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Tytuł:
A fully-coupled three-dimensional fluid-structure interaction study on the externally-pressurized collapsible tube and the internal flow
Autorzy:
Zhang, Sen
Liu, HaoFei
Powiązania:
https://bibliotekanauki.pl/articles/2200900.pdf
Data publikacji:
2023
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
fluid structure interaction
stability
eigenvalue problem
bifurcation
Opis:
We study the behavior of a collapsible tube conveying a fluid subject to external pressure that could occur in many physiological applications. The method of rotating spines is developed to enable an automatic mesh adaptation when the tube is deformed largely. We examine bifurcation diagrams when the tube is collapsed under a pressure driven condition and reveal that multiple solutions exist for a range of the Reynolds number. The stability characteristic of the system is discovered by determining stability of these solutions by the eigenvalue method for the first time, which is validated by solving a time-dependent problem of the system.
Źródło:
Journal of Theoretical and Applied Mechanics; 2023, 61, 2; 395--406
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new modified WINDMI jerk system with exponential and sinusoidal nonlinearities, its bifurcation analysis, multistability, circuit simulation and synchronization design
Autorzy:
Mohamed, Mohamad Afendee
Vaidyanathan, Sundarapandian
Hannachi, Fareh
Sambas, Aceng
Darwin, P.
Powiązania:
https://bibliotekanauki.pl/articles/27324008.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
chaos
jerk systems
chaotic systems
Lyapunov exponents
bifurcation
multistability
circuit simulation
backstepping control
Opis:
In this work, a new 3-D modified WINDMI chaotic jerk system with exponential and sinusoidal nonlinearities is presented and its dynamical behaviours and properties are investigated. Firstly, some properties of the system are studied such as equilibrium points and their stability, Lyapunov exponents and Kaplan-Yorke dimension. Also, we study the new jerk system dynamics using numerical simulations and analyses, including phase portraits, Lyapunouv exponent spectrum, bifurcation diagram and Poincaré map, 0-1 test. Next, we exhibit that the new 3-D chaotic modified WINDMI jerk system has multistability with coexisting chaotic attractors. Moreover, we design an electronic circuit using MultiSim 14.1 for real implementation of the modified WINDMI chaotic jerk system. Finally, we design an active synchronization scheme for the complete synchronization of the modified WINDMI chaotic jerk systems via backstepping control.
Źródło:
Archives of Control Sciences; 2023, 33, 4; 711--735
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new two-scroll 4-D hyperchaotic system with a unique saddle point equilibrium, its bifurcation analysis, circuit design and a control application to complete synchronization
Autorzy:
Vaidyanathan, Sundarapandian
Moroz, Irene M.
Sambas, Aceng
Powiązania:
https://bibliotekanauki.pl/articles/27312011.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
hyperchaos
hyperchaotic systems
bifurcation analysis
multi-stability analysis
synchronization
Multisim
circuit simulation
Opis:
In this work, we present new results for a two-scroll 4-D hyperchaotic system with a unique saddle point equilibrium at the origin. The bifurcation and multi-stability analysis for the new hyperchaotic system are discussed in detail. As a control application, we develop a feedback control based on integral sliding mode control (ISMC) for the complete synchronization of a pair of two-scroll hyperchaotic systems developed in this work. Numerical simulations using Matlab are provided to illustrate the hyperchaotic phase portraits, bifurcation diagrams and synchronization results. Finally, as an electronic application, we simulate the new hyperchaotic system using Multisim for real-world implementations.
