scholarly journals Lyapunov Exponents of Early Stage Dynamics of Parametric Mutations of a Rigid Pendulum with Harmonic Excitation

2019 ◽  
Vol 24 (4) ◽  
pp. 90 ◽  
Author(s):  
Śmiechowicz ◽  
Loup ◽  
Olejnik
Keyword(s):  
Dynamic Behavior ◽  
Lyapunov Exponents ◽  
Dynamic Systems ◽  
Early Stage ◽  
Harmonic Excitation ◽  
System Response ◽  
Suspension Point ◽  
Chaotic Motions ◽  
Forced Responses ◽  
Similar Dynamic

This paper considers three dynamic systems composed of a mathematical pendulum suspended on a sliding body subjected to harmonic excitation. A comparative dynamic analysis of the studied parametric mutations of the rigid pendulum with inertial suspension point and damping was performed. The examined system with parametric mutations is solved numerically, where phase planes and Poincaré maps were used to observe the system response. Lyapunov exponents were computed in two ways to classify the dynamic behavior at relatively early stage of forced responses using two proven methods. The results show that with some parameters three systems exhibit a very similar dynamic behavior, i.e., quasi-periodic and even chaotic motions.

Linear and Nonlinear Dynamic Behaviour

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Dynamic Behavior ◽  
Dynamic Systems ◽  
Dynamic Behaviour ◽  
Nonlinear Dynamical Systems ◽  
Logistic Map ◽  
Nonlinear Dynamical ◽  
Deterministic Dynamic ◽  
Random Behavior ◽  
Single Solution ◽  
Equivalent Systems

In this chapter, we describe how highly erratic dynamic behavior can arise from a nonlinear logistic map, and how this apparently random behavior is governed by a surprising order. With this lesson in mind, we should not be overly surprised that highly erratic and random appearing observed data might also be generated by parsimonious deterministic dynamic systems. At a minimum, we contend that researchers should apply NLTS to test for this possibility. We also introduced tools to analyze dynamic behavior that form the foundation for NLTS. In particular, we have stressed the quite unexpected capability to achieve some form of predictability even with only one trajectory at hand. In subsequent chapters, we treat known nonlinear dynamical systems as unknown, and investigate how NLTS methods rely on a single solution (or multiple solutions) generated by them to reconstruct equivalent systems. This is a conventional approach in the literature for seeing how NLTS methods work since we know what needs to be reconstructed.

MUTUAL AND SELF-COMPOUNDING OF CHAOTIC SYSTEMS

1996 ◽  
Vol 06 (04) ◽  
pp. 759-767
Author(s):  
R. SINGH ◽  
P.S. MOHARIR ◽  
V.M. MARU
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Dynamic Systems ◽  
Mantle Convection ◽  
Chaotic Systems ◽  
Compound System ◽  
Two Systems

The notion of compounding a chaotic system was introduced earlier. It consisted of varying the parameters of the compoundee system in proportion to the variables of the compounder system, resulting in a compound system which has in general higher Lyapunov exponents. Here, the notion is extended to self-compounding of a system with a real-earth example, and mutual compounding of dynamic systems. In the former, the variables in a system perturb its parameters. In the latter, two systems affect the parameters of each other in proportion to their variables. Examples of systems in such compounding relationships are studied. The existence of self-compounding is indicated in the geodynamics of mantle convection. The effect of mutual compounding is studied in terms of Lyapunov exponent variations.

scholarly journals Bifurcations of a Controlled Two-Bar Linkage Motion with Considering Viscous Frictions

2011 ◽  
Vol 18 (1-2) ◽  
pp. 365-375 ◽  
Author(s):  
Qingkai Han ◽  
Xueyan Zhao ◽  
Xingxiu Li ◽  
Bangchun Wen
Keyword(s):  
Phase Space ◽  
Lyapunov Exponents ◽  
Time Domain ◽  
Shooting Method ◽  
Viscous Friction ◽  
Dynamical Model ◽  
Chaotic Motions ◽  
Amplitude Spectra ◽  
Set Up ◽  
Joint Motions

In this paper, we investigate the joint viscous friction effects on the motions of a two-bar linkage under controlling of OPCL. The dynamical model of the two-bar linkage with an OPCL controller is firstly set up with considering the two joints' viscous frictions. Thereafter, the motion bifurcations of the two-bar linkage along the values of joint viscous frictions are obtained using shooting method. Then, single-periodic, multiple-periodic, quasi-periodic and chaotic motions of link rotating angles are simulated with given different viscous friction values, and they are illustrated in time domain waveforms, phase space portraits, amplitude spectra and Poincare mapping graphs, respectively. Additionally, for the chaotic case, Lyapunov exponents and hypothesis possibilities of the two joint motions are also estimated.

