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Research Papers

J. Comput. Nonlinear Dynam. 2019;14(5):051001-051001-9. doi:10.1115/1.4042692.

The present study uncovers the hyperchaotic dynamical behavior of the famous Murali-Lakshmanan-Chua (MLC) circuit, when suitably modified. In the conventional MLC oscillator, an inductor is introduced in parallel between the nonlinear element and the capacitor. Many novel and interesting dynamical behaviors such as reverse period-3 doubling, torus breakdown to chaos and hyperchaos, etc., were observed. Characterization techniques includes spectrum of Lyapunov exponents, one parameter bifurcation diagram, recurrence quantification analysis, correlation dimension, etc., were employed to analyze the different dynamical regimes. Explicit analytical solution of the model is derived and the results are corroborated with the numerical outcomes.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2019;14(5):051002-051002-9. doi:10.1115/1.4042494.

Synchronization for incommensurate Riemann–Liouville fractional competitive neural networks (CNN) with different time scales is investigated in this paper. Time delays and unknown parameters are concerned in the model, which is more practical. Two simple and effective controllers are proposed, respectively, such that synchronization between the salve system and the master system with known or unknown parameters can be achieved. The methods are more general and less conservative which can also be applied to commensurate integer-order systems and commensurate fractional systems. Furthermore, two numerical ensamples are provided to show the feasibility of the approach. Based on the chaotic masking method, the example of chaos synchronization application for secure communication is provided.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2019;14(5):051003-051003-12. doi:10.1115/1.4042690.

Modeling multibody systems subject to unilateral contacts and friction efficiently is challenging, and dynamic formulations based on the mixed linear complementarity problem (MLCP) are commonly used for this purpose. The accuracy of the MLCP solution method can be evaluated by determining the error introduced by it. In this paper, we find that commonly used MLCP error measures suffer from unit inconsistency leading to the error lacking any physical meaning. We propose a unit-consistent error measure, which computes energy error components for each constraint dependent on the inverse effective mass and compliance. It is shown by means of a simple example that the unit consistency issue does not occur using this proposed error measure. Simulation results confirm that the error decreases with convergence toward the solution. If a pivoting algorithm does not find a solution of the MLCP due to an iteration limit, e.g., in real-time simulations, choosing the result with the least error can reduce the risk of simulation instabilities and deviation from the reference trajectory.

Topics: Errors , Simulation
Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2019;14(5):051004-051004-15. doi:10.1115/1.4042602.

In order to understand dynamic responses of planar rigid-body mechanism with clearance, the dynamic model of the mechanism with revolute clearance is proposed and the dynamic analysis is realized. First, the kinematic model of the revolute clearance is built; the amount of penetration depth and relative velocity between the elements of the revolute clearance joint is obtained. Second, Lankarani-Nikravesh (L-N) and the novel nonlinear contact force model are both used to describe the normal contact force of the revolute clearance, and the tangential contact force of the revolute clearance is built by modified Coulomb friction model. Third, the dynamic model of a two degrees-of-freedom (2DOFs) nine bars rigid-body mechanism with a revolute clearance is built by the Lagrange equation. The fourth-order Runge–Kutta method has been utilized to solve the dynamic model. And the effects of different driving speeds of cranks, different clearance values, and different friction coefficients on dynamic response are analyzed. Finally, in order to prove the validity of numerical calculation result, the virtual prototype model of 2DOFs nine bars mechanism with clearance is modeled and its dynamic responses are analyzed by adams software. This research could supply theoretical basis for dynamic modeling, dynamic behaviors analysis, and clearance compensation control of planar rigid-body mechanism with clearance.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2019;14(5):051005-051005-12. doi:10.1115/1.4042294.

The shimmy problem causes considerable harm to vehicles and is difficult to solve, especially multiple limit cycle shimmy. Moreover, the dynamic behavior of the multiple limit cycle shimmy of vehicles based on a bisectional road is more complex. Shimmy is practically observed in trucks of cooperative factories during utilization. Thus, we take a heavy truck of a cooperative factory as the prototype and establish a dynamic model of the vehicle-road coupling shimmy system, considering the road adhesion coefficient and dry friction between the suspension and steering system. Based on the dynamic model, the Hopf bifurcation theory is used to qualitatively analyze the existence of the limit cycle for the vehicle shimmy system, and the multiple limit cycle shimmy phenomenon is successfully reproduced using a numerical method. Moreover, the effect of the road adhesion coefficient on the multiple limit cycle shimmy characteristic is studied. Results show that the speed interval and amplitude of the multiple limit cycle shimmy decrease with the road adhesion coefficient; when the coefficient is reduced to a certain extent, the multiple limit cycle shimmy phenomenon is not observed. In addition, the adhesion coefficient of the second axle has a stronger effect on the shimmy characteristic than that of the first axle.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2019;14(5):051006-051006-12. doi:10.1115/1.4042689.