Źródło:
Archives of Control Sciences; 2023, 33, 2; 277--298
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Assessing the maturity of the current global system for combating financial and cyber fraud
Autorzy:
Kuzmenko, Olha
Yarovenko, Hanna
Perkhun, Larysa
Powiązania:
https://bibliotekanauki.pl/articles/10560822.pdf
Data publikacji:
2023-02-24
Wydawca:
Główny Urząd Statystyczny
Tematy:
financial fraud
cyber fraud
phase portrait
bifurcation analysis
Opis:
The purpose of the article is to assess the maturity of systems for counteracting financial and cyber fraud with the view of their future integration at global-level. The calculations made by the authors were based on indicators for 76 countries, which characterized each country's level of cybersecurity and its ability to combat financial fraud in 2018. After optimising the input data and selecting relevant indicators, the authors built an integrated cybersecurity index using the Sundarovsky convolution method. Sigma-limited parameterisation and Pareto-optimisation were then used to identify the determinants of the ability to counter financial and cyber fraud, which were used as predictors. Nonlinear regression was applied to determine the dependency of the integrated cybersecurity index on the government efficiency index, the ease of doing business and on the crime indices. On this basis, the authors conducted a bifurcation analysis of the maturity of current global system for combating financial and cyber fraud and produced its phase portraits. It was found to be mature (“Government Efficiency Index – Ease of Doing Business” and “Ease of Doing Business – Crime Index”) and insufficient mature (“Government Efficiency Index – Crime Index”), with the components' imbalance indicating high system's sensitivity to react on changes. The constructed 'Equilibrium States' phase portraits showed non-equilibrium phase portraits of the 'saddle' type. The obtained results made it possible to identify determinants of a global integrated system's instability to combat financial and cyber fraud.
Źródło:
Statistics in Transition new series; 2023, 24, 1; 229-258
1234-7655
Pojawia się w:
Statistics in Transition new series
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Comparison of main geometric characteristics of deformed sphere and standard spheroid
Autorzy:
Kovalchuk, Vasyl
Mladenov, Ivaïlo M.
Powiązania:
https://bibliotekanauki.pl/articles/27311436.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
deformed sphere
standard spheroid
sphericity index
elliptic integrals
elliptic functions
tipping point
bifurcation point
sfera zdeformowana
sferoida standardowa
współczynnik sferyczności
punkt zwrotny
punkt bifurkacji
całka eliptyczna
funkcja eliptyczna
Opis:
In the paper we compare the geometric descriptions of the deformed sphere (i.e., the so-called λ-sphere) and the standard spheroid (namely, World Geodetic System 1984’s reference ellipsoid of revolution). Among the main geometric characteristics of those two surfaces of revolution embedded into the three-dimensional Euclidean space we consider the semi-major (equatorial) and semi-minor (polar) axes, quartermeridian length, surface area, volume, sphericity index, and tipping (bifurcation) point for geodesics. Next, the RMS (Root Mean Square) error is defined as the square-rooted arithmetic mean of the squared relative errors for the individual pairs of the discussed six main geometric characteristics. As a result of the process of minimization of the RMS error, we have obtained the proposition of the optimized value of the deformation parameter of the λ-sphere, for which we have calculated the absolute and relative errors for the individual pairs of the discussed main geometric characteristics of λ-sphere and standard spheroid (the relative errors are of the order of 10−6 – 10−9). Among others, it turns out that the value of the,sup> flattening factor of the spheroid is quite a good approximation for the corresponding value of the deformation parameter of the λ-sphere (the relative error is of the order of 10−4).
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 5; art. no. e147058
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Синергетический анализ словообразовательных процессов как реакции на казахстанскую действительность
Synergetic Analysis of Word-Forming Processes as Reactions to Kazakh Realness
Autorzy:
Жапарова, Тогжан
Powiązania:
https://bibliotekanauki.pl/articles/46468202.pdf
Data publikacji:
2023
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
synergetics
dissipativity
entropy
chaos and order
bifurcation
fluctuation
word formation
communicative environment
синергетика
диссипативность
энтропия
хаос и порядок
бифуркация
флуктуация
словообразование
коммуникативная среда
Opis:
В статье язык описывается не просто как способ общения, а как сложная и открытая система, способная реагировать на происходящую действительность. Подвергаясь влияниям извне, система языка утрачивает равновесность. Этот процесс усложняется в связи с перманентным потоком информации и ее обменом с внешней средой. В центре внимания находятся периоды переходного момента, замена на новое, обусловленная неупорядоченностью, образованием диссипативной системы, сопровождающаяся энтропией, периодом образования нового – бифуркационным процессом, а также притяжением (аттрактором) динамической системы, что приводит к частотным употреблениям и развитию словообразовательных форм. Это способствует формированию коррекции нормы или приобретению иных черт. Мы наблюдаем, как новые элементы укореняются в языке и в процессе функционирования двух языков – казахского и русского. Актуальность исследования заключается в анализе процесса возникновения словообразовательных явлений во время январских событий 2022 г. в Казахстане, показанных в современных средствах массовой информации. Весь процесс рассматривается с позиции синергетики. В данном случае синергетика дает возможность видеть в ней подходы для анализа изменений в языке посредством достижения точки равновесия, адаптации и принятия языковых элементов. Цель данной статьи – определить и изучить синергетический аспект адаптации словообразовательных форм в иноязычной среде, где определяется выбор из множества того, что является признанным в настоящее время. В статье отражаются базовые понятия данного направления в современной лингвистике.
