scholarly journals Existence and Stability of the Periodic Orbits Induced by Grazing Bifurcation in a Cantilever Beam System with Single Rigid Impacting Constraint

2021 ◽  
Author(s):  
Run Liu ◽  
Yuan Yue ◽  
Jianhua Xie
Keyword(s):  
Periodic Orbits ◽  
Cantilever Beam ◽  
Shooting Method ◽  
Jacobian Matrix ◽  
Mapping Method ◽  
Grazing Bifurcation ◽  
Beam System ◽  
Existence And Stability ◽  
The Stability ◽  
The Relationship

Abstract Grazing which can induce many nonclassical bifurcations, is a special dynamic phenomenon in some non-smooth dynamical systems such as vibro-impact systems with clearance. In this paper, the existence and stability of the periodic orbits induced by the grazing bifurcation in a cantilever beam system with impacts are uncovered. Firstly, the Poincaré mapping of the system is obtained by the discontinuous mapping method. Secondly, the periodic orbits are determined by means of shooting method, and Jacobian matrix in the case of non-impact is obtained subsequently. Thirdly, for various impacting patterns, a combination of inhomogeneous equations and inequations is obtained to determine the existence of period orbits after grazing. Furthermore, the stability criterion of the grazing-induced periodic orbits is given. Numerical results verify the effectiveness of theoretical analysis. What’s more, we also give a conjecture about the relationship between eigenvalues and the type of periodic orbits when eigenvalues are imaginary numbers.

COALESCENCE OF THE TWO SECONDARY RESPONSES IN COUPLED DUFFING EQUATIONS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250149
Author(s):  
TING-YU LAI ◽  
PI-CHENG TUNG ◽  
YUNG-CHIA HSIAO
Keyword(s):  
Periodic Orbits ◽  
Harmonic Balance ◽  
Shooting Method ◽  
Harmonic Balance Method ◽  
The Novel ◽  
Duffing Equations ◽  
Duffing System ◽  
Parametric Continuation ◽  
Continuation Algorithm ◽  
The Stability

The novel coalescence of the secondary responses for the coupled Duffing equations are observed in this study. Two secondary responses that do not bifurcate from the primary responses merge into one due to saddle-node bifurcation generation within a specific parameter range. The frequency responses of the coupled Duffing equations are calculated using the harmonic balance method while the periodic orbits are detected by the shooting method. The stability of the periodic orbits is determined on utilizing Floquet theory. The parametric continuation algorithm is used to obtain the bifurcation points and bifurcation lines for a Duffing system with two varying parameters. The analytical results demonstrate the novel phenomenon that occurs in the Duffing equations.

scholarly journals Global Analysis of a Planetary Gear Train

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Tongjie Li ◽  
Rupeng Zhu
Keyword(s):  
Periodic Orbits ◽  
Shooting Method ◽  
Global Analysis ◽  
Planetary Gear ◽  
Mapping Method ◽  
Gear Train ◽  
Planetary Gear Train ◽  
Long Term Stability ◽  
Meshing Stiffness ◽  
Study Results

By using the Poincaré-like cell-to-cell mapping method and shooting method, the global characteristics of a planetary gear train are studied based on the torsional vibration model with errors of transmission, time-varying meshing stiffness, and multiple gear backlashes. The study results reveal that the planetary with a certain set of parameters has four coexisting periodic orbits, which are P-1, P-2, P-4, and P-8, respectively. P-1 and P-2 motions are not of long-term stability, P-8 motion is of local stability, and P-4 motion is of global stability. Shooting method does not have the capacity of searching coexisting periodic orbits in a global scope, and it is easy to omit some periodic orbits which are far away from the main gropes of periodic orbits.

scholarly journals Heterogeneous Expectations and Speculative Behavior in Insurance-Linked Securities

