Academic literature on the topic 'Bifurcation plot'

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Journal articles on the topic "Bifurcation plot"

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HU, JIAZHU, and P. FRANK PAI. "BIFURCATION STRUCTURE FOR MODULATED VIBRATION OF STRINGS SUBJECTED TO HARMONIC BOUNDARY EXCITATIONS." International Journal of Bifurcation and Chaos 21, no. 11 (2011): 3259–72. http://dx.doi.org/10.1142/s0218127411030507.

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In the studies of nonlinear dynamics, phase plan plot is a most commonly used tool for solution characteristics interpretation. Phase plan plot provides an adequate representation of the dynamic characteristics of single solution, but it does not provide information on the interrelation between neighboring solutions; therefore, the evolution of solutions is studied by examining fragmented information of many individual responses. When the solution space becomes complicated, accurate information of the interrelation between responses is essential for an overall comprehension of the characterist
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ORRELL, DAVID, and LEONARD A. SMITH. "VISUALIZING BIFURCATIONS IN HIGH DIMENSIONAL SYSTEMS: THE SPECTRAL BIFURCATION DIAGRAM." International Journal of Bifurcation and Chaos 13, no. 10 (2003): 3015–27. http://dx.doi.org/10.1142/s0218127403008387.

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This paper presents methods to visualize bifurcations in flows of nonlinear dynamical systems, using the Lorenz '96 systems as examples. Three techniques are considered; the first two, density and max/min diagrams, are analagous to the bifurcation diagrams used for maps, which indicate how the system's behavior changes with a control parameter. However the diagrams are generally harder to interpret than the corresponding diagrams of maps, due to the continuous nature of the flow. The third technique takes an alternative approach: by calculating the power spectrum at each value of the control p
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Biswas, Sujay, and Alaka Das. "Patterns, Bifurcations, Multistability and Hysteresis in an Inhomogeneous Coupled Map Lattice." International Journal of Bifurcation and Chaos 26, no. 03 (2016): 1630008. http://dx.doi.org/10.1142/s0218127416300081.

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We investigate local interaction between logistic maps in an inhomogeneous lattice numerically with respect to an inhomogeneity parameter [Formula: see text] and the coupling constant [Formula: see text]. In our model, the inhomogeneity appears in the form of different values of the map parameter at different sites. The phase diagram of the model in the [Formula: see text]–[Formula: see text] plane gives seven qualitatively different patterns. These are: synchronized patterns, steady (fixed in time) patterns with spatial period-two, spatially chaotic together with temporally periodic patterns,
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Saha, Asit, and Amiya Das. "Dynamical behavior of nonlinear wave solutions of the generalized Newell–Whitehead–Segel equation." International Journal of Modern Physics C 31, no. 04 (2020): 2050059. http://dx.doi.org/10.1142/s012918312050059x.

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Dynamical behavior of nonlinear wave solutions of the perturbed and unperturbed generalized Newell–Whitehead–Segel (GNWS) equation is studied via analytical and computational approaches for the first time in the literature. Bifurcation of phase portraits of the unperturbed GNWS equation is dispensed using phase plane analysis through symbolic computation and it shows stable oscillation of the traveling waves. Chaotic behavior of the perturbed GNWS equation is obtained by applying different computational tools, like phase plot, time series plot, Poincare section, bifurcation diagram and Lyapuno
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Güzel, İsmail, Elizabeth Munch, and Firas A. Khasawneh. "Detecting bifurcations in dynamical systems with CROCKER plots." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 9 (2022): 093111. http://dx.doi.org/10.1063/5.0102421.

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Existing tools for bifurcation detection from signals of dynamical systems typically are either limited to a special class of systems or they require carefully chosen input parameters and a significant expertise to interpret the results. Therefore, we describe an alternative method based on persistent homology—a tool from topological data analysis—that utilizes Betti numbers and CROCKER plots. Betti numbers are topological invariants of topological spaces, while the CROCKER plot is a coarsened but easy to visualize data representation of a one-parameter varying family of persistence barcodes.
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Rajagopal, Karthikeyan, Prakash Duraisamy, Riessom Weldegiorgis, and Anitha Karthikeyan. "Multistability in Horizontal Platform System with and without Time Delays." Shock and Vibration 2018 (2018): 1–8. http://dx.doi.org/10.1155/2018/1092812.