The article characterizes language not only as a way of communication, but as a complex and open system that is capable to react to modern reality. Under the external influences, the language system loses its balance. This process becomes more complicated due to the constant flow of information and its exchange with the external environment. The focus is on periods of transition, replacement with a new one, caused by disordering, the formation of a dissipative system, accompanied with entropy, the period of formation of a new one – a bifurcation process, as well as the attraction (attractor) of a dynamic system, which leads to frequent use and the development of word-formation forms. As a result, it contributes to the formation or correction of the norm, other features are acquired, where we observe how new elements take root in the language and in the process of functioning of two languages – Kazakh and Russian. The relevance lies on the analysis of the process of a word-forming phenomenon during the January unrests in 2022, in Kazakhstan shown in mass media. The whole process is considered from the synergy position. In this case, synergetics makes it possible to see in it approaches for analyzing changes in the language by reaching a point of balance, adaptation and acceptance of language elements. The purpose of this article is to identify and study the synergistic aspects of the adaptation analyses of word-formation forms in a foreign language environment, where the choice is determined from the varieties of what is currently known. The article reflects the basic concepts of this trend in modern linguistics as well as.
Źródło:
Acta Universitatis Lodziensis. Folia Linguistica Rossica; 2023, 22; 73-83
1731-8025
2353-9623
Pojawia się w:
Acta Universitatis Lodziensis. Folia Linguistica Rossica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new multistable jerk chaotic system, its bifurcation analysis, backstepping control-based synchronization design and circuit simulation
Autorzy:
Vaidyanathan, Sundarapandian
Benkouider, Khaled
Sambas, Aceng
Powiązania:
https://bibliotekanauki.pl/articles/2106506.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaos
jerk systems
bifurcation
multistability
attractors
backstepping control
circuit design
Opis:
In this work, we present results for a new dissipative jerk chaotic system with three quadratic terms in its dynamics.We describe the bifurcation analysis for the new jerk system and also show that the proposed system exhibits multi-stability. Next, we describe a backstepping control-based synchronization design for a pair of new jerk chaotic systems. MATLAB simulations are put forth to exhibit the various findings in this work. Furthermore, we exhibit a circuit simulation for the new jerk system using MultiSim.
Źródło:
Archives of Control Sciences; 2022, 32, 1; 123--152
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
New Construction Methods and Performance Analysis of WINDMI Chaotic System
Autorzy:
Salih, Thair A.
Powiązania:
https://bibliotekanauki.pl/articles/2055254.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chaotic signals
fpaa
bifurcation
psd
correlation
Opis:
Chaos is an active topic of study in the field of secure communication systems that have garnered much consideration in recent years because of excessive sensitivity to a simple change in its initial conditions. In this paper, the essential features of the suggested WINDMI chaotic system like the phase portraits of the attractors, bifurcation, PSD, correlation, and balance property of the windmi chaotic system have been depicted in detail through MATLAB tools simulations and circuital application. The bifurcation examination detects a wealthy and attractive characteristic of the proposed windmi chaotic oscillator such as periodical multiple bifurcations, has two stable states chaotic demeanor, periodical windows, and recapture bifurcations. In this paper, after exploring the dynamic features of the windmi chaos paradigm, a practical chaotic circuit is implemented on the fpaa chip. Eventually, the circuit practical results of the windmi chaotic attractors present similarities with numerical simulations. The importance of the work is reflected in the use of field programmable analog array in the implementation of the windmi oscillator, and the possibility of varying the initial condition during the operation of the system. An unlimited number of signals can be generated, which enables it to be used as an oscillator utilized in many transceiver systems, that utilized an unlimited number of signals.