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Min Zheng
Keyword(s):  
Weighted Average ◽  
Efficient Frontier ◽  
Impact Factors ◽  
Heterogeneous Agent ◽  
Existence And Stability ◽  
Speculative Behavior ◽  
The Stability ◽  
The Impact ◽  
The Relationship ◽  
Heterogeneous Agent Models

Within the framework of heterogeneous agent models, this paper analyzes the impact factors on the issuance of an insurance-linked security (ILS), and gives an ILS pricing formula and the conditions of existence and stability of the issue price. We consider two cases: fixed supply and flexible supply. We find that, in the fixed volume case, to assure the successful issuance of an ILS, an appropriate volume of the ILS is necessary, and to attract investors, the ILS should pay a positive premium which can help investors to enhance the efficient frontier of their portfolio. In the flexible supply case, we show that the issue price of an ILS is given by the weighted average of different beliefs about the discounted ILS return, and the stability of the issue price depends on the numbers of investors and sponsors and the extrapolation rate to the ILS of investors. In addition, whether an ILS has the hedging ability to sponsors depends on their own understanding about the ILS coupon and the relationship between the recovery from the ILS and their liability, but how much the risk of sponsors can be hedged relies on the ILS coupon expected by investors.

A Static and Nonlinear Dynamic Analysis of Resonant Microbeams

2007 ◽  
Author(s):  
Samir A. Emam ◽  
Mahmoud E. Khater ◽  
Emil H. Gad
Keyword(s):  
Periodic Orbits ◽  
Shooting Method ◽  
Nonlinear Dynamic Analysis ◽  
Beam Theory ◽  
Electrostatic Forces ◽  
Reduced Order ◽  
Resonant Sensors ◽  
Discretization Technique ◽  
The Stability ◽  
Euler Bernoulli Beam

An investigation into the response of microbeams to DC and AC electric actuation is presented. The beam is modeled according to the Euler-Bernoulli beam theory and small strains and moderate rotation approximations are assumed. The governing equation is a nonlinear integral-partial-differential equation in space and time. The model accounts for mid-plane stretching, applied axial load, DC electrostatic forces, and AC harmonic forces. A reduced-order model based on the Galerkin discretization technique is introduced to simulate the behavior of microswitches and resonant sensors. The static behavior of the microbeam under electrostatic forces is studied and compared to the results available in the literature. The dynamic behavior of resonant microbeams under AC harmonic forces is investigated. An analytical solution for the vibration modes and natural frequencies of the microbeam around its statically deflected position is obtained. A shooting method is used to numerically integrate the nonlinear discretized equations and obtain periodic orbits of the response. The stability of these periodic orbits is investigated using Floquet theory. The sensitivity of the device to small-amplitude excitations is also investigated.

Optimal Positions for Multiple Flexoelectric Actuations on Beams

2015 ◽  
Author(s):  
B. L. Deng ◽  
H. Li ◽  
H. S. Tzou
Keyword(s):  
Cantilever Beam ◽  
Flexible Structures ◽  
Mechanical Force ◽  
Control Voltage ◽  
Flexoelectric Effect ◽  
Atomic Force ◽  
Multiple Actuators ◽  
The Stability ◽  
The Relationship ◽  
Tip Displacement

Inhomogeneous electric field induces internal stress in flexoelectric materials, which is known as the converse flexoelectric effect. The atomic force microscope (AFM) probe can be applied to actuate the flexoelectric patch laminated on flexible structures and, in turn, induce structural vibrations. In this study, multiple actuators (i.e., combination of multiple AFM probes and flexoelectric patches) are used to suppress the vibration of an elastic cantilever beam. The displacement of the beam under control is obtained by superposition of a mechanical force induced part and an actuator induced part. The optimal actuator positions are selected when the minimal tip displacement of the cantilever beam is achieved. In case studies, only three actuators are used and only first three beam modes are considered. Under resonance conditions where only one mode participates, the optimal positions are obtained and they only depend on the relationship between actuation factor and actuator’s position. The influence of the patch length is discussed, followed by the analysis of control voltages applied to actuators. When the control voltage is so small as to the induced displacement is far less than that induced by the mechanical force, the optimal actuation positions do not vary with the voltage magnitude; while when the voltage is relatively large the actuators keep adjusting their relative optimal positions with respect to the control voltage and the system becomes unstable. Furthermore, as long as the control voltage is relatively small below the stability threshold, the optimal positions do not change as the position where mechanical force placed along the beam. Under the small voltage condition, a smooth relationship between optimal positions and vibration frequency is obtained. There are four jump points of optimal positions and they are related to the tip displacement-actuator position curves under different frequencies. This study serves as the foundation of flexoelectric vibration control with multiple AFM/flexoelectric actuators on flexible structures.