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Chaotic behavior and bifurcation analysis of horizontal platform systems (HPS) have been investigated widely by many researchers. However, the multistable features of such systems have not been investigated, and hence we identified the multistable parameter and investigated the coexisting attractors of the HPS. To understand the effects of time delays on the nonautonomous and autonomous HPS, we introduced a constant time delay in the state feedback variable. Investigation of the bifurcation of the time delayed HPS with time delay and parameters reveals that the system behavior differs between
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LI, QINGDU, XIAO-SONG YANG, and FANGYAN YANG. "HYPERCHAOS IN A SIMPLE CNN." International Journal of Bifurcation and Chaos 16, no. 08 (2006): 2453–57. http://dx.doi.org/10.1142/s0218127406016197.

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In this paper we demonstrate hyperchaotic dynamics in a very simple Cellular Neural Network (CNN) which is a one-dimensional regular array of four cells. The Lyapunov spectrum is calculated in a range of parameters, and the bifurcation plot is presented as well.
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Liu, Zeyu, Tiecheng Xia, and Jinbo Wang. "Image Encryption Technology Based on Fractional Two-Dimensional Triangle Function Combination Discrete Chaotic Map Coupled with Menezes-Vanstone Elliptic Curve Cryptosystem." Discrete Dynamics in Nature and Society 2018 (2018): 1–24. http://dx.doi.org/10.1155/2018/4585083.

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A new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM) with the discrete fractional difference is proposed. We observe the bifurcation behaviors and draw the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits of the proposed map, respectively. On the application side, we apply the proposed discrete fractional map into image encryption with the secret keys ciphered by Menezes-Vanstone Elliptic Curve Cryptosystem (MVECC). Finally, the image encryption algorithm is analysed in four main aspects that indicate the proposed algor
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ZHENG, JIONGXUAN, JOSEPH D. SKUFCA, and ERIK M. BOLLT. "THE BUNDLE PLOT: EVOLUTION OF SYMBOLIC SPACE UNDER THE SYSTEM PARAMETER CHANGES." International Journal of Bifurcation and Chaos 23, no. 08 (2013): 1330028. http://dx.doi.org/10.1142/s0218127413300280.

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This paper provides a topological dynamics perspective on the full bifurcation unfolding in unimodal mappings. We present a bundle structure, visualized as a bundle plot, to show the evolution of symbolic space as we vary a system parameter. The bundle plot can be viewed as a limit process of an assignment plot, which are line assignments between points from two dynamical systems. Such line assignments are determined by a commuter, which is a coordinates transformation function that satisfies a commuting relationship but not necessarily a homeomorphism. The bundle structure is studied by under
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Zati Iwani Abdul Manaf, Nur Adiba Lyana Rosli, Nurul Aini Mahmood, and Noor Alia Yamin. "The Effect of Mosquito Biting Rate on the Malaria Transmission Model using Bifurcation Analysis." Journal of Mathematics and Computing Science 8, no. 1 (2022): 25–35. https://doi.org/10.24191/jmcs.v8i1.6972.

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This paper analyses a simple malaria transmission model to investigate the effect of parameter changes in mosquitoes per capita biting rate on human population, , by using the bifurcation analysis. For further investigation, we first formulated the malaria transmission model into a non-dimensionalized equation. Next, we employed the stability analysis of disease-free equilibrium and endemic equilibrium point of malaria transmission. Using the same non-dimensionalized equation, the one-parameter bifurcation analysis was conducted. A few graphs of the bifurcation diagram, phase plane and time se
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Dissertations / Theses on the topic "Bifurcation plot"

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Sendrowski, Janek. "Feigenbaum Scaling." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-96635.

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In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. A more intricate approach drawing from renormalization theory as well as a short consideration of some of the topological properties will also be presented. I was furthermore trying to put great emphasis on diagrams throughout the text to make the contents more comprehensible and intuitive.
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Book chapters on the topic "Bifurcation plot"

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Zerbato, Luca, Enrico Galvagno, and Mauro Velardocchia. "Bifurcation Analysis of a Nonlinear Vehicle Model on Banked Road." In Lecture Notes in Mechanical Engineering. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-70392-8_6.

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AbstractTowards the transition to automated driving, lateral stability of the vehicle represents a key requirement to guarantee the safety of passengers and vulnerable road users, especially during emergency operating conditions where nonlinearities arise. The present paper aims at investigating the effect of road banking angle on vehicle plane motion stability. To perform this analysis, a pure lateral nonlinear double track model is numerically derived for an oversteering vehicle. Lateral load transfer and its distribution among the axles are included for exploiting the tyre saturation region
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Du, Xiaolei, and Yong Xu. "Dynamical Behaviours of the Nose Landing Gear with Freeplay and Stochastic Disturbance." In Lecture Notes in Mechanical Engineering. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-70392-8_68.