Extensive research has been devoted to engineering analysis in the presence of only parameter uncertainty. However, in modeling process, model-form uncertainty arises inevitably due to the lack of information and knowledge, as well as assumptions and simplifications made in the models. It is undoubted that model-form uncertainty cannot be ignored. To better quantify model-form uncertainty in vibration systems with multiple degrees-of-freedom, in this paper, fractional derivatives as model-form hyperparameters are introduced. A new general model calibration approach is proposed to separate and reduce model-form and parameter uncertainty based on multiple fractional frequency response functions (FFRFs). The new calibration method is verified through a simulated system with two degrees-of-freedom. The studies demonstrate that the new model-form and parameter uncertainty quantification method is robust.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2019;14(5):051007-051007-10. doi:10.1115/1.4042691.

Microscale dynamic simulations can require significant computational resources to generate desired time evolutions. Microscale phenomena are often driven by even smaller scale dynamics, requiring multiscale system definitions to combine these effects. At the smallest scale, large active forces lead to large resultant accelerations, requiring small integration time steps to fully capture the motion and dictating the integration time for the entire model. Multiscale modeling techniques aim to reduce this computational cost, often by separating the system into subsystems or coarse graining to simplify calculations. A multiscale method has been previously shown to greatly reduce the time required to simulate systems in the continuum regime while generating equivalent time histories. This method identifies a portion of the active and dissipative forces that cancel and contribute little to the overall motion. The forces are then scaled to eliminate these noncontributing portions. This work extends that method to include an adaptive scaling method for forces that have large changes in magnitude across the time history. Results show that the adaptive formulation generates time histories similar to those of the unscaled truth model. Computation time reduction is consistent with the existing method.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2019;14(5):051008-051008-12. doi:10.1115/1.4042638.

This paper describes models of dynamics for articulated vehicles (tractor with a semitrailer and a tractor with a trailer). The models are obtained by using joint coordinates and homogenous transformations. Yawing velocities of the vehicle units have been measured during a sharp turn maneuver. The results of experimental measurements are then used to calibrate the mathematical models, which means the parameters of tires for the Dugoff–Uffelman model are chosen in such a way that the results of calculations and measurements are compatible. In order to solve this problem, an optimization method is used. Satisfactory results have been achieved and they are presented in this paper. Further, the model calibrated is used to analyze how the friction in the connections between the tractor and semitrailer, as well as between the dolly and the trailer, influences the motion of the vehicle.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Comput. Nonlinear Dynam. 2019;14(5):054501-054501-6. doi:10.1115/1.4042999.

The stabilization problem of fractional-order nonlinear systems for 0<α<1 is studied in this paper. Based on Mittag-Leffler function and the Lyapunov stability theorem, two practical stability conditions that ensure the stabilization of a class of fractional-order nonlinear systems are proposed. These stability conditions are given in terms of linear matrix inequalities and are easy to implement. Moreover, based on these conditions, the method for the design of state feedback controllers is given, and the conditions that enable the fractional-order nonlinear closed-loop systems to assure stability are provided. Finally, a representative case is employed to confirm the validity of the designed scheme.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2019;14(5):054502-054502-5. doi:10.1115/1.4043000.

The dynamic model of a robotic system is prone to parametric and structural uncertainties, as well as dynamic disturbances, such as dissipative forces, input noise and vibrations, to name a few. In addition, it is conventional to access only a part of the state, such that, when just the joint positions are available, the use of an observer, or a differentiator, is required. Besides, it has been demonstrated that some disturbances are not necessarily differentiable in any integer-order sense, requiring for a physically realizable but robust controller to face them. In order to enforce a stable tracking in the case of nondifferentiable disturbances, and accessing just to the robot configuration, an output feedback controller is proposed, which is continuous and induces the convergence of the system state into a stable integral error manifold, by means of a fractional-order reaching dynamics. Simulation and experimental studies are conducted to show the reliability of the proposed scheme.

Commentary by Dr. Valentin Fuster

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