An Experimental Investigation on Thermal Conductivity and Viscosity of Graphene doped CNTs /TiO2 Nanofluid

2020 ◽  
Vol 17 (3) ◽  
Author(s):  
A.M. Zetty Akhtar ◽  
M.M. Rahman ◽  
K. Kadirgama ◽  
M.A. Maleque
Keyword(s):  
Thermal Conductivity ◽  
Zeta Potential ◽  
Base Fluid ◽  
Minimum Quantity Lubrication ◽  
Cutting Fluid ◽  
Cutting Zone ◽  
Observation Method ◽  
The Stability ◽  
The Relationship ◽  
Zeta Potential Analysis

This paper presents the findings of the stability, thermal conductivity and viscosity of CNTs (doped with 10 wt% graphene)- TiO2 hybrid nanofluids under various concentrations. While the usage of cutting fluid in machining operation is necessary for removing the heat generated at the cutting zone, the excessive use of it could lead to environmental and health issue to the operators. Therefore, the minimum quantity lubrication (MQL) to replace the conventional flooding was introduced. The MQL method minimises the usage of cutting fluid as a step to achieve a cleaner environment and sustainable machining. However, the low thermal conductivity of the base fluid in the MQL system caused the insufficient removal of heat generated in the cutting zone. Addition of nanoparticles to the base fluid was then introduced to enhance the performance of cutting fluids. The ethylene glycol used as the base fluid, titanium dioxide (TiO2) and carbon nanotubes (CNTs) nanoparticle mixed to produce nanofluids with concentrations of 0.02 to 0.1 wt.% with an interval of 0.02 wt%. The mixing ratio of TiO2: CNTs was 90:10 and ratio of SDBS (surfactant): CNTs was 10:1. The stability of nanofluid checked using observation method and zeta potential analysis. The thermal conductivity and viscosity of suspension were measured at a temperature range between 30˚C to 70˚C (with increment of 10˚C) to determine the relationship between concentration and temperature on nanofluid’s thermal physical properties. Based on the results obtained, zeta potential value for nanofluid range from -50 to -70 mV indicates a good stability of the suspension. Thermal conductivity of nanofluid increases as an increase of temperature and enhancement ratio is within the range of 1.51 to 4.53 compared to the base fluid. Meanwhile, the viscosity of nanofluid shows decrements with an increase of the temperature remarks significant advantage in pumping power. The developed nanofluid in this study found to be stable with enhanced thermal conductivity and decrease in viscosity, which at once make it possible to be use as nanolubricant in machining operation.

A FORECAST OF PRODUCTIVE LONGEVITY OF HOLSTEIN COWS BY INDIRECT SIGNS

2020 ◽  
Author(s):  
З.С. САНОВА
Keyword(s):  
Correlation Coefficient ◽  
Aging Process ◽  
Direct Relationship ◽  
Stability Index ◽  
Age At First Calving ◽  
Group I ◽  
Predicted Values ◽  
The Stability ◽  
Relationship Of ◽  
The Relationship