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AbstractShimmy dynamics of a dual wheel nose landing gear system with torsional freeplay under stochastic lateral disturbances is studied. Dynamic characteristics of the deterministic case are numerically analyzed, especially the shimmy of the landing gear through bifurcation analysis. Meanwhile, the influences of the freeplay nonlinearity on shimmy behaviours are examined in detail. Impacts of stochastic lateral disturbances on the shimmy of the landing gear system are performed via time history and recurrence plots. Our results show that the interaction between the freeplay nonlinearity and
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Janmohamed, Abdul R. "Nadine Gordimer The Degeneration of the Great South African Lie." In Nadine Gordimer’s Burger’s Daughter. Oxford University PressNew York, NY, 2003. http://dx.doi.org/10.1093/oso/9780195147162.003.0007.

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Abstract The Excellence Of Burger’s Daughter is due to a judicious combination of the relative simplicity of its plot, the elegance and appropriateness of its style, and the integrity, acuteness, and courage of Rosa Burger’s attempt to define her “self.” The novel is primarily concerned with Rosa’s examination of the priority of her own values, desires, and needs against a nexus of values furnished by the apartheid society in South Africa, by the bourgeois culture in Europe, and by the discipline, compassion, and political ideas inherited from her Communist Father. Given the simplicity of the
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Jordan, D. W., and P. Smith. "Poincaré sequences, homoclinic bifurcation, and chaos." In Nonlinear ordinary differential equations. Oxford University PressOxford, 1999. http://dx.doi.org/10.1093/oso/9780198565635.003.0013.

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Abstract Important features can be totally obscured in such a diagram, but Poincare maps can be used to detect underlying structure, such as periodic solutions having the forcing or a subharmonic frequency. In this context the investigation of periodic solutions, nearly periodic solutions, and similar phenomena is to a considerable extent an exploratory matter in which computation plays at the present time a very significant part. A search for hidden periodicities, such as subharmonic periods, is best carried out by starting with a period in mind and then looking for solutions with this period
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Abdullah Qadha, Sarah, Muneera Abdullah Qadha, and Haibo Chen. "Existence of limit cycles for a class of quintic Kukles homogeneous system." In Recent Research in Polynomials [Working Title]. IntechOpen, 2023. http://dx.doi.org/10.5772/intechopen.1000859.

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We investigated the existence of limit cycles for quintic Kukles polynomial differential systems depending on a parameter in this chapter. These systems are important in practical applications and theoretical advances. We first used formal series method based on Poincaré’s ideas to prove this point and determine the centre-focus problem. We then utilised the Dulac function to prove the non-existence of closed orbits. We determined the sufficient condition for the existence of the limit cycles, which bifurcate from the equilibrium point, using Hopf bifurcation theory. Lastly, we provided some n
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Blagojević, Nenad, and Velimir Ilić. "РАЗВОЈ ЖАНРА АЛТЕРНАТИВНЕ ИСТОРИЈЕ У РУСКОЈ КЊИЖЕВНОЈ ФАНТАСТИЦИ." In JEZIK, KNJIŽEVNOST, ALTERNATIVE/LANGUAGE, LITERATURE, ALTERNATIVES - Književna istraživanja. Filozofski fakultet u Nišu, 2022. http://dx.doi.org/10.46630/jkal.2022.3.

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Since in the alternative history as a genre of literary fiction, the bifurcation point, namely the fantastic assumptions that at some of the turning points in history there was an alternative development of events, has a central role, this genre of literature has become quite useful in the analysis of the perception of national history through examination of the impact of certain events on the historical development of a given culture. In this paper, through the prism of the development of the genre of alternative history in Russian literary fiction, we look at historical events which stand ou
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Kanti Das, Mrinal, and Lal Mohan Saha. "Chaotic Dynamics and Complexity in Real and Physical Systems." In Advances in Dynamical Systems Theory, Models, Algorithms and Applications. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.96573.

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Emergence of chaos and complex behavior in real and physical systems has been discussed within the framework of nonlinear dynamical systems. The problems investigated include complexity of Child’s swing dynamics , chaotic neuronal dynamics (FHN model), complex Food-web dynamics, Financial model (involving interest rate, investment demand and price index) etc. Proper numerical simulations have been carried out to unravel the complex dynamics of these systems and significant results obtained are displayed through tables and various plots like bifurcations, attractors, Lyapunov exponents, topolog
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Alain, Kammogne Soup Tewa, Kengne Romanic, Ahmad Taher Azar, Sundarapandian Vaidyanathan, Fotsin Hilaire Bertrand, and Ngo Mouelas Adèle. "Dynamics Analysis and Synchronization in Relay Coupled Fractional Order Colpitts Oscillators." In Advances in System Dynamics and Control. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-4077-9.ch011.

