degree Of Freedom ◽  
Non Linear ◽  
Two Degree Of Freedom

The non-linear torsional oscillation of the system is analyzed by means of a variant of Kryloff and Bogoliuboff’s method. It is shown that each mode of the system can perform oscillations of large amplitude in a number of critical speed ranges, and that hysteresis effects and discontinuous jumps in amplitude are to be expected in these speed ranges if the damping is light.

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