Fractal Boundary Explorations for a Nonlinear Two Degree-of-Freedom System

2012 ◽  
Author(s):  
Benjamin A. M. Owens ◽  
Brian P. Mann
Keyword(s):  
Initial Conditions ◽  
Coupled System ◽  
Basins Of Attraction ◽  
Degree Of Freedom ◽  
Fractal Boundary ◽  
Final State ◽  
Potential Wells ◽  
Mechanical Coupling ◽  
Mass Spring ◽  
Two Degree Of Freedom

This paper explores a two degree-of-freedom nonlinearly coupled system with two distinct potential wells. The system consists of a pair of linear mass-spring-dampers with a non-linear, mechanical coupling between them. This nonlinearity creates fractal boundaries for basins of attraction and forced well-escape response. The inherent uncertainty of these fractal boundaries is quantified for errors in the initial conditions and parameter space. This uncertainty relationship provides a measure of the final state and transient sensitivity of the system.

scholarly journals Analysis of controllers in suppressing the structural building vibration

2019 ◽  
Vol 15 (1) ◽  
pp. 112-116
Author(s):  
Normaisharah Mamat ◽  
Fitri Yakub ◽  
Sheikh Ahmad Zaki Sheikh Salim
Keyword(s):  
Fuzzy Logic ◽  
Sliding Mode ◽  
Degree Of Freedom ◽  
Control Voltage ◽  
Sliding Mode Controller ◽  
Building Structure ◽  
Matlab Simulink ◽  
Mass Spring ◽  
Earthquake Vibration ◽  
Two Degree Of Freedom

Two degree of freedom (2 DOF) mass spring damper system is used in representing as building structure that dealing with the earthquake vibration. The real analytical input is used to the system that taken at El Centro earthquake that occurred in May 1940 with magnitude of 7.1 Mw. Two types of controller are presented in controlling the vibration which are fuzzy logic (FL) and sliding mode controller (SMC). The paper was aimed to improve the performance of building structure towards vibration based on proposed controllers. Fuzzy logic and sliding mode controller are widely known with robustness character. The mathematical model of two degree of freedom mass spring damper wasis derived to obtain the relationship between mass, spring, damper, force and actuator. Fuzzy logic and sliding mode controllers were implemented to 2 DOF system to suppress the earthquake vibration of two storeys building. Matlab/Simulink was used in designing the system and controllers to present the result of two storeys displacement time response and input control voltage for uncontrolled and controlled system. Then the data of earthquake disturbance was taken based on real seismic occurred at El Centro to make it as the force disturbance input to the building structure system. The controllers proposed would minimize the vibration that used in sample earthquake disturbance data. The simulation result was carried out by using Matlab/Simulink. The simulation result showed sliding mode controller was better controller than fuzzy logic. In specific, by using the controller, earthquake vibration can be reduced.

The Onset of Chaos in a Two-Degree-of-Freedom Impacting System

1989 ◽  
Vol 56 (1) ◽  
pp. 168-174 ◽  
Author(s):  
Jinsiang Shaw ◽  
Steven W. Shaw
Keyword(s):  
Piecewise Linear ◽  
Global Bifurcation ◽  
Degree Of Freedom ◽  
Chaotic Motions ◽  
Impact Damper ◽  
Onset Of Chaos ◽  
Spring System ◽  
Stability And Bifurcations ◽  
Mass Spring ◽  
Two Degree Of Freedom

The dynamic response of a two-degree-of-freedom impacting system is considered. The system consists of an inverted pendulum with motion limiting stops attached to a sinusoidally excited mass-spring system. Two types of periodic response for this system are analyzed in detail; existence, stability, and bifurcations of these motions can be explicitly computed using a piecewise linear model. The appearance and loss of stability of very long period subharmonics is shown to coincide with a global bifurcation in which chaotic motions, in the form of Smale horseshoes, arise. Application of this device as an impact damper is also briefly discussed.

scholarly journals Small amplitude chimeras for coupled clocks

2020 ◽  
Vol 102 (3) ◽  
pp. 1541-1552
Author(s):  
Dawid Dudkowski ◽  
Patrycja Jaros ◽  
Krzysztof Czołczyński ◽  
Tomasz Kapitaniak
Keyword(s):  
Energy Balance ◽  
Small Amplitude ◽  
Complex Dynamics ◽  
Initial Conditions ◽  
Basins Of Attraction ◽  
Degree Of Freedom ◽  
Energy Balance Method ◽  
Chimera States ◽  
Additional Degree ◽  
Energy Flows

AbstractWe report the arise of small amplitude chimera states in three coupled pendulum clocks suspended on an oscillating base. Two types of chimeras are identified and described by the character of the behaviour of particular units (which can be both regular or irregular). The regions of the appearance of the dynamical patterns are determined and the scenarios of their coexistence with typical synchronization states are discussed. We investigate the chimeras’ basins of attraction, showing that the arise of complex dynamics is not straightforward and highly depends on the system’s parameters and the initial conditions. The latter is confirmed by the probability analysis, exhibiting the rare character of the observed attractors. The scenarios of bifurcations between the chimeric patterns are studied and supported using the energy balance method, which allows to describe the changes of the energy flows between particular nodes of the system. The results presented in this paper confirm the ones obtained for the previous models, extending the analysis with an additional degree of freedom.

scholarly journals A Solution Procedure Combining Analytical and Numerical Approaches to Investigate a Two-Degree-of-Freedom Vibro-Impact Oscillator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1374
Author(s):  
Nicolae Herisanu ◽  
Vasile Marinca
Keyword(s):  
Analytical Solutions ◽  
Initial Conditions ◽  
Solution Procedure ◽  
Degree Of Freedom ◽  
Impact Oscillator ◽  
New Approach ◽  
Analytical Technique ◽  
The Stability ◽  
Two Degree Of Freedom ◽  
Numerical Approaches

In this paper, a new approach is proposed to analyze the behavior of a nonlinear two-degree-of-freedom vibro-impact oscillator subject to a harmonic perturbing force, based on a combination of analytical and numerical approaches. The nonlinear governing equations are analytically solved by means of a new analytical technique, namely the Optimal Auxiliary Functions Method (OAFM), which provided highly accurate explicit analytical solutions. Benefiting from these results, the application of Schur principle made it possible to analyze the stability conditions for the considered system. Various types of possible motions were emphasized, taking into account possible initial conditions and different parameters, and the explicit analytical solutions were found to be very useful to analyze the kinetic energy loss, the contact force, and the stability of periodic motions.

Design of Seeking Control Based on Two-Degree-of-Freedom Controller Using Frequency Shaped Final-State Control

2008 ◽  
Vol 41 (2) ◽  
pp. 1803-1808 ◽  
Author(s):  
Hyun Jae Kang ◽  
Choong Woo Lee ◽  
Chung Choo Chung ◽  
Ho-Seong Lee
Keyword(s):  
Degree Of Freedom ◽  
State Control ◽  
Final State ◽  
Two Degree Of Freedom

Robust end point tracking control of a two-degree-of-freedom mass-spring-damper system

1994 ◽  
Vol 59 (5) ◽  
pp. 1309-1324
Author(s):  
M. M. BRIDGES ◽  
J. Y. ZHU ◽  
D. M. DAWSON ◽  
Z. QU
Keyword(s):  
Tracking Control ◽  
Degree Of Freedom ◽  
End Point ◽  
Point Tracking ◽  
Mass Spring ◽  
Two Degree Of Freedom
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