Influence of Nonzero Mean Impulse Amplitudes on the Response Statistics of Dynamical Systems

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Siu-Siu Guo ◽  
Qing-Xuan Shi ◽  
Hai-Tao Zhu
Keyword(s):  
Dynamical Systems ◽  
Parametric Excitation ◽  
External Excitation ◽  
Itô Calculus ◽  
Nonzero Mean ◽  
Fpk Equation ◽  
Simulation Results ◽  
Polynomial Closure ◽  
Correction Terms ◽  
And Diffusion

This paper investigates the influences of nonzero mean Poisson impulse amplitudes on the response statistics of dynamical systems. New correction terms of the extended Itô calculus, as a generalization of the Wong–Zakai correction terms in the case of normal excitations, are adopted to consider the non-normal property in the case of Poisson process. Due to these new correction terms, the corresponding drift and diffusion coefficients of Fokker–Planck–Kolmogorov (FPK) equation have to be modified and they become more complicated. Herein, the exponential–polynomial closure (EPC) method is employed to solve such a complex FPK equation. Since there are no exact solutions, the efficiency of the EPC method is numerically evaluated by the simulation results. Three examples of different excitation patterns are considered. Numerical results indicate that the influence of nonzero mean impulse amplitudes on system responses depends on the excitation patterns. It is negligible in the case of parametric excitation on displacement. On the contrary, the influence becomes significant in the cases of external excitation and parametric excitation on velocity.

Nonlinear Vibration of Sheet Metal Plates Under Interacting Parametric and External Excitation During Manufacturing

2005 ◽  
Vol 127 (1) ◽  
pp. 36-43 ◽  
Author(s):  
Chung Hwan Kim ◽  
Chong-Won Lee ◽  
N. C. Perkins
Keyword(s):  
Sheet Metal ◽  
Parametric Resonance ◽  
Parametric Excitation ◽  
Synergistic Effects ◽  
Broad Band ◽  
Metal Plate ◽  
Time Dependent ◽  
Single Frequency ◽  
Cubic Nonlinearity ◽  
External Excitation

This study is motivated by the vibrations that plague coating processes used in the manufacturing of coated sheet metal. These vibrations arise from time-dependent tension fluctuations within the sheet metal plate as well as from the eccentricity of the rollers used to transport the plate. The time-dependent tension is observed to be rather broad-band and creates multi-frequency parametric excitation. By contrast, the roller eccentricity is largely single-frequency (synchronized with the roller speed) and creates single-frequency external excitation. The plate and excitation sources are studied herein using a single-degree-of-freedom model with a cubic nonlinearity, subject to combined parametric and external excitation. In our study, we investigate the resonances that arise from the synergistic effects of multi-frequency parametric excitation and single-frequency external excitation. For the simpler case of single-frequency parametric excitation, we observe both sum and difference combination resonances in addition to principal parametric resonance. For the case of multi-frequency parametric excitation, we observe a frequency shift for the parametric resonance that derives from the cubic nonlinearity and external excitation. Moreover, the phase relationships of the external and each parametric excitation source have a significant effect on the resulting response amplitude. We use these analyses to explain the resonance mechanisms observed in experiments conducted on an example sheet metal coating process.

Simultaneous Resonance and Anti-Resonance in Dynamical Systems Under Asynchronous Parametric Excitation

2020 ◽  
Vol 15 (9) ◽  
Author(s):  
Artem Karev ◽  
Peter Hagedorn
Keyword(s):  
Dynamical Systems ◽  
Parametric Excitation ◽  
Analytical Method ◽  
Normal Forms ◽  
High Sensitivity ◽  
Combination Resonance ◽  
Concurrent Study ◽  
The Stability ◽  
Analytical Expressions ◽  
Special Case

Abstract Since the discovery of parametric anti-resonance, parametric excitation has also become more prominent for its stabilizing properties. While resonance and anti-resonance are mostly studied individually, there are systems where both effects appear simultaneously at each combination resonance frequency. With a steep transition between them and a high sensitivity of their relative positions, there is a need for a concurrent study of resonance and anti-resonance. The semi-analytical method of normal forms is used to derive approximate analytical expressions describing the magnitude of the stability impact as well as the precise locations of stabilized and destabilized areas. The results reveal that the separate appearance of resonance and anti-resonance is only a special case occurring for synchronous parametric excitation. In particular, in circulatory systems the simultaneous appearance is expected to be much more common.

OSCILLATIONS ON THE EDGE OF CHAOS VIA DISSIPATION AND DIFFUSION

2007 ◽  
Vol 17 (05) ◽  
pp. 1531-1573 ◽  
Author(s):  
MAKOTO ITOH ◽  
LEON O. CHUA
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Reaction Diffusion ◽  
Coupled System ◽  
Reaction Diffusion Equations ◽  
Nonlinear Dynamical ◽  
Edge Of Chaos ◽  
Secondary Purpose ◽  
Spatio Temporal ◽  
And Diffusion

The primary purpose of this paper is to show that simple dissipation can bring about oscillations in certain kinds of asymptotically stable nonlinear dynamical systems; namely when the system is locally active where the dissipation is introduced. Furthermore, if these nonlinear dynamical systems are coupled with appropriate choice of diffusion coefficients, then the coupled system can exhibit spatio-temporal oscillations. The secondary purpose of this paper is to show that spatio-temporal oscillations can occur in spatially discrete reaction diffusion equations operating on the edge of chaos, provided the array size is sufficiently large.

