Accepted Manuscripts

Technical Brief  
Chandan Kumar and Somnath Sarangi
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037995
Planar dynamics of a rotor supported by long hydrodynamic journal bearing is investigated theoretically. An analytical model of the long journal bearing system is numerically integrated for analysis of fixed point and periodic oscillations. The nonlinearities in the system arise due to a nonlinear fluid film force acting on the journal. The influences of three dimensionless parameters viz. bearing parameter, unbalance, and rotor speed on the dynamic behavior of the rotor bearing system is studied and compared with the short journal bearing. For the same bearing parameter, short bearing has large operating speed compared to a long bearing. Results are presented in the form of a bifurcation diagram and Poincare´ map of the oscillations based on numerical computation. The considered unbalanced system shows periodic, multiperiodic and quasi-periodic motion in different speed range. Jumping phenomenon is also observed for a high value of bearing parameter with unbalance.
TOPICS: Fluid-dynamic forces, Bearings, Rotors, Dynamic response, Journal bearings, Oscillations, Dynamics (Mechanics), Fluid films, Bifurcation, Computation
Hiroki Yamashita, Paramsothy Jayakumar, Mustafa Alsaleh and Hiroyuki Sugiyama
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037994
A physics-based deformable tire-soil interaction simulation capability that can be fully integrated into the monolithic multibody dynamics computer algorithm is developed by extending a deformable tire model based on the flexible multibody dynamics approach to off-road mobility simulations with a moving soil patch technique and it is validated against test data. A locking-free nine-node brick element is developed for modeling large plastic soil deformation using the multiplicative finite strain plasticity theory along with the capped Drucker-Prager failure criterion. To identify soil parameters including cohesion and friction angle, the triaxial compression test is carried out, and the soil model developed is validated against the test data. In addition to the component level validation for the tire and soil models, the tire-soil simulation capability developed in this study is validated against the soil bin mobility test results. The tire forces and rolling resistance coefficients predicted by the simulation model agree well with the test results. It is shown that effect of the wheel loads and tire inflation pressures are well predicted in the simulation model. Furthermore, it is demonstrated that the moving soil patch technique, with which soil behavior only in the vicinity of the rolling tire is solved to reduce the soil model dimensionality, leads to a significant reduction in computational time, thereby enabling use of the high-fidelity physics-based tire-soil interaction model in the large-scale off-road mobility simulation.
TOPICS: Physics, Simulation, Roads, Soil, Tires, Mechanical admittance, Simulation models, Multibody dynamics, Wheels, Rolling friction, Stress, Algorithms, Modeling, Computers, Compression, Failure, Plasticity, Deformation, Friction, Bricks, Cohesion
A. M. Nagy, Nasser Sweilam and Adel A. El-Sayed
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037922
The multi-term fractional variable-order differential equation has a massive application in physics and engineering problems. Therefore, a numerical method is presented to solve a class of variable order fractional differential equations (FDEs) based on an operational matrix of shifted Chebyshev polynomials of the fourth kind. Utilizing the constructed operational matrix, the fundamental problem is reduced to an algebraic system of equations which can be solved numerically. Error estimate of the proposed method is studied. Finally, the accuracy, applicability, and validity of the suggested method are illustrated through several examples.
TOPICS: Differential equations, Numerical analysis, Errors, Polynomials, Algebra, Physics
Shantanu Rajendra Gaikward and Ashok Kumar Pandey
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037923
In this paper, we investigate the linear and nonlinear response of SMA based Duffing and Quadratic oscillator under large deflection conditions. To do the study, we first present the thermomechanical constitutive modeling of SMA with a single degree of freedom system. Subsequently, we solve the equation to obtain linear frequency and nonlinear frequency response using the method of harmonic balance and validate it with numerical solution as well as averaging method under isothermal condition. However, for non-isothermal condition, we analyze the influence of cubic and quadratic nonlinearity on the nonlinear response based on the method of harmonic balance. The analysis of results lead to various ways of controlling the nature and extent of nonlinear response of SMA based oscillators. Such findings can be effectively used to control the external vibration of different systems.
