Galloping Vibration of Nonlinear Cables Through a Two Degree-of-Freedom Oscillator

In this paper, galloping vibrations of a lightly iced transmission line are investigated through a two-degree-of-freedom (2-DOF) nonlinear oscillator. The 2-DOF nonlinear oscillator is used to describe the transverse and torsional motions of the galloping cables. The analytical solutions of periodic motions of galloping cables are presented through generalized harmonic balanced method. The analytical solutions of periodic motions for the galloping cable are compared with the numerical solutions, and the corresponding stability and bifurcation of periodic motions are analyzed by the eigenvalues analysis. To demonstrate the accuracy of the analytical solutions of periodic motions, the harmonic amplitudes are presented. This investigation will help one better understand galloping mechanism of iced transmission lines.

Influence of Fractional Damping and Time Delay on Maxwell-Voigt Model for Vibration Isolation

Models of vibration isolators are very commonly used for the design and analysis of isolation systems. Accurate isolator modeling is critical for a successful prediction of the dynamic characteristics of isolated systems. Isolators exhibit a complex behavior that depends on multiple parameters such as frequency, displacement amplitude, temperature and loading conditions. Therefore, it is important to choose a model that is accurate while adequately representing the relationships with relevant parameters. Recent literature has indicated some inherent advantages of fractional derivatives that can be exploited in the modeling of elastomeric isolators. Furthermore, time delay of damping is also seen to provide a realistic representation of damping. This paper examines the Maxwell-Voigt model with fractional damping and a time delay. This model is compared with the conventional Maxwell-Voigt model (without time delay or fractional damping) and the Voigt model in order to comprehend the influence of fractional damping and time delay on dynamic characteristics. Multiple simulations are performed after identifying model parameters from the data collected for a passive elastomeric isolator. The analysis results are compared and it is observed that the Voigt model is highly sensitive to fractional damping as well as time delay.

The Optimization of Time-Frequency Control: Using Non-Autonomous Time-Delay Feedback Systems as Example

A novel time-frequency nonlinear scheme demonstrated to be feasible for the control of dynamic instability including bifurcation, non-autonomous time-delay feedback oscillators, and route-to-chaos in many nonlinear systems is applied to the control of a time-delayed system. The control scheme features wavelet adaptive filters for simultaneous time-frequency resolution. Specifically Discrete Wavelet transform (DWT) is used to address the nonstationary nature of a chaotic system. The concept of active noise control is also adopted. The scheme applied the filter-x least mean square (FXLMS) algorithm which promotes convergence speed and increases performance. In the time-frequency control scheme, the FXLMS algorithm is modified by adding an adaptive filter to identify the system in real-time in order to construct a wavelet-based time-frequency controller capable of parallel on-line modeling. The scheme of such a construct, which possesses joint time-frequency resolution and embodies on-line FXLMS, is able to control non-autonomous, nonstationary system responses. Although the controller design is shown to successfully moderate the dynamic instability of the time-delay feedback oscillator and unconditionally warrant a limit cycle, parameters are required to be optimized. In this paper, the setting of the control parameters such as control time step, sampling rate, wavelet filter vector, and step size are studied and optimized to control a time-delay feedback oscillators of a nonautonomous type. The time-delayed oscillators have been applied in a broad set of fields including sensor design, manufacturing, and machine dynamics, but they can be easily perturbed to exhibit complex dynamical responses even with a small perturbation from the time-delay feedback. These responses for the system have a very negative impact on the stability, and thus output quality. Through employingfrequency-time control technique, the time responses of the time-delay feedback system to external disturbances are properly mitigated and the frequency responses are also suppressed, thus rendering the controlled responses quasi-periodic.

