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To prevent unpleasant incidents, preservation high-speed railway vehicle stability has vital importance. For this purpose, the Railway vehicle dynamic is modeled using a 38-DOF includes the longitudinal, lateral and vertical displacements, roll, pitch and yaw angles. A heuristic nonlinear creep model and the elastic rail are used for simulation of the wheel and rail contact. To solve coupled and nonlinear differential equations, Matlab software and Runge Kutta methods are used. In order to study stability, bifurcation analyses are performed. In bifurcation analysis, speed is considered as the bifurcation parameter. These analyses are carried out for different wheel conicity and radius of the curved track. It is revealed that critical hunting speed decreases by increasing the wheel conicity or decreasing the radius of the curved track. Keywords: railway vehicle dynamics, nonlinear creep model, critical hunting speed, numerical simulation, bifurcation analysis Keywords: railway vehicle dynamics, nonlinear creep model, critical hunting speed, numerical simulation, bifurcation analysis

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In this study a new approach for investigating the flutter speed of nonlinear aeroelastic systems is proposed. In this approach, the compatibility of nonlinear random vibration analysis based on the statistical properties of response is used and extended to the nonlinear aeroelastic systems to analyze the instability of these systems with using neither time domain analysis nor limit cycle oscillations. To this aim a 2-degree nonlinear airfoil with cubic torsional spring under quasi steady flow is considered as an aeroelastic system. At first, one random Gaussian white noise is added to the aerodynamic lift force then the statistical linearization and the random vibration analysis of the nonlinear systems are used to obtain a nonlinear map of response-variance with flow velocity as the control parameter. This nonlinear map leads to a nonlinear algebraic equation which consists of two parameters as the flow velocity and variance of the response. By solving this nonlinear equation for various flow velocities, the flutter speed is considered as the maximum of response-variance. Finally the jump phenomenon is also investigated where tangent bifurcation occurs.

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In this paper, the nonlinear behavior, instability and bifurcation phenomena in the response of a cylindrical shallow shell under lateral ‎white noise excitation are studied. The structure interacts with a general non aging viscous medium that can be modeled by relaxation or ‎creep kernels. Using the powerful FPK equation and some practical and logical simplifications, an exact solution for such complex system ‎including nonlinearity, viscoelasticity and randomness is obtained. Since all statistical properties of response such as mean, variance, ‎statistical moments, central moments, etc. can be obtained from the probability density function, the behavior of this function including the ‎number and sign of its roots and their effects on the stability, bifurcation phenomenon and the type of bifurcation is investigated and ‎studied. In this process, using some non dimensional quantities, the governing equation and the probability density function are rearranged ‎such that the results of simulations can be used for a broad band of cylindrical shallow shells. Finally, using some examples, the variations ‎of the non dimensional quantities on the whole behavior, stability and bifurcation type of response are studied. ‎

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It is known from the previous studies that blades can cause resonance in bladed rotors under specific conditions. In this paper, the behavior of a nonlinear rotor, which faces with this kind of resonance, is investigated. In order to reach this goal, a bladed rotor, in which the disk and shaft are rigid, is considered. The blades are modeled by flexible beams. It is assumed that the disk is supported by elastic and nonlinear bearings. The nonlinear term of the bearing stiffness function is cubic. The rotating system vibrations include both cylindrical and conical whirling. The bifurcation equation is obtained by the method of multiple time scales method. The nonlinear effects are studied by the bifurcation equation. It is revealed that the system behavior, when it encounters Hamiltonian Hopf bifurcation, is dependent on the bearing stiffness nonlinearity type. Accordingly, both subcritical and supercritical Hopf bifurcation is possible. A numerical simulation is performed in order to study the effects of damping coefficients on the path of rotating disk center. The results and methods, which are used in this paper, are applicable for studying Hamiltonian Hopf bifurcation in other fields.

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In this study, static/dynamic instability and nonlinear vibrations of FG plates resting on elastic foundation under parametric forcing excitation, are investigated. Based on CPT, applying the von-Karman nonlinear strain–displacement relation and the Hamilton’s principle, the governing nonlinear coupled partial differential equations are derived. By considering six vibration modes, the Galerkin’s procedure is used to reduce the equations of motion to nonlinear Mathieu equations. In the absence of elastic foundation, the validity of the formulation for analyzing the static buckling, dynamic instability and nonlinear deflection is accomplished by comparing the results with those of the literature. Then in the presence of the foundation and by deriving the regions of dynamic instability, it is shown that as the parameters of the foundation increases, the natural frequency and the critical buckling load increase and the dynamic instability occurs at higher excitation frequencies. The frequency response equations in the steady-state condition are derived by applying the multiple scales method, and the parametric resonance is analyzed. Then the conditions of existence and stability of nontrivial solutions are discussed. Moreover, the effects of the system parameters, including excitation frequency, amplitude of excitation, foundation parameters and damping, on the nonlinear dynamics of the FG plate are investigated. Also it is shown that the presence of the foundation has a considerable influence on the resonance characteristic curves.