Control of Multichaotic Systems Using the Extended OGY Method

2015 ◽  
Vol 25 (08) ◽  
pp. 1550096 ◽  
Author(s):  
Ensieh Nobakhti ◽  
Ali Khaki-Sedigh ◽  
Nastaran Vasegh
Keyword(s):  
Dynamical Systems ◽  
Decentralized Control ◽  
Chaotic Maps ◽  
Control Design ◽  
Complex Dynamical Systems ◽  
Design Scheme ◽  
Simulation Results ◽  
The Individual ◽  
Systems Simulation

This paper considers the problem of controlling coupled chaotic maps. Coupled chaotic maps or multichaotic subsystems are complex dynamical systems that consist of several chaotic sub-systems with interactions. The OGY methodology is extended to deal with the control of such systems. It is shown that the decentralized control design scheme in which the individual controllers share no information is not generally able to control multichaotic systems. Simulation results are used to support the main conclusions of the paper.

Cellular Differential Evolution for Optimization

2011 ◽  
Vol 474-476 ◽  
pp. 1770-1775
Author(s):  
Gui Wu Hu ◽  
Xiao Yong Du
Keyword(s):  
Cellular Automata ◽  
Differential Evolution ◽  
Information Exchange ◽  
Cellular Structure ◽  
Mutation Operator ◽  
Solution Quality ◽  
Base Vector ◽  
Quality Stability ◽  
Simulation Results ◽  
And Diffusion

This paper is to illustrate the Cellular Differential Evolution with the cellular structure originated from Cellular automata. Cellular neighbor local search has been designed; base vector or global best in mutation operator is substituted by neighborhood-best, which overcomes the weakness of single selection relating to global best, and balances the contradiction of local and global search, and improves the diversity of population. In addition, cellular structure ensures information exchange, inheritance and diffusion. Finally, a specific algorithm has been implemented: compared with similar variants of DE, the simulation results on 9 benchmark functions demonstrate that cellular differential evolutions are provided with obvious advantages in the solution-quality, stability and speed. <b></b>

scholarly journals Distribution of Sodium and Diffusion Mechanism in Sodium Silicate Liquid

2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Nguyen Thi Thanh Ha
Keyword(s):  
Distribution Function ◽  
Sodium Silicate ◽  
Structural Characteristics ◽  
Diffusion Mechanism ◽  
Silicate Liquid ◽  
Parallel Processes ◽  
Resident Time ◽  
Simulation Results ◽  
The One ◽  
And Diffusion

Molecular dynamic simulation is employed to study the structural properties and diffusion mechanism in sodium silicate (Na2O.4SiO4). Structural characteristics are clarified through the pair radial distribution function, distribution of SiOx coordination units, network structure. The simulation results reveal the structure of Na2O.4SiO4 liquid consists of one Si-O network that is mainly formed by SiO4 units. The spatial distribution of sodium is non-uniform; sodium tends to be in the non-bridging oxygen-simplexes and in larger-radius simplex. Moreover, the sodium density for non-bridging oxygen region is significantly higher than the one for other region. Further, we find that Si and O diffuse by bond break-reformation mechanism, while the motion of Na consists of two parallel processes. Firstly, Na atoms hop from one to another O within a disordered network where each bridging oxygen (BO) has one site, while a non-bridging oxygen (NBO) possesses two sites. The average resident time for Na staying near NBO is much longer than that near BO.

scholarly journals Local Measurement and Diffusion Reconstruction for Signals on a Weighted Graph

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Yingchun Jiang ◽  
Ting Li
Keyword(s):  
Real Life ◽  
Weighted Graph ◽  
Local Measurement ◽  
Original Signal ◽  
Bandlimited Signals ◽  
Simulation Results ◽  
And Diffusion ◽  
Unweighted Graph ◽  
Improved Algorithm

Bandlimited graph signals on an unweighted graph can be reconstructed by its local measurement, which is a generalization of decimation. Since most signals are weighted in real life, we extend and improve the iterative local measurement reconstruction (ILMR) by introducing the diffusion operators to reconstruct bandlimited signals on a weighted graph. We prove that the proposed reconstruction converges to the original signal. Moreover, the simulation results demonstrate that the improved algorithm has better convergence and has robustness against noise.

scholarly journals Component-oriented acausal modeling of the dynamical systems in Python language on the example of the model of the sucker rod string

2019 ◽  
Author(s):  
Volodymyr B Kopei ◽  
Oleh R Onysko ◽  
Vitalii G Panchuk
Keyword(s):  
Dynamical Systems ◽  
Difference Equations ◽  
Hybrid Modeling ◽  
Third Party ◽  
Modeling Languages ◽  
Algebraic Equations ◽  
Symbolic Form ◽  
Basic Set ◽  
Simulation Results ◽  
Acausal Modeling

As a rule, the limitations of specialized modeling languages for acausal modeling of the complex dynamical systems are: limited applicability, poor interoperability with the third party software packages, the high cost of learning, the complexity of the implementation of hybrid modeling and modeling systems with the variable structure, the complexity of the modifications and improvements. In order to solve these problems, it is proposed to develop the easy-to-understand and to modify component-oriented acausal hybrid modeling system that is based on: (1) the general-purpose programming language Python, (2) the description of components by Python classes, (3) the description of components behavior by difference equations using declarative tools SymPy, (4) the event generation using Python imperative constructs, (5) composing and solving the system of algebraic equations in each discrete time point of the simulation. The classes that allow creating the models in Python without the need to study and apply specialized modeling languages are developed. These classes can also be used to automate the construction of the system of difference equations, describing the behavior of the model in a symbolic form. The basic set of mechanical components is developed — 1D translational components "mass", "spring-damper", "force". Using these components, the models of sucker rods string are developed and simulated. These simulation results are compared with the simulation results in Modelica language. The replacement of differential equations by difference equations allow simplifying the implementation of the hybrid modeling and the requirements for the modules for symbolic mathematics and for solving equations.

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