Experimental and Computational Studies of Chaotic Stirring in Complex 3D Flows

2002 ◽  
Author(s):  
Fotis Sotiropoulos ◽  
Tahirih C. Lackey ◽  
S. Casey Jones
Keyword(s):  
Swirling Flow ◽  
Experimental Studies ◽  
Computational Studies ◽  
Poincaré Maps ◽  
Poincare Maps ◽  
Numerical Studies ◽  
Helical Vortices ◽  
3D Flows ◽  
Confined Flows ◽  
Particle Paths

Recent progress in experimental and computational studies of complex chaotically advected 3D flows is reviewed for the confined swirling flow in a cylindrical container with a rotating bottom and the open flow in a helical static mixer. The concept of Lagrangian averaging along particle paths, whose theoretical foundation stems from ergodic theory, is proposed as a powerful tool for constructing Poincare´ maps in numerical studies of confined flows. The same concept has also been employed to develop the first non-intrusive experimental technique for constructing Poincare´ maps in complex 3D flows. The potential of these ergodic concepts is demonstrated in computational and experimental studies for the confined swirling flow. Numerical computations for the helical mixer flow show that increasing the Reynolds number from Re = 100 to 500 leads to the appearance of unmixed islands in the flow. The mechanism that leads to the formation of such islands is shown to be linked to the growth of coherent helical vortices in the flow.

A Numerical and Experimental Investigation of Period-n Bifurcations in Milling

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Andrew Honeycutt ◽  
Tony Schmitz
Keyword(s):  
Bifurcation Diagrams ◽  
Poincaré Maps ◽  
Vibration Signals ◽  
Stability Behavior ◽  
Poincare Maps ◽  
Numerical Studies ◽  
Stability Maps ◽  
The Stability ◽  
Milling Vibration ◽  
Equations Of Motions

Numerical and experimental analyses of milling bifurcations, or instabilities, are detailed. The time-delay equations of motions that describe milling behavior are solved numerically and once-per-tooth period sampling is used to generate Poincaré maps. These maps are subsequently used to study the stability behavior, including period-n bifurcations. Once-per-tooth period sampling is also used to generate bifurcation diagrams and stability maps. The numerical studies are combined with experiments, where milling vibration amplitudes are measured for both stable and unstable conditions. The vibration signals are sampled once-per-tooth period to construct experimental Poincaré maps and bifurcation diagrams. The results are compared to numerical stability predictions. The sensitivity of milling bifurcations to changes in natural frequency and damping is also predicted and observed.

Bifurcations and chaos in converters. Discontinuous vector fields and singular Poincaré maps

Nonlinearity ◽  
2000 ◽  
Vol 13 (4) ◽  
pp. 1095-1121 ◽  
Author(s):  
Gerard Olivar ◽  
Enric Fossas ◽  
Carles Batlle
Keyword(s):  
Vector Fields ◽  
Poincaré Maps ◽  
Poincare Maps ◽  
Discontinuous Vector Fields

CHAOS AND TWO-TORI IN A NEW FAMILY OF 4-CNNS

2007 ◽  
Vol 17 (03) ◽  
pp. 953-963 ◽  
Author(s):  
XIAO-SONG YANG ◽  
YAN HUANG
Keyword(s):  
Neural Networks ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Cellular Neural Networks ◽  
Lyapunov Spectrum ◽  
Regular Array ◽  
Poincaré Maps ◽  
One Dimensional ◽  
Poincare Maps ◽  
New Family

In this paper we demonstrate chaos, two-tori and limit cycles in a new family of Cellular Neural Networks which is a one-dimensional regular array of four cells. The Lyapunov spectrum is calculated in a range of parameters, the bifurcation plots are presented as well. Furthermore, we confirm the nature of limit cycle, chaos and two-tori by studying Poincaré maps.

Film thickness in elastohydrodynamically lubricated slender elliptic contacts: Part I – numerical studies of central film thickness

2021 ◽  
pp. 135065012110477
Author(s):  
Marius Wolf ◽  
Sergey Solovyev ◽  
Fatemi Arshia
Keyword(s):  
Film Thickness ◽  
State Of The Art ◽  
Experimental Studies ◽  
Elastohydrodynamic Lubrication ◽  
Large Parameter ◽  
Numerical Studies ◽  
Minimum Film Thickness ◽  
Subsequent Publication ◽  
New Formula ◽  
Increasing Load

In this paper, analytical equations for the central film thickness in slender elliptic contacts are investigated. A comparison of state-of-the-art formulas with simulation results of a multilevel elastohydrodynamic lubrication solver is conducted and shows considerable deviation. Therefore, a new film thickness formula for slender elliptic contacts with variable ellipticity is derived. It incorporates asymptotic solutions, which results in validity over a large parameter domain. It captures the behaviour of increasing film thickness with increasing load for specific very slender contacts. The new formula proves to be significantly more accurate than current equations. Experimental studies and discussions on minimum film thickness will be presented in a subsequent publication.