TOPICS: Degrees of freedom, Modeling, Vibration, Deflection, Frequency response, Shapes, Thermomechanics
Yongkang Shen, Shan Yin, Guilin Wen and Huidong Xu
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037924
Based on the special dynamical property of continuous transition at certain degenerate grazing points in the single degree-of-freedom impact oscillator, the control problem of the grazing induced chaos is investigated in this paper. To design degenerate grazing bifurcations, we show how to obtain the degenerate grazing points of the 1/n impact periodic motions by the existence and stability analysis firstly. Then, a discrete-in-time feedback control strategy is used to suppress the grazing induced chaos into the 1/n impact periodic motions precisely by the desired degenerate grazing bifurcation. The feasibility of the control strategy is verified by numerical simulations.
TOPICS: Chaos, Feedback, Bifurcation, Stability, Computer simulation, Degrees of freedom, Design
Jie Liu, Bing Li, Huihui Miao, Anqi He and Shangkun Zhu
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037927
With the growing structural complexity and growing demands on structural reliability, nonlinear parameters identification is an efficient approach to provide better understanding of dynamic behaviors of the nonlinear system and contribute significantly for improving system performance. However, the dynamic response at nonlinear location which cannot always be measured by the sensor is the basis for most of these identification algorithms, and the clearance nonlinearity which always exists to degrade the dynamic performance of mechanical structures is rarely identified in previous studies. In this paper, based on the thought of output feedback which the nonlinear force is viewed as the internal feedback force of the nonlinear system acting on the underlying linear model, a frequency-domain nonlinear response reconstruction method is proposed to reconstruct the dynamic response at the nonlinear location from the arbitrary location where the sensor can be installed. For the clearance nonlinear system, the force graph method which is based on the reconstructed displacement response and nonlinear force is presented to identify the clearance value. The feasibility of the reconstruction method and identification method is verified by simulation data from a cantilever beam model with clearance nonlinearity. A clearance test-bed which is a continuum structure with adjustable clearance nonlinearity is designed to verify effectiveness of proposed methods. The experimental results show that the reconstruction method can precisely reconstruct the displacement response at clearance location from measured responses at reference locations, and based on the reconstructed response, the force graph method can also precisely identify the clearance parameter.
TOPICS: Clearances (Engineering), Nonlinear systems, Displacement, Dynamic response, Feedback, Sensors, Cantilever beams, Reliability, Simulation, Mechanical structures, Algorithms
Yuxiang Guo and Baoli Ma
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037929
This paper is mainly concerned with asymptotic stability for a class of fractional-order nonlinear system with application to stabilization a fractional permanent magnet synchronous motor. First of all, we discuss the stability problem of a class of fractional time-varying systems with nonlinear dynamics. By employing Gronwall-Bellman's inequality, Laplace transform and its inverse transform, and estimate forms of Mittag-Leffler functions, when the fractional-order belongs to the interval (0, 2), several stability criterions for fractional time-varying system described by Riemann-Liouville's definition is presented. Then, it is generalized to stabilize a fractional-order nonlinear permanent magnet synchronous motor system. Furthermore, it should be emphasized here that the asymptotic stability and stabilization of Riemann-Liouville type fractional-order linear time invariant system with nonlinear dynamics is proposed for the first time. Besides, some problems about the stability of fractional time-varying systems in existing literatures are pointed out. Finally, numerical simulations are given to show the validness and feasibleness of our obtained stability criterions.
TOPICS: Engines, Motors, Permanent magnets, Stability, Time-varying systems, Nonlinear dynamics, Time-invariant systems, Computer simulation, Nonlinear systems, Laplace transforms
Chengyuan Zhang and Jian Xiao
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037931
The fractional differential equations of the single degree of freedom (DOF) quarter vehicle with a magnetorheological (MR) suspension system under the excitation of sine are established and the numerical solution is acquired based on predictor-corrector method. The analysis of phase trajectory, time domain response, and Poincaré section shows that the nonlinear dynamic characteristics between fractional and integer order suspension systems are quite different, which proves the superiority of using fractional order to describe the physical properties. By discussing the influence of each parameter on the vibration, the range of parameters to avoid the chaotic vibration is obtained. The variable feedback control is used to control the chaotic vibration effectively..