В статье представлены материалы о взаимосвязи продолжительности продуктивного использования коров с характеристикой устойчивости к деградации, с возрастом отела и удоем. В исследованной, разнородной по происхождению, группе животных для прогноза продуктивного периода коров, обусловленного устойчивостью к деградации и возрастом первого отела, пригодно уравнение регрессии, аргументами в котором являются индекс устойчивости, возраст первого отела в первой и второй степенях. Коэффициент корреляции межу предсказанными значениями продуктивного периода и его фактическими величинами в I группе составляет 0,502, во II - 0,604. При этом крайние варианты прогнозируются со статистическими ошибками 5 мес при оценке индекса устойчивости по 2 лактациям и 4,1 мес по 3, а средние варианты, соответственно, 1,6 и 1,51 мес. Индекс устойчивости к процессу старения является важной характеристикой биологических особенностей коров, определяющий их продуктивное долголетие. Его оценка по первым 2 и 3 лактациям имеет прямолинейную связь с продуктивным периодом (r=0,4109 и r=0,5270), соответственно. Зависимость продуктивного периода от возраста первого отела криволинейная — с увеличением возраста первого отела сокращается срок продуктивного использования, при возрасте первого отела более 1400 дней срок продуктивного использования колеблется от 1,33 до 1,41 лактации. Коэффициент корреляции между этими характеристиками коров составляет - 0,2164 в I и - 0,2620 во II группах. The article presents materials about the relationship of the duration of productive use of cows with the characteristic of resistance to degradation, with the age of calving and milk yield. In the studied group of animals, which is heterogeneous in origin, the regression equation is suitable for predicting the productive period of cows due to resistance to degradation and the age of the first calving, the arguments of which are the stability index, the age of the first calving in the first and second degrees. The correlation coefficient between the predicted values of the productive period and its actual values in group I is 0.502, in group II - 0.604. At the same time, the extreme variants are predicted with statistical errors of 5 months when evaluating the stability index for 2 lactations and 4.1 months for 3, and the average variants, respectively, are 1.6 and 1.51 months. The index of resistance to the aging process is an important characteristic of the biological characteristics of cows, which determines their productive longevity. Its estimate for the first 2 and 3 lactations has a direct relationship with the productive period (r=0.4109 and r=0.5270), respectively. The dependence of the productive period age at first calving curvilinear with increasing age at first calving reduces the time to productive use, while age at first calving of more than 1400 days, the period of productive use ranges from 1.33 to 1.41 lactation. The correlation coefficient between these characteristics of cows is-0.2164 in I and-0.2620 in II groups.

Substantiation the machine with a basket for the application of mineral fertilizers and other bulk materials with the upper arrangement of the feeding device

2019 ◽  
pp. 37-43
Author(s):  
Fesenko, H.
Keyword(s):  
Fat Body ◽  
Mineral Fertilizer ◽  
The Body ◽  
Mineral Fertilizers ◽  
Analytical Mechanics ◽  
Bulk Materials ◽  
The Stability ◽  
Working Bodies ◽  
The Relationship ◽  
Stable Flow

Purpose. Increasing the uniformity of distribution of mineral fertilizers and other bulk materials due to the stability of their feed from the body to the spreading working bodies using the top feeder. Methods. The following methods are used to achieve this aim: the method of comparing the differences between individual groups of fertilizers, the method of analyzing the properties of a new technical system, the method of functional inventiveness, and the methods of theoretical and analytical mechanics. Results. The traction body of the conveyor of the upper feed of the body fat body machine for mineral fertilizers and other bulk materials was substantiated and the relationship between the height of its scrapers and the distance between them was established, as well as the nature of the mineral fertilizer pressure on the curvilinear wall of the body. In addition, the design of the advanced body fertilizer spreader is justified, which ensures a stable flow of fertilizers from the body due to the improvement of the top feeder. Conclusions. Because of the conducted researches, the advantages of machines equipped with top feeder are found. They create the conditions for the forced feeding mineral fertilizers and other loose materials from the container to the distribution bodies, which is a prerequisite for their evenness on the surface. With this, the imperfection of known machines with the top feeder constrains their introduction into agricultural production. On this account, a more thoroughly constructed solution of the body feeder of the top feed is substantiated, in which the conveyor provides a stable supply of fertilizers from the body with reduced energy consumption during operation. Keywords: analysis, feed, upper device, conveyor, stability, fertilizers, flow ability, body.

