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J. Comput. Nonlinear Dynam. 2019;14(3):031001-031001-11. doi:10.1115/1.4042139.

This manuscript investigates the effect of nonconservative electromechanical energy transfer on the onset of interwell motions in multistable piezoelectric energy harvesters. Multistable piezoelectric energy harvesters have been proven to outperform their linear counterparts when they undergo interwell oscillations. The conditions for interwell oscillations in such harvesters are generally characterized in terms of their potential energy function. This is accurate for a stand-alone mechanical oscillator but when the piezoelectric patches and a load resistance are included, a part of the kinetic energy supplied to the system is converted into electrical energy. In this manuscript, the Melnikov necessary conditions for interwell oscillations are derived, considering the effect of this nonconservative piezoelectric energy transfer. Through Melnikov theoretic analysis, it is shown that in a tristable harvester with all the three potential wells having the same depth, a higher excitation level is required to enable exits from the middle well to the outer wells when compared to the exits from the outer wells to the middle well. This is in stark contrast to a stand-alone tristable mechanical oscillator wherein interwell motions are simultaneously enabled for all the wells having the same depth.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2019;14(3):031002-031002-10. doi:10.1115/1.4042293.

In this study, a new finite time control method is suggested for robotic manipulators based on nonsingular fast terminal sliding variables and the adaptive super-twisting method. First, to avoid the singularity drawback and achieve the finite time convergence of positional errors with a fast transient response rate, nonsingular fast terminal sliding variables are constructed in the position errors' state space. Next, adaptive tuning laws based on the super-twisting scheme are presented for the switching control law of terminal sliding mode control (TSMC) so that a continuous control law is extended to reject the effects of chattering behavior. Finally, a new finite time control method ensures that sliding motion will take place, regardless of the effects of the perturbations and uncertainties on the robot system. Accordingly, the stabilization and robustness of the suggested control system can be guaranteed with high-precision performance. The robustness issue and the finite time convergence of the suggested system are totally confirmed by the Lyapunov stability principle. In simulation studies, the experimental results exhibit the effectiveness and viability of our proposed scheme for joint position tracking control of a 3DOF PUMA560 robot.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2019;14(3):031003-031003-11. doi:10.1115/1.4042142.

An efficient and accurate model for the dynamic assessment of vehicle-track behavior subjected to cross wind actions is developed in this paper, where the wind–vehicle–track interaction is regarded as a coupled vibration system. First, a vehicle–track interaction model is proposed by taking the hypotheses of wheel/rail rigid contact and displacement complementarity. Unlike explicit force-based methods, the vehicle-track systems are wholly coupled by interaction matrices and load vectors, which are computationally more efficient than most of the existing methods and fairly accurate in low frequency vibrations. Then, the fluctuating cross winds are simulated by the fast Fourier transform technique from spectral representations with the consideration of spatial correlation of multipoint wind time histories and vehicle movement. The unsteady cross wind forces are obtained by introducing weighting function. Finally, a modeling framework, with the coupled interactions between cross winds, vehicle, and the tracks included, is built effectively. Through the validated dynamic model, the cross wind effects on vehicle-track dynamic performance can be fully revealed. Besides, it is concluded that the dynamic performance of vehicle-track systems differs significantly in various excitation modes, i.e., average cross wind, fluctuating cross wind, and track irregularities.

Topics: Vehicles , Wind , Rails , Wheels
Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2019;14(3):031004-031004-9. doi:10.1115/1.4042324.

The dynamic stability of a cantilevered beam actuated by a nonconservative follower force has previously been studied for its interesting dynamical properties and its applications to engineering designs such as thrusters. However, most of the literature considers a linear model. A modest number of papers consider a nonlinear model. Here, a system of nonlinear equations is derived from a new energy approach for an inextensible cantilevered beam with a follower force acting upon it. The equations are solved in time, and the agreement is shown with published results for the critical force including the effects of damping (as determined by a linear model). This model readily allows the determination of both in-plane and out-of-plane deflections as well as the constraint force. With this novel transparency into the system dynamics, the nonlinear postcritical limit cycle oscillations (LCO) are studied including a concentration on the force which enforces the inextensibility constraint.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2019;14(3):031005-031005-8. doi:10.1115/1.4042017.

This paper investigates the voltage–amplitude response of superharmonic resonance of second order (order two) of alternating current (AC) electrostatically actuated microelectromechanical system (MEMS) cantilever resonators. The resonators consist of a cantilever parallel to a ground plate and under voltage that produces hard excitations. AC frequency is near one-fourth of the natural frequency of the cantilever. The electrostatic force includes fringe effect. Two kinds of models, namely reduced-order models (ROMs), and boundary value problem (BVP) model, are developed. Methods used to solve these models are (1) method of multiple scales (MMS) for ROM using one mode of vibration, (2) continuation and bifurcation analysis for ROMs with several modes of vibration, (3) numerical integration for ROM with several modes of vibration, and (4) numerical integration for BVP model. The voltage–amplitude response shows a softening effect and three saddle-node bifurcation points. The first two bifurcation points occur at low voltage and amplitudes of 0.2 and 0.56 of the gap. The third bifurcation point occurs at higher voltage, called pull-in voltage, and amplitude of 0.44 of the gap. Pull-in occurs, (1) for voltage larger than the pull-in voltage regardless of the initial amplitude and (2) for voltage values lower than the pull-in voltage and large initial amplitudes. Pull-in does not occur at relatively small voltages and small initial amplitudes. First two bifurcation points vanish as damping increases. All bifurcation points are shifted to lower voltages as fringe increases. Pull-in voltage is not affected by the damping or detuning frequency.

Commentary by Dr. Valentin Fuster
J. Comput. Nonlinear Dynam. 2019;14(3):031006-031006-12. doi:10.1115/1.4042323.

This paper presents a new method in multibody dynamics and applies it to the challenge of stabilizing ship motion induced by onboard crane operations. Norwegian industries are constantly assessing new technologies for more efficient and safer production in the aquacultural, renewable energy, and oil and gas industries. They share a common challenge to install new equipment and transfer personnel in a safe and controllable way between ships, fish farms, and oil platforms. This paper deploys the moving frame method (MFM) to analyze the motion induced by a crane, yet controlled by a gyroscopic inertial device. We represent the crane as a simple two-link system that transfers produce and equipment to and from barges. We analyze how an inertial flywheel can stabilize the ship during the transfer. Lie group theory and the work of Elie Cartan are the foundations of the MFM. This, together with a restriction on the variation of the angular velocity used in Hamilton's principle, enables an effective way of extracting the equations of motion for an open-loop system. Furthermore, this work displays the results in three-dimensional (3D) on cell phones. The long-term results of this work lead to a robust 3D active compensation method for loading/unloading operations offshore. Finally, the simplicity of the analysis anticipates the impending time of artificial intelligence when machines, equipped with onboard central processing units and internet protocol addresses, are empowered with learning modules to conduct their operations.

Commentary by Dr. Valentin Fuster

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