TOPICS: Suspension systems, Feedback, Vibration, Excitation, Trajectories (Physics), Degrees of freedom, Differential equations, Vehicles
Li Ma and Changpin Li
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037930
This paper is devoted to investigating the relation between Hadamard-type fractional derivatives and finite part integrals in Hadamard sense, that is to say, the Hadamard-type fractional derivative of a given function can be expressed by the finite part integral of a strongly singular integral which does not exist. Besides, our results also cover that some fundamental properties on absolutely continuous functions, and the logarithmic series expansion formulas at the right end point of interval for functions in certain absolutely continuous spaces.
Christian M. Firrone, Giuseppe Battiato and Bogdan I. Epureanu
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037796
The complex architecture of aircraft engines requires demanding computational efforts when the dynamic coupling of their components has to be predicted. For this reason numerically efficient Reduced Order Models (ROM) have been developed with the aim of performing modal analyses and forced response computations on complex multi-stage assemblies being computationally fast. In this paper the flange joint connecting two turbine disks of a multi-stage assembly is studied as a source of nonlinearities due to friction damping occurring at the joint contact interface. An analytic contact model is proposed to calculate the local microslip based on the different deformations that the two flanges in contact take during vibration. The model is first introduced using a simple geometry representing two flanges in contact and then it is applied to a reduced FE model in order to calculate the nonlinear forced response.
TOPICS: Dynamics (Mechanics), Manufacturing, Flanges, Disks, Modeling, Turbines, Vibration, Computation, Finite element model, Geometry, Aircraft engines, Modal analysis, Damping, Deformation, Friction
Ashu Sharma and Subhash C. Sinha
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037797
Parametrically excited linear systems with oscillatory coefficients have been generally modeled by Mathieu or Hill equations (periodic coefficients) because their stability and response can be determined by Floquét theory. However, in many cases the parametric excitation is not periodic but consists of frequencies that are incommensurate, making them quasi-periodic. Unfortunately, there is no complete theory for linear dynamic systems with quasi-periodic coefficients. Motivated by this fact, in this work, an approximate approach has been proposed to determine the stability and response of quasi-periodic systems. It is suggested here that a quasi-periodic system may be replaced by a periodic system with an appropriate large principal period and thus making it suitable for an application of the Floquét theory. Based on this premise, a systematic approach has been developed and applied to three typical quasi-periodic systems. The approximate boundaries in stability charts obtained from the proposed method are very close to the exact boundaries of original quasi-periodic equations computed numerically using maximal Lyapunov exponents. Further, the frequency spectra of solutions generated near approximate and exact boundaries are found to be almost identical ensuring a high degree of accuracy. In addition, state transition matrices are also computed symbolically in terms of system parameters using Chebyshev polynomials and Picard iteration method. Stability diagrams based on this approach are found to be in excellent agreement with those obtained from numerical methods. The coefficients of parametric excitation terms are not necessarily small in all cases.
TOPICS: Stability, Spectra (Spectroscopy), Numerical analysis, Linear dynamic system, Linear systems, Polynomials, Excitation
Hao Zhu, Weidong Zhu, Yumei Hu and Xuefeng Wang
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037764
A complete dynamic model of a timing belt drive system with an oval cogged pulley and an auto-tensioner is established in this work. Periodic torsional vibrations of all accessory pulleys and the tensioner arm are calculated using a modified incremental harmonic balance (MIHB) method based on the complete dynamic model. Calculated results from the MIHB method are verified by comparing them with those obtained from Runge-Kutta method. Influences of tensioner parameters and oval pulley parameters on torsional vibrations of camshafts and other accessory pulleys are investigated. A sequence quadratic programming method with oval pulley parameters selected as design variables is applied to minimize the overall torsional vibration amplitude of all the accessory pulleys and the tensioner arm in the timing belt drive system at different operational speeds. It is demonstrated that torsional vibrations of the timing belt drive system are significantly reduced by matching the belt stretch with speed variations of the crankshaft and fluctuating torque loads on camshafts. The timing belt drive system with optimal oval parameters given in this work has better performance in the overall torsional vibration of the system than that with oval parameters provided by the kinematic model and the simplified dynamic model in previous research.