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In this chapter, the dynamics of a particular topology of Colpitts oscillator with fractional order dynamics is presented. The first part is devoted to the dynamics of the model using standard nonlinear analysis techniques including time series, bifurcation diagrams, phase space trajectories plots, and Lyapunov exponents. One of the major results of this innovative work is the numerical finding of a parameter region in which the fractional order Colpitts oscillator's circuit experiences multiple attractors' behavior. This phenomenon was not reported previously in the Colpitts circuit (despite
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Conference papers on the topic "Bifurcation plot"

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Chen, Guo, and Rong Tao Hou. "Nonlinear Dynamic Response Analysis of Rotor-Ball Bearing-Stator Coupling System Including Unbalance-Rubbing Coupling Faults." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34186.

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In this paper, a new rotor-ball bearing-stator coupling system dynamic model is established. In the model, the rotor mass unbalance and rubbing faults are included, and the nonlinear factors of ball bearing such as the clearance of bearing, nonlinear Hertzian contract force between balls and races, and the varying compliance vibration coming from the periodical variety of contact positions between balls and races are modeled. The numerical integral method is employed to obtain system’s responses, and the vibration amplitude-rotating speed curve, bifurcation plot, phase plane plot, shaft centre
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Momin, Marzia, Nusrat Ara, and M. Tarik Arafat. "Analysis of Blood Flow Patterns to Estimate Atherosclerosis Formation in the Left Carotid Artery by CFD Simulation." In ASME 2020 Fluids Engineering Division Summer Meeting collocated with the ASME 2020 Heat Transfer Summer Conference and the ASME 2020 18th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/fedsm2020-20052.

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Abstract The purpose of this computational fluid dynamics (CFD) study is to simulate left carotid artery models to evaluate the influence of hematocrit (Hct) level and angle of bifurcation on the formation of atherosclerosis. Bifurcation angle can vary from person to person based on sex, age or diseased condition which has an impact on hemo-dynamic parameters. From the anatomical study, it is seen that the carotid artery bifurcation is the preferential region for atherosclerosis formation. The combination of bifurcation, curvature and diameter change in this bifurcation region causes the blood
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Kumar, Pankaj, S. Narayanan, and Sayan Gupta. "Dynamic Parameters Estimation and Fault Identification From Random Response of Rolling Element Bearing in a Rotor Bearing System." In ASME 2019 Gas Turbine India Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gtindia2019-2565.

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Abstract This paper presents a procedure for determination of dynamic properties of rolling element bearing by using the vibration signals picked up at the bearing caps. The rotor-bearing assembly is idealized as Duffing oscillator and random vibration signals modelled as exponentially correlated (Ornstein-Uhlenbeck) colored noise. Expressing the excitation as a first order filtered white noise enables the direct formulation of the 3D-Fokker Planck (FP) equation for system response through the Markov vector approach. Closed form solution of the stationary FP equation is derived. Subsequently t
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Mohekar, Ajit, Burt Tilley, and Vadim Yakovlev. "PLANE WAVE IRRADIATION OF A LAYERED SYSTEM: RESONANCE-BASED CONTROL OVER THERMAL RUNAWAY." In Ampere 2019. Universitat Politècnica de València, 2019. http://dx.doi.org/10.4995/ampere2019.2019.9940.

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The loss factor of a material is a key characteristic behind heat generation during EM heating. For typical ceramics, the loss factor increases exponentially with temperature potentially initiating thermal runaway which can damage the material through melting or cracking. Equilibrium of EM heating can be represented by a parametric plot of the average steady-state temperature as function of the applied power that is known as a power response curve. In a layered structure, for wavelengths of the incident wave that are much larger than the layer’s thickness, the power response curve is an S-shap
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Pancharia, Pankaj, Vikram Ramanan, Baladandayuthapani Nagarajan, and S. R. Chakravarthy. "Investigation on Effect of Inlet Flow Turbulence on the Combustion Instability Using Simultaneous PIV and CH* Chemiluminescence in a Backward Facing Step Combustor." In ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gt2019-92022.