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In this study, the nonlinear vibration of a sandwich FG plate resting on a nonlinear Pasternak foundation which is simultaneously subjected to transverse harmonic forcing excitation and in-plane static force is investigated. Based on the Modified First-Order Shear Deformation Theory (FSDT), applying the von-Karman nonlinear strain–displacement relation and the Hamilton’s principle, the governing nonlinear coupled partial differential equations are derived. Then, the Galerkin’s procedure is used to reduce the equations of motion to nonlinear ordinary differential equations. In the absence of foundation, the validity of the formulation for analyzing the modified shear correction factors for shear stresses is accomplished by comparing the results with those reported in the literature. By applying the multiple scales method and considering the second order nonlinear approximation of solution, the primary resonance of the system under the transverse forcing excitation is analyzed. Under the steady-state condition, the frequency-response, the force-response and the damping-response equations are derived. Then the conditions of existence and stability of multiple coexisting non-trivial solutions for amplitude of the responses are discussed and the saddle node bifurcation points of the characteristic curves are derived. It is shown that, the variation of the system parameters in the resonance boundary may cause the jump phenomenon. Moreover, the effects of the system parameters including, excitation frequency, foundation parameters, damping, and amplitude of the harmonic and in-plane forces on the system nonlinear dynamics are investigated. Also it is shown that the presence of the foundation has a considerable influence on the resonance characteristic curves.

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In this article, using finite element method the effects of the preload on the nonlinear dynamic behavior of the noncircular two lobe aerodynamic journal bearing have been investigated. Assuming that the rotor is solid, the governing Rynolds equations for both the gas lubricant and rotor equation of motion in static and dynamic conditions have been derived and performance of the noncircular aerodynamic journal bearing in different conditions has been evaluated. Rung Kutta method has been used to solve the time dependent equations of motions of noncircular aerodynamic journal bearing and its gas lubricant. Using the numerical results, to investigate the motion of the center of the rotor in dynamic conditions, the graphs of frequency response, power spectrum, dynamic trajectory, Poincare map and bifurcation diagram have been plotted. The results show periodic, quasi periodic and chaotic rotor behavior for different bearing preload. It is concluded that appropriate selection of rotor parameters like its preload and suitable design and fabrication of rotor and its bearing can prevent any undesirable perturbed motions of the shaft and both the collision and wear of the rotor and bearing.

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Oil journal bearings are one of the most common parts of high load carrying rotating machine. Stability of these bearings can be affected by various stimulus such as changes in loading and lubrication conditions. Therefore, identification of the dynamic response of journal bearings can improve the control and fault detection process of rotor-bearings systems and prevent them from placing in critical operation condition. Since past, the mass unbalance of rotor is proposed as an effective factor on the dynamic behavior and long life of bearings. For this reason, in this research the effects of this parameter on the stability of hydrodynamic two lobe noncircular journal bearing with micropolar lubricant is investigated based on the nonlinear dynamic model. To achieve this goal, the governing Reynolds equation is modified with respect to micropolar fluid theory and the equations of rotor motion are derived considering the mass unbalance parameter. The static and dynamic pressure distributions of the lubricant film and the components of displacement, velocity and acceleration of the rotor are obtained by simultaneous solution of the Reynolds equation and the equations of rotor motion. Investigation of results in terms of dynamic trajectory, power spectrum, bifurcation diagram and Poincare map show that the dynamic behavior of two lobe bearings appears in different manner with variation of mass unbalance of rotor. The response of analyzed dynamic system include converge oscillations to the equilibrium point, periodic, KT periodic and quasi periodic behavior and also divergent disturbances which leads to collision between the rotor and bearing.

