Research Papers

J. Comput. Nonlinear Dynam. 2018;13(6):061001-061001-9. doi:10.1115/1.4039682.

A hybrid approach which combines the reduced sequential quadratic programing (SQP) method with the shooting method is proposed to search the worst resonance response of nonlinear systems. The shooting method is first employed to construct the nonlinear equality constraints for the constrained optimization problem. Then, the complex optimization problem is simplified and solved numerically by the reduced SQP method. By virtue of the coordinate basis decomposition scheme which exploits the gradients of nonlinear equality constraints, the nonlinear equality constraints are eliminated, resulting in a simple optimization problem subject to bound constraints. Moreover, the second-order correction (SOC) technique is adopted to overcome Maratos effect. The novelty of the approach described lies in the capability to efficiently handle nonlinear equality constraints. The effectiveness of the proposed algorithm is demonstrated by two benchmark examples seen in the literature.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2018;13(6):061002-061002-6. doi:10.1115/1.4039839.

Vibrational resonance (VR) is a nonlinear phenomenon which occurs when a bistable system is subjected to a biharmonic excitation consisting of a small-amplitude resonant excitation and a large-amplitude high-frequency excitation. The result is that, under some conditions, the high-frequency excitation amplifies the resonant response associated with the slow dynamics. While VR was studied extensively in the open literature, most of the research studies used optical and electrical systems as platforms for experimental investigation. This paper provides experimental evidence that VR can also occur in a mechanical bistable twin-well oscillator and discusses the conditions under which VR is possible. The paper also demonstrates that the injection of the high frequency excitation can be used to change the effective stiffness of the slow response. This can be used for amplification/deamplification of the output signal which can be useful for sensitivity enhancement and/or vibration mitigation.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2018;13(6):061003-061003-9. doi:10.1115/1.4039877.

A computational methodology to model and analyze planar rigid mechanical system with stick–slip friction in revolute clearance joint is presented. In this work, the LuGre friction model, which captures the Stribeck effect and spring-like characteristics for stiction, is employed to estimate the stick–slip friction in revolute clearance joint. A hybrid contact force model, combining Lankarani–Nikravesh model, and improved elastic foundation model, is used to establish contact model. The generalized-α method, which can dissipate the spurious high-frequency responses caused by the strongly nonlinear contact force and friction in numerical simulation, is adopted to solve the equations of motion and make the result closer to the physics of the problem. A slider-crank mechanism with revolute clearance joint based on LuGre friction model and modified coulomb friction model are simulated, respectively, and utilized to discuss the influences of the Stribeck effect and stiction on dynamic behavior of the mechanism. Different test scenarios are considered to investigate the effects of the clearance size and friction coefficient on the dynamic response of the mechanism. The results show that the mechanism based on LuGre friction model has better energy dissipation characteristics, while there are stiction phenomena of the contacting surfaces in many cases. When the relative velocity is zero or close to zero, the contact force of mechanism based on the LuGre friction model is significantly lower than that based on the modified coulomb friction model. Clearance size and friction coefficient obviously affect dynamic behavior of the mechanism.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2018;13(6):061004-061004-9. doi:10.1115/1.4039878.

Bed-load transport in natural rivers exhibits nonlinear dynamics with strong temporal memory (i.e., retention due to burial) and/or spatial memory (i.e., fast displacement driven by turbulence). Nonlinear bed-load transport is discrete in nature due to the discontinuity in the sediment mass density and the intermittent motion of sediment along river beds. To describe the discrete bed-load dynamics, we propose a discrete spatiotemporal fractional advection-dispersion equation (D-FADE) without relying on the debatable assumption of a continuous sediment distribution. The new model is then applied to explore nonlinear dynamics of bed-load transport in flumes. Results show that, first, the D-FADE model can capture the temporal memory and spatial dependency characteristics of bed-load transport for sediment with different sizes. Second, fine sediment particles exhibit stronger super-diffusive features, while coarse particles exhibit significant subdiffusive properties, likely due to the size-selective memory impact. Third, sediment transport with an instantaneous source exhibits stronger history memory and weaker spatial nonlocality, compared to that with a continuous source (since a smaller number of particles might be blocked or buried relatively easier). Hence, the D-FADE provides a strict computational model to quantify discrete bed-load transport, whose nonlinear dynamics can be sensitive to particle sizes and source injection modes, both common in applications.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2018;13(6):061005-061005-10. doi:10.1115/1.4039962.

Dissipation mechanisms and dissipative forces play a pivotal role in the operations and performance of human-machine interfaces and particularly in haptic systems. Dissipation is a very difficult phenomenon to model. Coulomb friction in general can be the most influential element in systems involving multiple direct contact connections such as joints with transmissions or mechanically guided components. Coulomb friction includes nonsmooth discontinuity and can induce complex dynamic behaviors. The effect of Coulomb friction is often neglected in haptics. The part of the literature which deals with friction mainly focuses on friction compensation and/or simulation of friction for haptic rendering. In this paper, the nature of the dynamic behavior caused by Coulomb friction in haptic sampled-data systems is illustrated by experiment, analysis, and simulation. It is also demonstrated that a simple model can represent this behavior and show the effects of the haptic system parameters on this dynamics.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2018;13(6):061006-061006-7. doi:10.1115/1.4039876.

The main goal of this paper is to design a state feedback control that makes a point mass track a non-Zeno reference trajectory in a planar billiard. This objective is achieved by first determining a continuous-time dynamical model, whose trajectories approximate the solutions of the hybrid system. Hence, a state feedback that makes the hybrid system track a reference trajectory of the continuous-time one is proposed. Finally, these two techniques are combined in order to find a state feedback that achieves tracking of the trajectories of the unforced system. Examples are reported all throughout the paper to illustrate the theoretical results.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2018;13(6):061007-061007-10. doi:10.1115/1.4039900.

In this paper, a new numerical scheme is proposed for multidelay fractional order optimal control problems where its derivative is considered in the Grunwald–Letnikov sense. We develop generalized Euler–Lagrange equations that results from multidelay fractional optimal control problems (FOCP) with final terminal. These equations are created by using the calculus of variations and the formula for fractional integration by parts. The derived equations are then reduced into system of algebraic equations by using a Grunwald–Letnikov approximation for the fractional derivatives. Finally, for confirming the accuracy of the proposed approach, some illustrative numerical examples are solved.

Topics: Optimal control
Commentary by Dr. Valentin Fuster


J. Comput. Nonlinear Dynam. 2018;13(6):068001-068001-1. doi:10.1115/1.4039840.

Dynamic modeling and analysis have broad relevance to many biological processes and biomedical applications, such as heart dynamics, DNA/RNA, cell mobility, surgical robotics, and so on. Various analytical and numerical techniques have been developed to qualitatively and quantitatively study dynamics associated with design, diagnosis, and control in these problems.

Commentary by Dr. Valentin Fuster

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