Dynamic Analysis of a Lü Model in Six Dimensions and Its Projections

2017 ◽  
Vol 18 (5) ◽  
pp. 371-384 ◽  
Author(s):  
Luis Alberto Quezada-Téllez ◽  
Salvador Carrillo-Moreno ◽  
Oscar Rosas-Jaimes ◽  
José Job Flores-Godoy ◽  
Guillermo Fernández-Anaya
Keyword(s):  
Dynamic Analysis ◽  
Complex Variables ◽  
Bifurcation Diagrams ◽  
Poincaré Maps ◽  
Five Dimensions ◽  
Strange Nonchaotic Attractor ◽  
The Real ◽  
Poincare Maps ◽  
Extended Complex ◽  
Six Dimensions

AbstractIn this article, extended complex Lü models (ECLMs) are proposed. They are obtained by substituting the real variables of the classical Lü model by complex variables. These projections, spanning from five dimensions (5D) and six dimensions (6D), are studied in their dynamics, which include phase spaces, calculations of eigenvalues and Lyapunov’s exponents, Poincaré maps, bifurcation diagrams, and related analyses. It is shown that in the case of a 5D extension, we have obtained chaotic trajectories; meanwhile the 6D extension shows quasiperiodic and hyperchaotic behaviors and it exhibits strange nonchaotic attractor (SNA) features.

scholarly journals Investigations on Torsion of the Two-Chords Single Laced Members

2017 ◽  
Vol 25 (2) ◽  
pp. 147-160
Author(s):  
Paweł Lorkowski ◽  
Bronisław Gosowski
Keyword(s):  
Cross Sections ◽  
Experimental Studies ◽  
The Finite Element Method ◽  
Second Moment ◽  
Steel Columns ◽  
Numerical Studies ◽  
Traction Network ◽  
Railway Traction ◽  
Parametric Analyses ◽  
The Relationship

Abstract The paper presents experimental and numerical studies to determine the equivalent second moment of area of the uniform torsion of the two-chord steel single laced members. The members are used as poles of railway traction network gates, and steel columns of framed buildings as well. The stiffness of uniform torsion of this kind of columns allows to the determine the critical loads of the spatial stability. The experimental studies have been realized on a single - span members with rotation arrested at their ends, loaded by a torque applied at the mid-span. The relationship between angle of rotation of the considered cross-section and the torque has been determined. Appropriate numerical model was created in the ABAQUS program, based on the finite element method. A very good compatibility has been observed between experimental and numerical studies. The equivalent second moment of area of the uniform torsion for analysed members has been determined by comparing the experimental and analytical results to those obtained from differential equation of non-uniform torsion, based on Vlasov’s theory. Additionally, the parametric analyses of similar members subjected to the uniform torsion, for the richer range of cross-sections have been carried out by the means of SOFiSTiK program. The purpose of the latter was determining parametrical formulas for calculation of the second moment of area of uniform torsion.

scholarly journals Structural Pounding Detection by Using Wavelet Scalogram

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Shutao Xing ◽  
Marvin W. Halling ◽  
Qingli Meng
Keyword(s):  
Experimental Studies ◽  
Shake Table Tests ◽  
Rigid Barrier ◽  
Single Degree Of Freedom ◽  
Structural Pounding ◽  
Numerical Studies ◽  
Bridge Model ◽  
On Line ◽  
Potential Damage ◽  
Bridge Responses

Structural pounding can cause considerable damage and even lead to collapse of structures. Most research focuses on modeling, parameter investigation, and mitigation approaches. With the development of structural health monitoring, the on-line detection of pounding becomes possible. The detection of pounding can provide useful information of potential damage of structures. This paper proposed using wavelet scalograms of dynamic response to detect pounding and examined the feasibility of this method. Numerical investigations were performed on a pounding system that consisted of a damped single-degree-of-freedom (SDOF) structure and a rigid barrier. Hertz contact model was used to simulate pounding behavior. The responses and pounding forces of the system under harmonic and earthquake excitations were numerically solved. The wavelet scalograms of acceleration responses were used to identify poundings. It was found that the scalograms can indicate the occurrence of pounding and occurrence time very well. The severity of the poundings was also approximately estimated. Experimental studies were carried out, in which shake table tests were conducted on a bridge model that underwent pounding between its different components during ground motion excitation. The wavelet scalograms of the bridge responses indicated pounding occurrence quite well. Hence the conclusions from the numerical studies were verified experimentally.

scholarly journals Falling weight impact test of a new-type flexible rock-shed

2018 ◽  
Vol 38 (2) ◽  
pp. 242-252
Author(s):  
Jianrong Yang ◽  
Zhiyu Zhang
Keyword(s):  
Experimental Studies ◽  
Steel Tube ◽  
Time Interval ◽  
Explicit Finite Element ◽  
Numerical Studies ◽  
Structural Details ◽  
Tensile Forces ◽  
New Type ◽  
Falling Weight ◽  
The Impact

A new concept of a flexible rock-shed is presented for protection of the railway from falling rocks. The flexible rock-shed is made of flexible nets connected by specific spring spacer bars to an array of reinforced concrete portable frames which are linked by a longitudinal steel tube truss. To evaluate the performance of the flexible rock-shed, experimental and numerical studies are carried out in the present study. Impact tests are conducted on a full-scale partial model of the prototype structure when it is subjected to a falling block of 340 kg. The impact time interval, maximum deflection of the flexible net, tensile forces in the supporting ropes, and axial strains of spring spacer bars are recorded. To further examine the dynamic behavior of the flexible rock-shed, numerical simulations are also carried out by using the explicit finite element code ANSYS/LS-DYNA. It is found that the numerical results coincide well with the experimental data and both the numerical and experimental studies reveal that the structure can withstand impact energy of 50 kJ with all the materials working in the elastic range. The structural details are improved and the basis for the design and construction of similar structures in the future is provided.<br>

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