Dynamic Behavior Analysis of Three-Span Rotor-Bearing System with Rub-Impact Fault

2012 ◽  
Vol 460 ◽  
pp. 160-164 ◽  
Author(s):  
Song He Zhang ◽  
Yue Gang Luo ◽  
Bin Wu ◽  
Bang Chun Wen
Keyword(s):  
Nonlinear Dynamics ◽  
Behavior Analysis ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Rotor System ◽  
System Response ◽  
Rotor Bearing ◽  
Set Up ◽  
Bearing System ◽  
Main Influence

The dynamic model of the three-span rotor-bearing system with rub-impact fault was set up. The influence to nonlinear dynamics behaviors of the rotor-bearing system that induced by rub-impact of one disc, two discs and three discs were numerically studied. The main influence of the rotor system response by the rub-impact faults are in the supercritical rotate speed. There are mutations of amplitudes in the responses of second and third spans in supercritical rotate speed when rub-impact with one disc, and there are chaotic windows in the response of first span, and jumping changes in second and third spans when rub-impact with two or three discs.

System Dynamic Modeling of Vapor Compression Cycles

2012 ◽  
Author(s):  
Eric S. Miller ◽  
Soumya S. Patnaik ◽  
Milind A. Jog
Keyword(s):  
Thermal Management ◽  
Dynamic Behavior ◽  
Lagrangian Method ◽  
System Response ◽  
Vapor Compression ◽  
Wide Range ◽  
Compression Cycle ◽  
Cycle Systems ◽  
Component Models ◽  
And Control

Vapor Compression cycle Systems (VCSs) are being considered for thermal management aboard modern aircraft where dynamic changes in heat loads are very common. Predicting dynamic behavior of VCSs is critical to design, sizing, and control of aircraft thermal management systems. A novel Lagrangian method to model the dynamic behavior of VCSs has been developed. This approach divides each fluid flow into a large number of elements having fixed mass, but variable volume and position. At discrete time steps, heat transferred to or from each mass element is determined by component models. This paper gives simulation results showing system startup under PID feedback control. Then, from steady state, the system response to an increase in heat load, an increase in sink availability, a decrease in valve throttle and an increase in compressor speed are simulated and the results reported. Results indicate that the Lagrangian method can provide results for a wide range of cases and that VCC systems require extensive control to meet performance objectives.

scholarly journals Effects of Eccentricity on the Dynamic Behavior for Electromechanical Integrated Toroidal Drive

2013 ◽  
Vol 20 (2) ◽  
pp. 273-286 ◽  
Author(s):  
Lizhong Xu ◽  
Haifeng Li
Keyword(s):  
Dynamic Behavior ◽  
Natural Frequencies ◽  
Drive System ◽  
The Other ◽  
Dynamic Equations ◽  
Electromechanical Integrated ◽  
Drive Systems ◽  
Forced Responses ◽  
Design And Manufacture ◽  
Center Distance

In electromechanical integrated toroidal drive, eccentric center errors occur which has important influences on the dynamic behavior of the drive system. Here, the dynamic equations of the drive system with eccentric center are presented. Changes of the natural frequencies and vibrating modes along with eccentric center distance are analyzed. The forced responses of the drive system to eccentric center excitation are investigated. Results show that the eccentric center causes some natural frequencies to increase, and the other natural frequencies to drop. It also causes some vibrations to become weak, and the other vibrations to become strong. The eccentric center has more obvious effects on the dynamic behavior of the planets. The results are useful in design and manufacture of the drive systems.

Analysis of Free Nonlinear Vibration Behavior for Curved Embedded Carbon Nanotubes on Elastic Foundation

2010 ◽  
Author(s):  
M. Rezaee ◽  
H. Fekrmandi
Keyword(s):  
Carbon Nanotubes ◽  
Dynamic Behavior ◽  
Continuum Mechanics ◽  
Nonlinear Term ◽  
Nonlinear Oscillations ◽  
Equation Of Motion ◽  
System Response ◽  
Response Curves ◽  
Vibration Behavior ◽  
The Continuum