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Abstract The present study investigates the role of inlet turbulence intensity on the stability characteristics of a lab scale backward facing step combustor (BFS). Turbulence generator placed upstream of the flame holder is used to vary the turbulence levels. The present study utilizes simultaneous chemiluminescence, particle image velocimetry (PIV) and unsteady pressure fluctuation measurement are done in a time-resolved manner to study the role of inlet turbulence intensity on the flame-flow dynamics and identify different modes of combustion instability as a result of the same. The bifurca
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Nelon, Christopher M., Jonathan Figueroa, Oliver J. Myers, and Aaron Shepard. "Non-Traditional Shape Variations on Bistable Carbon Fiber Reinforced Polymer Laminates." In ASME 2020 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/smasis2020-2291.

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Abstract The ability of a material to display two equilibrium states, called bistability, has been previously observed in carbon fiber reinforced polymers (CFRPs). For bistability to occur, the laminate must consist of an unsymmetric layup about its midplane which generates internal residual stress from thermal contraction. Prior studies have observed bistability in CFRPs with small-scale rectangular geometries where all sides were less than 250 mm. The aim of this paper is to demonstrate the existence of bistability in large-scale CFRPs with rectangular and non-rectangular geometries. Experim
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Wang, Wei, Guixian Li, and Guangbin Yu. "The Bifurcation Analysis of High-Speed Vehicle and Mechanism of Jumping Rail." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34336.

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The dynamics phenomena of half railway carriage model with 17 degrees of freedom are investigated. The model is set to run on a straight track with the speed range between 85 and 165m/s. Shen-Hedrick-Elkins theory is used to describe the nonlinear relation between the creepage and the creep forces. A new method of flange contact as multi-body collision is also presented. Bifurcation diagram and the critical speed for jumping rail are obtained and further validated by the simulation. Finally, the phase plots of the flange contact are discussed.
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Shah, Chhote Lal, Dipanjan Majumdar, and Sunetra Sarkar. "Delaying the Chaotic Onset in the Flow-Field of Flapping Foil With Flexible Aft Tail." In ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-23868.

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Abstract The present study is focused on examining the flow-field dynamics of a flapping foil with a flexible aft tail as compared to a rigid configuration where tail flexibility is infinite. The flow around the oscillating body is governed by the incompressible Navier-Stokes equations. An in-house Fluid-Structure Interaction solver has been developed following a discrete forcing type Immersed Boundary Method coupled with an inextensible filament structural model. The flapping amplitude is considered as a bifurcation parameter, and as the bifurcation parameter is increased, the periodic wake t
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Swetha, Juturu, Ganesh Tamadapu, and Shaikh Faruque Ali. "Workspace Evolution of Hard Magnetic Soft Elastica." In ASME 2022 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/smasis2022-91001.

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Abstract Workspace, the set of all possible positions reached by the end effector, must be large for a continuum robot for safe steer-ability. Magnetically actuated soft robots have high workspace due to their millimetre-scale size and large flexibility, enabling them to navigate constrained environments. When subjected to an external magnetic field, they undergo large deflections by interacting with magnetic particles. This work develops closed-form (assuming 2D planar) and numerical solutions to rotation and deflection for uniformly magnetised elastica at an angle using Cosserat rod theory.
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Ghayesh, Mergen H., and Michael P. Pai¨doussis. "Dynamics of a Fluid-Conveying Cantilevered Pipe With Intermediate Spring Support." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-30084.

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The aim of this study is to investigate the three-dimensional (3-D) nonlinear dynamics of a fluid-conveying cantilevered pipe, additionally supported by an array of four springs attached at a point along its length. In the theoretical analysis, the 3-D equations are discretized via Galerkin’s technique, yielding a set of coupled nonlinear differential equations. These equations are solved numerically using a finite difference technique along with the Newton-Raphson method. The dynamic behaviour of the system is presented in the form of bifurcation diagrams, along with phase-plane plots, time-h
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Reports on the topic "Bifurcation plot"

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Kozmina, Jelena, and Alytis Gruodis. Tool QUATTRO-20 for Examining of the Recurrent Sequencies Generated by Discrete Analogue of the Verhulst Equation. Publishing House - Vilnius Business College, 2023. http://dx.doi.org/10.57005/ab.2023.1.3.

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QUATTRO-20 as advanced tool for estimation of the recurrent sequences was created and tested. Discrete analogue of Verhulst equation x(t+1)=F(x(t)), F(x)=rx(1-x), t=0, 1, 2, ..., was selected as the model of recurrent sequence. Related mathematical material is presented in user-friendly form: convergence conditions, Lyapunov index, behaviour of the sequencies generated by second, third, fourth compositions of function F(x). QUATTRO-20 contains several visualization methods such as xy plot, Bifurcation diagram, distribution of Lyapunov index, CobWeb plot, graphical solution. Novel graphical tec
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