Źródło:
International Journal of Electronics and Telecommunications; 2022, 68, 1; 129--136
2300-1933
Pojawia się w:
International Journal of Electronics and Telecommunications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stability and bifurcation analysis for an airfoil model with a high-order nonlinear spring
Autorzy:
Li, Shuqun
Zhou, Liangqiang
Powiązania:
https://bibliotekanauki.pl/articles/2086970.pdf
Data publikacji:
2022
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
nonlinear airfoil model
bifurcation
stability
normal form
Opis:
In this paper, the stability and bifurcation of an airfoil model with a high-order nonlinear spring are investigated both analytically and numerically. Two possible types of bifurcation at the equilibrium point are studied. It is proved that the zero characteristic root can only be a single zero. With the help of the center manifold theory and the normal form theory, the expressions of critical bifurcation curves leading to initial bifurcation and secondary bifurcation are obtained. Numerical simulations confirm the theoretical results.
Źródło:
Journal of Theoretical and Applied Mechanics; 2022, 60, 2; 185--197
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Coronary bifurcations – anatomy, physiology and treatment with selected aspects of left main stem bifurcation
Bifurkacje wieńcowe – anatomia, fizjologia i leczenie z wybranymi aspektami bifurkacji pnia lewej tętnicy wieńcowej
Autorzy:
Milejski, Wojciech
Morawiec, Beata
Sacha, Jerzy
Nowalany-Kozielska, Ewa
Gierlotka, Marek
Kawecki, Damian
Powiązania:
https://bibliotekanauki.pl/articles/1426903.pdf
Data publikacji:
2021-03-30
Wydawca:
Śląski Uniwersytet Medyczny w Katowicach
Tematy:
coronary bifurcation
left main coronary artery
percutaneous coronary angioplasty
bifurkacja wieńcowa
pień lewej tętnicy wieńcowej
przezskórna angioplastyka wieńcowa
Opis:
Coronary bifurcation remains a unique region of the coronary tree. The specific anatomy and blood flow determine the complex mechanisms of atherosclerotic plaque location. The treatment strategy should be chosen with caution as the failure of percutaneous coronary interventions (PCI) may expose a significantly larger area of the myocardium to ischemia than in the case of single vessel PCI. In order to understand the complexity of the clinical situation in patients after the treatment of coronary bifurcation, and the constantly evolving techniques of the procedure itself, this review presents basic information on the anatomy and classification, up-to-date step-by-step analysis of the optimal technique for PCI, beginning with qualification, planning and preparation for the procedure, through stent selection and ending with optimization techniques. Different PCI strategies are presented and explained, the indications for one- vs. two-stent techniques are evaluated, the available and recommended imaging and physiological methods for detailed bifurcation assessment are reviewed. Particular attention has been paid to left main stem bifurcation, a distinctive anatomical and physiological spot within the coronary circulation.