TOPICS: Design, Vibration, Pulleys, Timing belts, Dynamic models, Camshafts, Kinematics, Torque, Stress, Belts, Quadratic programming, Runge-Kutta methods
Dumitru Baleanu, Mustafa Inc, Abdullahi Yusuf and Aliyu Isa Aliyu
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037765
In this work, Lie symmetry analysis for the time fractional third-order evolution (TOE) equation with Riemann-Liouville (RL) derivative is analyzed. We transform the time fractional TOE equation to nonlinear ordinary differential equation (ODE) of fractional order using its Lie point symmetries with a new dependent variable. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. We obtain a kind of an explicit power series solution for the governing equation based on the power series theory. Using Ibragimov's nonlocal conservation method to time fractional partial differential equations, we compute conservation laws (Cls) for the TOE equation. 2-D, 3-D, and contour plots for the explicit power series solution are presented.
TOPICS: Differential equations, Partial differential equations
Technical Brief  
Feng Liang, Xiao-Dong Yang, Y. -J. Qian and Wei Zhang
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037594
The forced vibration of gyroscopic continua is investigated by taking the pipes conveying fluid as an example. The nonlinear normal modes and a numerical iterative approach are used to perform numerical response analysis. The nonlinear non-autonomous governing equations are transformed into a set of pseudo-autonomous ones by using the harmonic balance method. Based on the pseudo-autonomous system, the nonlinear normal modes are constructed by the invariant manifold method on the state space and substituted back into the original discrete equations. By repeating the above steps, the dynamics responses can be numerically obtained asymptotically using such iterative approach. Quadrature phase difference between the general coordinates is verified for the gyroscopic system and traveling waves instead of standing waves are found in the time-domain complex modal analysis.
TOPICS: Pipes, Fluids, Standing waves, Phase (Wave motion), Dynamics (Mechanics), Vibration, Manifolds, Traveling waves, Modal analysis
Peiman Naseradinmousavi, Hashem Ashrafiuon and Mohammad A. Ayoubi
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037593
Catastrophic chaotic and hyperchaotic dynamical behavior have been experimentally observed in the so-called "Smart Valves" network, given certain critical parameters and initial conditions. The centralized network-based control of these coupled systems may effectively mitigate the harmful dynamics of the valve-actuator configuration which can be potentially caused by a remote set and would gradually affect the whole network. In this work, we address the centralized control of two bi-directional solenoid actuated butterfly valves dynamically coupled in series subject to the chaotic and hyperchaotic dynamics. An interconnected adaptive scheme is developed and examined to vanish both the chaotic and hyperchaotic dynamics and return the coupled network to its safe domain of operation.
TOPICS: Dynamics (Mechanics), Valves, Solenoids, Valve actuators
Sze-Hong Teh, Ko-Choong Woo and Hazem Demrdash
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037595
This paper investigates the possibility of energy generation via pendulum rotations when the source of vertical excitation is chaotic in nature. The investigations are conducted using an additional height-adjustable mechanism housing a secondary spring to optimize a configuration of experimental pendulum setup. Chaotic oscillations of the pendulum pivot are made possible at certain excitation conditions due to a piecewise-linear stiffness characteristic introduced by the modification. A velocity control method is applied to maintain the rotational motion of the pendulum as it interacts with the vertical oscillator. The control input is effected by a motor, and a generator is used to quantify the energy extraction. The experimental results imply the feasibility of employing a pendulum device in a chaotic vibratory environment for energy harvesting purpose.