FINANCIAL CRISES AND THE PUBLICATION OF THE FINANCIAL STATEMENTS OF BANKS IN SPAIN, 1844–1868

2004 ◽  
Vol 31 (2) ◽  
pp. 1-26 ◽  
Author(s):  
Mercedes Bernal Lloréns
Keyword(s):  
19Th Century ◽  
Financial Reporting ◽  
Economic Performance ◽  
Financial Crises ◽  
Limited Liability ◽  
Financial Statements ◽  
Early Response ◽  
Banking Regulations ◽  
The Stability ◽  
The Relationship

Financial crises have had a decisive influence on banking regulations in Spain. During the mid-19th century the publication of the financial statements of banks was considered key to the stability of the financial system. All new joint stock banking companies were to publish their statements in the Madrid Gazette in return for the privilege of limited liability. Similar obligations were placed on issuing banks. The copious publication of financial statements coincided with a period of financial prosperity. However, the crises that followed from 1864 to 1868 led to a reduction in the official publication of statements. This paper is concerned with an early response to crises in financial reporting. The study focuses on the relationship between the publication of accounting statements by banks and the GDP in Spain during the mid-19th century. The results suggest that the frequency of publication of financial statements may be an indicator of economic performance.

scholarly journals Cats in the forest: predicting habitat adaptations from humerus morphometry in extant and fossil Felidae (Carnivora)

Paleobiology ◽  
10.1666/12001 ◽  
2013 ◽  
Vol 39 (3) ◽  
pp. 323-344 ◽  
Author(s):  
Carlo Meloro ◽  
Sarah Elton ◽  
Julien Louys ◽  
Laura C. Bishop ◽  
Peter Ditchfield
Keyword(s):  
Morphological Variability ◽  
Olduvai Gorge ◽  
Environmental Predictors ◽  
Linear Measurements ◽  
Multivariate Statistical ◽  
Linear Discriminant ◽  
Related Group ◽  
Discriminant Analyses ◽  
The Stability ◽  
The Relationship

Mammalian carnivores are rarely incorporated in paleoenvironmental reconstructions, largely because of their rarity within the fossil record. However, multivariate statistical modeling can be successfully used to quantify specific anatomical features as environmental predictors. Here we explore morphological variability of the humerus in a closely related group of predators (Felidae) to investigate the relationship between morphometric descriptors and habitat categories. We analyze linear measurements of the humerus in three different morphometric combinations (log-transformed, size-free, and ratio), and explore four distinct ways of categorizing habitat adaptations. Open, Mixed, and Closed categories are defined according to criteria based on traditional descriptions of species, distributions, and biome occupancy. Extensive exploratory work is presented using linear discriminant analyses and several fossils are included to provide paleoecological reconstructions.We found no significant differences in the predictive power of distinct morphometric descriptors or habitat criteria, although sample splitting into small and large cat guilds greatly improves the stability of the models. Significant insights emerge for three long-canine cats:Smilodon populator,Paramachairodus orientalis, andDinofelissp. from Olduvai Gorge (East Africa).S. populatorandP. orientalisare both predicted to have been closed-habitat adapted taxa. The false “sabertooth”Dinofelissp. from Olduvai Gorge is predicted to be adapted to mixed habitat. The application of felid humerus ecomorphology to the carnivoran record of Olduvai Gorge shows that the older stratigraphic levels (Bed I, 1.99–1.79 Ma) included a broader range of environments than Beds II or V, where there is an abundance of cats adapted to open environments.

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