Papers by Keyword: Bifurcation

Abstract: In this study, a novel numerical method to analyze the bifurcation problemof a rate dependent material using the finite element method is proposed. The consistent stiffness matrix, which is required for a bifurcation analysis using the finite element method, for a rate dependent material is generally hard to compute, therefore, a computational method to calculate the tangent stiffness matrix based on a numerical differential is introduced so that exact bifurcation analyses for the rate dependent material can be conducted. A numerical example of the proposed method is demonstrated, and the adequacy of the proposed method is discussed.

Abstract: A numerical investigation is performed into the heat transfer and entropy generation of a variable thermal conductivity magnetohydrodynamic flow of Al₂O₃-water nanofluid in a vertical channel of varying width with right porous wall, which enable the fluid to enter. The effects of the Lorentz force, buoyancy force, viscous dissipation and Joule heating are considered and modeled using the transverse momentum and energy balance equations respectively. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using appropriate similarity transformations and then solved numerically using power series with Hermite-Padé approximation method. A stability analysis has been performed for the local rate of shear stress and Nusselt number that indicates the existence of dual solution branches. Numerical results are achieved for the fluid velocity, temperature as well as the rate of heat transfer at the wall and the entropy generation of the system. The present results are original and new for the flow and heat transfer past a channel of varying width in a nanofluid which shows that the physical parameters have significant effects on the flow field.

Abstract: The magneto-rheological(MR) suspension system has been established, by employing the modified Bouc-wen force-velocity (F-v) model of magneto-rheological damper(MRD). The possibility of chaotic motions in MR suspension is discovered by employing nonlinear systems stability theory. With the bifurcation diagram and corresponding Lyapunov exponent spectrum diagrams detected through numerical calculation, we can observe the complex dynamical behaviors and oscillating mechanism of alternating periodic oscillations, quasi-periodic oscillations and chaotic oscillations with different profiles of road excitation, as well as the dynamical evolution to chaos by period-doubling bifurcations, saddle-node bifurcations and reverse period-doubling bifurcations.

Abstract: The paper deals with nonlinear phenomena that occurs during vibration of nuclear fuel rod (FR). The FR is considered as a system consisting of two impact-interacting subsystems FR cladding (zircalloy tube) and fuel pellets stack placed inside FR cladding. Between both subsystems, there is a small radial clearance. The FR is bottom-end-fixed, and at eight equidistant levels, the FR cladding is supported by spacer grids (SG). Both subsystems are modelled by means of finite element method for one-dimensional Euler-Bernoulli continua. During fuel assembly (FA) motion caused by pressure pulsations of the coolant, the FR vibrates and impacts can possibly occur between FR cladding and fuel pellets stack. The paper focuses on qualitative change of vibration with change of bifurcation parameters clearance between FR cladding and fuel pellets stack and stiffness of spacer grids cells. The change of vibration quality is shown by extremes of relative radial displacements of both continua in discretization nodes and by phase trajectories. Dependence of impact motion on modal properties of both subsystems is shown.

Abstract: Cr, Ni, Mo, V exist in materials of high, medium and low pressure turbine rotor. Its composition contains higher carbon content, so leads to poor hardenability. Shear characteristics of martensite phase transformation is caused by a large number of micro defects inside crystal of microstructure in rotor during the service status. Martensite phase transformation is by strengthening because of plastic deformation in cutting process. Mechanical properties and phase transformation plasticity in cutting process show that rotor is hard machining material. Plastic deformation aggravates tool wear, and leads to an increased cutting force; hard points of uneven material internal organization lead to fluctuation of cutting force, and induced cutting chatter. During the course of machining critical or ultra-supercritical rotor, boring bar becomes a flexible system surrounded by rotating stirred vortex cutting fluid inside and outside it. BTA processing system is in a complicated hydraulic-solid coupling environment. Whether or not BTA deep hole boring processing system is stable, the essence is converted into estimating dynamic stability of BTA boring bar coupled fluid--solid with multi-physics environment. The system will be triggered cutting chatter, fluid flutter and self-excited vibration combination. This paper establishes nonlinear mathematical physics model on BTA deep hole processing system. The perturbation equation and Lyapunov function of BTA system are obtained, through introducing the stable Rumjantsev part variables analysis theory. Based on stability characteristic under the significance of Lyapunov, the constraint condition undisturbed stability is gotten and the global bifurcation analysis is finished. Hyperbolic periodic orbit and heteroclinic connection are found throughout the entire phase space of Hamiltonian system. The bifurcation condition on quadratic heteroclinic is acquired, by analyzing intersection relationship between hyperbolic stable manifold and its unstable manifold of Poincare mapping. The intersection critical conditions are shown on hyperbolic fixed stable manifold and its unstable manifold, by using computer numerical simulation to draw 3-D surface relationship among resonant frequency, cutting fluids flow velocity and the radius of free surface. The result could provide a reference on multi-machining parameters optimization for BTA deep hole boring process practical production.