TOPICS: Pendulums, Excitation, Springs, Stiffness, Oscillations, Rotation, Engines, Motors, Energy generation, Energy harvesting, Generators
Samer Ezz-Eldien and Ahmed El-Kalaawy
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037597
This paper presents an efficient approximation scheme for the numerical solution of a fractional variational problem (FVP) and fractional optimal control problem (FOCP). As basis function for the trial solution, we employ the shifted Jacobi orthonormal polynomial. We state and derive a new operational matrix of right-sided Caputo fractional derivative of such polynomial. The new methodology of the present scheme is based on the derived operational matrix with the help of the Gauss-Lobatto quadrature formula and the Lagrange multiplier technique. Accordingly, the aforementioned problems are reduced into systems of algebraic equations. The error bound for the operational matrix of right-sided Caputo derivative is analyzed. In addition, the convergence of the proposed approach is also included. The results obtained through numerical procedure and comparing our method with other methods demonstrate the high accuracy and powerful of the present approach.
TOPICS: Computer simulation, Optimal control, Optimization, Approximation, Errors, Polynomials, Algebra
Mergen Ghayesh
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037596
This paper, for the first time, investigates the nonlinear dynamics of a three-layered microplate. The von Kármán plate theory together with the modified couple stress theory (MCST) is employed to derive the nonlinear size-dependent transverse and in-plane equations of motion in a Hamiltonian framework. A nonconservative damping force of viscous type as well as an external excitation load consisting of a harmonic term is considered in the model. All the transverse and in-plane displacements and inertia are considered (not neglected) in both the theoretical modelling and numerical simulations; this leads to difficulties in the complex nonlinear model and simulations. These difficulties are overcome here by means of the systematic modelling of the kinetic and potential energies corresponding to each layer of the microplate and through use of a well-optimised numerical scheme. The effect of different arrangements and different material percentages of each layer on the force-amplitude and frequency-amplitude curves of the microsystem, with special attention to the effect of the length-scale parameter, are investigated. The results of this study are helpful in designing three-layered microplates in MEMS industry.
TOPICS: Nonlinear dynamics, Microplates, Modeling, Stress, Microelectromechanical systems, Damping, Design, Engineering simulation, Equations of motion, Inertia (Mechanics), Computer simulation, Simulation, Plate theory, Excitation
Samaneh Mohammadpour and Tahereh Binazadeh
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037672
This paper considers the robust synchronization of chaotic systems in the presence of non-symmetric input saturation constraints. The synchronization happens between two nonlinear master and slave systems in the face of model uncertainties and external disturbances. A new adaptive sliding mode controller is designed in a way that the robust synchronization occurs. In this regard, a theorem is proposed and according to the Lyapunov approach the adaptation laws are derived and it is proved that the synchronization error converges to zero despite of the uncertain terms in master and slave systems and non-symmetric input saturation constraints. Finally, the proposed method is applied on chaotic gyro systems to show its applicability. Computer simulations verify the theoretical results and also show the effective performance of the proposed controller.
TOPICS: Chaos synchronization, Synchronization, Control equipment, Computer simulation, Errors, Uncertainty, Theorems (Mathematics)
Yongjun Pan and Javier García de Jalón
J. Comput. Nonlinear Dynam   doi: 10.1115/1.4037417
A number of strategies can be followed to efficiently simulate multibody systems. The main contributing factor to computational efficiency is usually the algorithm itself (the number of equations and their structure, the number of coordinates, the time integration scheme, etc.). Additional (but equally important) aspects have to do with implementation (linear solvers, sparse matrices, parallel computing, etc.). In this paper, an iterative refinement technique is introduced into a semirecursive multibody formulation. First, the formulation is summarized and its basic features are highlighted. Then, the basic goal is to iteratively solve the fundamental system of equations to obtain the accelerations. The iterative process is applied to compute corrections of the solution in an economic way, terminating as soon as a given precision is reached. We show that, upon implementation of this method, the computation time can be reduced at a very low implementation and accuracy costs. Two vehicles are simulated to prove the numerical benefits, namely a 16-degree-of-freedom sedan vehicle and a 40-degree-of-freedom semitrailer truck. In short, a simple method to iteratively solve for the accelerations of multibody systems in an efficient way is presented.
TOPICS: Algorithms, Vehicles, Vehicle dynamics, Computation, Trucks, Multibody systems

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In