Bifurkacja wieńcowa jest miejscem szczególnym w obrębie krążenia wieńcowego. Charakterystyczna anatomia oraz cechy przepływu krwi w złożony sposób wiążą się z rozmieszczeniem blaszek miażdżycowych. Wybór strategii leczenia zmian bifurkacji wieńcowych wymaga szczególnej uwagi, gdyż wszelkie powikłania w tym rejonie narażają na niedokrwienie istotnie większy obszar miokardium niż w przypadku pojedynczego naczynia. Niniejsza publikacja stanowi przegląd podstawowych informacji o anatomii, klasyfikacji oraz kolejnych krokach aktualnie zalecanych technik leczenia przezskórnego zmian bifurkacji wieńcowych, poczynając od kwalifikacji, przygotowania, poprzez wybór stentu, po optymalizację efektu zabiegu. Podkreśla kliniczną złożoność problemu leczenia zmian bifurkacji wieńcowych, która wymusza stały rozwój technik zabiegowych. Przedstawione zostały strategie leczenia, wskazania do wyboru techniki z użyciem pojedynczego stentu oraz zamierzonego zastosowania dwóch stentów. Zaprezentowano również zalecane metody obrazowej oraz czynnościowej oceny istotności zmian w obrębie rozwidlenia tętnic wieńcowych. Szczególną uwagę poświęcono odrębnościom bifurkacji pnia lewej tętnicy wieńcowej.
Źródło:
Annales Academiae Medicae Silesiensis; 2021, 75; 24-32
1734-025X
Pojawia się w:
Annales Academiae Medicae Silesiensis
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stochastic P-bifurcation of a 3-DOF airfoil with structural nonlinearity
Autorzy:
Hao, Ying
Du, Xuewen
Hu, Yuda
Wu, Zhiqiang
Powiązania:
https://bibliotekanauki.pl/articles/1839715.pdf
Data publikacji:
2021
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
stochastic P-bifurcation
structural nonlinearity
stochastic parametric excitation
Opis:
In this paper, the stochastic-aeroelastic nonlinear response of a three-degree-of-freedom (3-DOF) structural nonlinear airfoil with a control flap is presented. The critical parameter conditions of stochastic P-bifurcation are solved by using the improved average method, the stochastic average method combined with the singularity theory. The results show that the periodic solution produced by Hopf bifurcation has involved a second bifurcation, the nonlinear critical speed of saddle node bifurcation points is advanced, and the airfoil appears bi-stable. The stochastic singularity analysis shows that the increasing stochastic disturbance intensity will cause a greater probability for a large amplitude stochastic flutter.
Źródło:
Journal of Theoretical and Applied Mechanics; 2021, 59, 2; 307-317
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis of multiple bifurcation behavior for periodic structures
Autorzy:
Ario, I.
Nakazawa, M.
Powiązania:
https://bibliotekanauki.pl/articles/38606394.pdf
Data publikacji:
2020
Wydawca:
Instytut Podstawowych Problemów Techniki PAN
Tematy:
periodic symmetry
post-buckling analysis
multiple bifurcation
hill-top bifurcation
multi-folding microstructure
Opis:
The classification of simple singularities in the post-buckling analysis of truss structures is well-known for elastic stability. To focus on multiple singularities including a hilltop bifurcation point (h-BP) and its bifurcation paths, we reviewed the multiple bifurcation analysis of multi-folding microstructure (MFM) models with periodic symmetry. Because the Jacobian at the h-BP of the MFM involves multiple 0-eigenvalues, it is challenging to analyse the bifurcation paths from the h-BP accurately. In this study, we investigated the multiple folding mechanism by analysing the neighbourhood of the h-BP and the symmetric subgroups of the geometric system in the two-dimensional plane and three-dimensional core of the MFM. We demonstrated that through the classification of multiple h-BP and bifurcation paths, it is possible to determine the unknown bifurcation equilibrium paths following h-BP, based on the Jacobian stability and the mechanism of symmetric subgroups in group theory containing the relationships between the primary path and the known bifurcation path(s) in the MFM system with periodic symmetry.
Źródło:
Archives of Mechanics; 2020, 72, 4; 283-306
0373-2029
Pojawia się w:
Archives of Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bifurcation and Stability Analysis of the Dynamics of Gonorrhea Disease in the Population
Autorzy:
Adediipo, Adeola D.
Akanni, John O.
Shangodare, Olasunkanmi M.