Carbon nanotubes (CNTs) are expected to have significant impact on several emerging nanoelectromechanical (NEMS) applications. Vigorous understanding of the dynamic behavior of CNTs is essential for designing novel nanodevices. Recent literature show an increased utilization of models based on elastic continuum mechanics theories for studying the vibration behavior of CNTs. The importance of the continuum models stems from two points; (i) continuum simulations consume much less computational effort than the molecular dynamics simulations, and (ii) predicting nanostructures behavior through continuum simulation is much cheaper than studying their behavior through experimental verification. In numerous recent papers, CNTs were assumed to behave as perfectly straight beams or straight cylindrical shells. However, images taken by transmission electron microscopes for CNTs show that these tiny structures are not usually straight, but rather have certain degree of curvature or waviness along the nanotubes length. The curved morphology is due to process-induced waviness during manufacturing processes, in addition to mechanical properties such as low bending stiffness and large aspect ratio. In this study the free nonlinear oscillations of wavy embedded multi-wall carbon nanotubes (MWCNTs) are investigated. The problem is formulated on the basis of the continuum mechanics theory and the waviness of the MWCNTs is modeled as a sinusoidal curve. The governing equation of motion is derived by using the Hamilton’s principle. The Galerkin approach was utilized to reduce the equation of motion to a second order nonlinear differential equation which involves a quadratic nonlinear term due to the curved geometry of the beam, and a cubic nonlinear term due to the stretching effect. The system response has been obtained using the incremental harmonic balanced method (IHBM). Using this method, the iterative relations describing the interaction between the amplitude and the frequency for the single-wall nanotube and double-wall nanotube are obtained. Also, the influence of the waviness, elastic medium and van der Waals forces on frequency-response curves is researched. Results present some useful information to analyze CNT’s nonlinear dynamic behavior.

Dynamics of Deformable Fractal Surface in Contact with Harmonically Excited Rigid Flat

2017 ◽  
Vol 7 (2) ◽  
pp. 38-62
Author(s):  
Tamonash Jana ◽  
Anirban Mitra ◽  
Prasanta Sahoo
Keyword(s):  
Rough Surface ◽  
Dynamic Properties ◽  
Element Model ◽  
Harmonic Excitation ◽  
System Response ◽  
Fractal Surface ◽  
Fractal Rough Surface ◽  
Mass Damper ◽  
Relationship Of ◽  
Force Displacement

Dynamics of contact between a deformable fractal rough surface and a rigid flat is studied under harmonic excitation to the flat surface. Fractal surface is generated from the modified Weierstrass-Mandelbrot function and is imported to ANSYS to construct the finite element model of the same. A parameter called ‘nonlinearity exponent', is obtained from the force-displacement relationship of the rough surface and is used to find out the dynamic properties of the contacting interface using single spring-mass-damper model. The effect of variation in surface roughness and material properties on the system response is analyzed. The system exhibits superharmonic responses for different values of the nonlinearity exponent. The phase plot and time-displacement plots for the system are also furnished.

scholarly journals High mobility of lattice molecules and defects during the early stage of protein crystallization

Soft Matter ◽  
2020 ◽  
Vol 16 (8) ◽  
pp. 1955-1960 ◽  
Author(s):  
Tomoya Yamazaki ◽  
Alexander E. S. Van Driessche ◽  
Yuki Kimura
Keyword(s):  
Dynamic Behavior ◽  
Early Stage ◽  
Protein Crystallization ◽  
High Mobility ◽  
Protein Crystals

Dynamic behavior of defects in lysozyme protein crystals reveals that the lattice molecules are mobile throughout the crystal.

scholarly journals Improving the Dynamic Behavior of Adjacent Buildings with Fluid Viscous Dampers

2016 ◽  
Vol 10 (12) ◽  
pp. 245
Author(s):  
Solmaz Yaghobzadeh
Keyword(s):  
Control Systems ◽  
Dynamic Behavior ◽  
Time History ◽  
Tall Buildings ◽  
System Response ◽  
Response Analysis ◽  
Viscous Dampers ◽  
Fluid Viscous Dampers ◽  
Adjacent Buildings ◽  
The Impact

Explained ways to strengthen structures against lateral dynamic loads can be divided into two broad categories. The first part is the structural systems for controlling seismic displacement and second part is the use of applying systems of control forces. Response mechanism of structures using control systems are improved and greatly reduce the risks of damage caused by earthquakes.Today the use of these control systems in buildings have been increased and it’s important to reduce vibration of structures is felt more than ever. As well as to improve the dynamic behavior of nearby buildings, control systems can be installed between adjacent buildings as activated, semi-active and inactivated systems. The main purpose of this study is the use of control systems in two similar adjacent buildings to reduce the entire system response which will be the analytical study of the impact of viscous dampers to control system performance.In order to analysis of modeling to improve the dynamic behavior of different adjacent buildings connected with dampers, two models of the original sample will be examined in this article. All examples are different from each other and to elicit response analysis and time history software SAP 2000was used. According to the results the effect of fluid viscous dampers for tall buildings compared shorter building, is less. Also, these dampers for adjacent buildings with different heights than buildings with same height are more effective.

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