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One of the most common problems that occur during machining is Machine tool chatter, which adversely affects surface finish, dimensional accuracy, tool life and machine life. Machine tool chatter can be modeled as a linear time invariant differential equation with time delay or delay differential equation. Infinite dimensional nature of delay differential equations is apparent in the study of time delay systems. The analytical stability methods are thus more difficult for these differential equations and approximate methods do not give accurate results. In this paper, a new method is developed to determine the exact stable region(s) in the parameter space of machine tool chatter. In this method, first, the bifurcation points are determined. Then, the Lambert function is used to decide on the stability characteristics of each particular region. The advantages of this method are simple implementation and applicability to high order linear time delay systems. By resulting stability regions from this method, we can choose an optimal spindle speed to suppress the chatter. The new approach is the most acceptable method with comparison to traditional graphical, computational and approximate methods due to excellent accuracy and other advantages.

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This paper investigates vibration analysis of a clamped-clamped beam attached to a nonlinear energy sink (with nonlinear stiffness and damping) under an external harmonic force. The bream is modeled using the Euler-Bernouli beam theory. Different locations for nonlinear energy sink are chosen and the effects of various parameters on behavior of the system are considered. Required conditions for occurring the Saddle-node bifurcations and the Hopf bifurcations in the system are studied. In vibration analysis, the frequency response diagram of the system is very important because it shows the best regions for attenuation of vibration and is a good criterion for designing nonlinear energy sinks; hence Complexification-Averaging method is used to find simply the amplitude of oscillation in terms of excitation load. For validation and comparison, numerical simulation (Runge-Kuta method) is used. The results demonstrate that by approaching the position of nonlinear energy sink to the beam supports, probability of occurrence of the Hopf and the saddle-node bifurcations decreases and increases, respectively, detached response curve will be formed in smaller range of external amplitude force. Moreover, by increasing external amplitude force, the steady state amplitude of the system increases smoothly.

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Dynamics analysis of the rotational axially moving pipe conveying fluid under simply supported condition investigated in this research. The pipe assumed as Euler Bernoulli beam. The gyroscopic force and mass eccentricity were considered in the research. Equations of motion are derived using Hamilton’s principle, resulting in two partial differential equations for the transverse motions. The non-dimensional equations were discretized via Galerkin’ method and were solved using Rung Kutta method (order 15s). The frequency response curve obtained in terms of non-dimensional rotational speed. The bifurcation diagrams are represented in the case that the non-dimensional fluid speed, non-dimensional axial speed and non-dimensional rotational speed were respectively varied and the dynamical behavior is numerically identified based on the Poincare' portrait. Numerical simulations indicated that the system response increases by increasing non-dimensional axial speed of the pipe, non-dimensional fluid speed and non-dimensional rotational speed of the pipe and then decreases after passing critical area. The system is unstable at critical point associated with non-dimensional axial speed. Poincare portrait indicates periodic motion in transverse vibrations of the pipe at some points of control parameters. Phase portrait and FFT (Fast Fourier Transform) diagrams were used for validation of the results.

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Passive limit cycle walking is a special type of walking happening on a flat and slight downhill surface, without any energy injection and control, and in a cyclic manner. Compensation of energy lost through every heel strike by gravity effect, creates the cyclic behavior for the walking. The main advantage of this type of walking is getting higher efficiency, leading researchers to extend their studies in order to make passive dynamic based walkers. These bipeds can walk on level ground surface by little energy injection, instead of the gravity effect. This fact describes the standpoint of this article. In this research, with impulsive push-off actuation in hand and developing the related models, the walking of an actuated planar parametric model on level ground surface is simulated. Also the stability (with respect to the area of basin of attraction) and gait length has been analyzed by changing design parameters such as actuator’s location and foot shape. The results of this investigation indicates increase in relative stability and gait length for larger foot’s radius and of symmetrical shape.

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Passive vibration control of rotating nonlinear beams is crucial due to its potential to mitigate harmful vibrations in various engineering applications, including aerospace and industrial sectors. This study examines how different system parameters and inherent nonlinearities influence the vibrations of a nonlinear rotating beam subjected to periodic external forces. A nonlinear energy sink (NES) is attached to the beam's tip to attenuate vibrations. The system is modeled using the Euler-Bernoulli beam theory and von Kármán strain-displacement relations, with equations of motion derived via Hamilton’s principle. Complexification Averaging and Runge-Kutta methods are applied for analytical and numerical solutions, respectively. The findings reveal that increasing the stiffness reduces vibration amplitude, while a rise in the nonlinear coefficient induces hardening behavior. The system exhibits saddle-node and Hopf bifurcations under certain conditions, indicating complex dynamic transitions. These phenomena, driven by the beam's nonlinearity and the NES, effectively diminish the vibration amplitude, highlighting the system's complex dynamic responses and the NES's efficacy in vibration mitigation