Abstract: This research concerns the metals behavior as varying, with increasing cyclic stress level, in the transition range between the ultrahigh cycle (UHCF) and high cycle (HCF) fatigue regimes. Having analyzed the synergetics of surface crack initiation, the authors propose to identify the UHCF-to-HCF transition with a certain stress level corrected, with the respective dimensionless functions, for the effect of the environmental attacks, temperature, surface roughness of the test piece, etc. on the crack initiation behavior. Subsurface initiation of a fatigue crack occurs in the test-material susceptible of a deformation-induced transition to superplasticity state, which favors formation of the nanocrystalline zone bordered by a fine-granular area Another case of subsurface cracking is in that a local even area forms owing to the vortex-like deformation combined with the diffusion of the retained gases toward and into the discontinuity. A proposed equation is plainly descriptive of the subsurface growth of fatigue-cracks and allowing to acquire the crack growth duration from the fractography data.Nomenclature

Abstract: This work presents a numerical investigation of the natural convection in a saturated porous medium bounded by two horizontal concentric cylinders, modeled taking into account the Brinkman term. The governing equations (in the stream function and temperature formulation) were solved using the ADI (Alternating Direction Implicit) method. The results obtained for the bifurcation point are in a good agreement with the available published data for Da≈0. A study of the effect of Darcy number on the bifurcation point is conducted.

Abstract: Bifurcation of rupture path is studied for the effect of linear and nonlinear cubic damping. Momentum equation with Rayleigh factor was transformed into ordinary differential form. Bernoulli differential equation was obtained and solved by the method separation of variables. Analytical solutions yield the bifurcation of linear and nonlinear cubic damping was visible at imaginary part when the wave was non dispersive. For the dispersive wave, bifurcation of rupture path was invisible due to lower cubic damping. Amplitude attenuated during the seismic moment. Imaginary parts of the solutions illustrate the intersection or collision of soliton, for which, the bifurcation of rupture path is initiated. Intersection is not visible if the energy is well dispersed. Wave profile illustrates the existing of linear exciting and nonlinear damping effect during seismic moment.

Abstract: Magnetization dynamics in a three-layered nanopillar Co/Cu/Co structure with one fixed and one free layer driven by external magnetic field and spin-polarized electric current was investigated using methods of the theory of bifurcations. Mathematical model is based on the Landau-Lifshits-Gilbert equation with the current term in the Sloncžewski–Berger form. Orientation of applied magnetic field was considered to be parallel to the anisotropy axis. Physical model included the magnetocrystalline anisotropy field and the demagnetizing field. Because of small size of the structure, the space dependence of magnetization, as usually, was not taken into account. The resulting system of equations has the form of the nonlinear dynamical system with the polynomial right sides. Mathematical simulation of magnetization dynamics for several typical values of field and current was performed. The numerical experiments revealed the features of switching process in more detail and permitted to find new regimes of magnetization dynamics, such as incomplete and accidental switching.

Abstract: A water price-supply model is presented to describe the relationship between water price and water supplier's decision in a closed irrigation district. Then some nonlinear studies are implemented, such as Neimark-Sacker bifurcation , chaotic attractor, Lyapunov exponents and time series. It shows that the parameter of the water price can lead the price-supply system from stability into bifurcation and chaos.