Powiązania:
https://bibliotekanauki.pl/articles/1030149.pdf
Data publikacji:
2020
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Basic Reproduction Number
Bifurcation analysis
Gonorrhea disease
Lyapunov function
Sensitivity analysis
Stability Analysis
Opis:
The model was governed by a system of ordinary differential equations; the population into susceptible individuals (S), Exposed individuals (E), infected individuals (I) and Recovered individuals (Q). Theory of positivity and boundedness was used to investigate the well-posedness of the model. Equilibrium solutions were investigated analytically. The basic reproduction number (R0) were calculated using the next generation operator method. Bifurcation analysis and global stability of the model were carried out using centre manifold theory and Lyapunov functions respectively. The effects of parameters such as efficacy of Condom (κ), Effective Contact Rate (β), Compliance of Condom (θ), Progression Rate (ρ) and Treatment Rate (α) on R0 were explored through sensitivity analysis. The possibility of mitigating the spread of gonorrhea in the population has been studied. It can be concluded that parameters representing efficacy of Condom, Effective Contact Rate, Compliance of Condom, Progression Rate and Treatment Rate are significant in reducing the burden of gonorrhea disease in the population.
Źródło:
World Scientific News; 2020, 143; 139-154
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Determination of Hopf bifurcation sets of a chemicalreactors by two-parameter continuation method
Autorzy:
Berezowski, Marek
Powiązania:
https://bibliotekanauki.pl/articles/185121.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
chemical reactor
Hopf bifurcation
thank reactor
bifurcation diagram
steady state
stability
dynamics
reaktor chemiczny
Rozwidlenie Hopfa
diagram bifurkacji
stan stabilny
stabilność
dynamika
Opis:
A two-parameter continuation method was developed and shown in the form of an example, allowingdetermination of Hopf bifurcation sets in a chemical reactor model. Exemplary calculations weremade for the continuous stirred tank reactor model (CSTR). The set of HB points limiting the rangeof oscillation in the reactor was determined. The results were confirmed on the bifurcation diagramof steady states and on time charts. The method is universal and can be used for various models ofchemical reactors.
Źródło:
Chemical and Process Engineering; 2020, 41, 3; 221--227
0208-6425
2300-1925
Pojawia się w:
Chemical and Process Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Analysis of Jump and Bifurcation Phenomena in a Forced Vibration of Geometrical Nonlinear Cantilever Beam: Application of Differential Transformation Method
Autorzy:
Sobamowo, M. G.
Yinusa, A. A.
Adeleye, O. A.
Oyelade, A. O.
Sadiq, O. M.
Powiązania:
https://bibliotekanauki.pl/articles/1031911.pdf
Data publikacji:
2020
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Bifurcation Phenomenon
Differential transformation method
Jump phenomenon
Nonlinear vibration
Phase plane
Opis:
One of the classical features exhibited in nonlinear dynamics of engineering systems is the jump phenomenon, which is the discontinuous change in the steady state response of a system as a parameter is slowly varied. Such phenomenon is characterized by large amplitude dynamic responses of systems to small amplitude disturbances. It is established that this phenomenon cannot be described by the standard asymptotic and perturbation methods because they are limited to the study of small amplitude responses to small disturbances. Therefore, this paper presents the application of differential transformation method-Padé approximant to the solution of jump and bifurcation phenomena for a geometrical nonlinear cantilever beam subjected to a harmonic excitation. The accuracy and validity of the analytical solutions obtained by the differential transformation method are shown through a comparison of the results of the analytical solution with the corresponding results of the numerical solution obtained by fourth-order Runge-Kutta method and also with the results in a past study using harmonic balancing method. With the aid of the differential transformation method-Padé approximant, the effects of the nonlinear parameters in the model equation on the dynamic response of the beam are investigated. Also, the sensitivity of the beam to the external excitation amplitude is analyzed. In the distributed forced vibration, the jump phenomenon appeared in the response amplitude by variation of the excitation frequency while in the resonance frequency, the beat phenomenon with harmonic motion is seen for low level of excitation amplitude. At a certain frequency, the jump and bifurcation phenomena are seen in the curves of responses versus excitation amplitude. Additionally, the plots of the phase plane and time history of the system response are shown. It is established that the differential transformation method is a very useful mathematical tool for dealing with the nonlinear problems.
Źródło:
World Scientific News; 2020, 140; 26-58
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 75

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