Active Torque Vectoring in High Speed Lane Change Maneuvers

Emergency lane changes are often the best course of action when avoiding obstacles on the road, but this maneuver has the possibility of sending the vehicle out of control. The University of Washington EcoCAR team has a hybrid-electric vehicle outfitted with an electric drivetrain and variable torque control to each of the rear wheels. Each rear wheel has an electric motor that is independently controlled to provide torque to the wheel. A lateral vehicle dynamics model is used to develop a torque control strategy to improve the safety and maneuverability of a modified hybrid-electric 2016 Camaro as part of the EcoCAR 3 competition. The specific scenario simulated is a two-lane lane change at a speed of 55 mph. We would like to increase the yaw and lateral accelerations that the vehicle can perform safely by controlling differing torques out of the two motors. Regulating these accelerations requires a control strategy over the left and right motor torques. Equal-torque control of the electric motors will be used as a baseline.

On Time-Delay Effects on Period-1 Motions in a Periodically Forced, Time-Delayed, Duffing Oscillator

In recent decades, nonlinear time-delay systems were often applied in controlling nonlinear systems, and the stability of such time-delay systems was very actively discussed. Recently, one was very interested in periodic motions in nonlinear time-delay systems. Especially, the semi-analytical solutions of periodic motions in time-delay systems are of great interest. From the semi-analytical solutions, the nonlinearity and complexity of periodic motions in the time-delay systems can be discussed. In this paper, time-delay effects on periodic motions of a periodically forced, damped, hardening, Duffing oscillator are analytically discussed through a semi-analytical method. The semi-analytical method is based on discretization of the differential equation of such a Duffing oscillator to obtain the corresponding implicit discrete mappings. Through such implicit mappings and mapping structures of periodic motions, period-1 motions varying with time-delay are discussed, and the corresponding stability and bifurcation analysis of periodic motions are carried out through eigenvalue analysis. Numerical results of periodic motions are illustrated to verify analytical predictions. The corresponding harmonic amplitude spectrums and harmonic phases are presented for a better understanding of periodic motions in such a nonlinear oscillator.

Analytical Bifurcation Trees of a Periodically Excited Pendulum

In this paper, the bifurcation trees of a periodically excited pendulum are investigated. Implicit discrete maps for such a pendulum are developed to construct discrete mapping structures. Bifurcation trees of the corresponding periodic motions are predicted semi-analytically through the discrete mapping structure. The corresponding stability and bifurcation analysis are carried out through eigenvalue analysis. Finally, numerical illustrations of various periodic motions are given to verify the analytical prediction. The accurate periodic motions in the periodically forced pendulum are predicted for the first time through the implicit mapping systems, and the corresponding bifurcation trees of periodic motion to chaos are obtained.

Analysis and Control of the 1st Order Interior Noise and Vibration Induced by Driveline Imbalance for 4WD Vehicle

Based on the influence coefficient method of the single-plane and multi-plane imbalance, an experimental method of a 4WD driveline system imbalance is proposed. A sensitivity theory and a testing method of influence of the 4WD driveline system imbalance on the vehicle interior 1st order vibration and noise are proposed. According to the influence coefficient method of the single plane, this paper puts forward an imbalance separation method for the driveline components, especially the imbalance separation between the driveshaft and the axle. Based on the problems and phenomena of the 1st order interior vibration and noise induced by the driveline imbalance transferring through the body floor and the interior acoustic cavity, the driveline imbalance sensitivity, the dynamic imbalance of the driveshaft and the driveline system are analyzed separately. Finally, the control methods of the dynamic imbalance and sensitivity of the 4WD vehicle driveline system are provided.

Development of an Active Curved Beam Model Using a Moving Frame Method

In order to develop an active large-deformation beam model for slender, flexible or soft robots, the d’Alembert principle of virtual work is derived for three-dimensional elastic solids from Hamilton’s principle. This derivation is accomplished by refining the definition of the Cauchy stress tensor as a vector-valued 2-form to exploit advanced geometrical operations available for differential forms. From the three-dimensional principle of virtual work, both the beam principle of virtual work and beam equations of motion with consistent boundary conditions are derived, adopting the kinematic assumption of rigid cross-sections of a deforming beam. In the derivation of the beam model, Élie Cartan’s moving frame method is utilized. The resulting large-deformation beam equations apply to both passive and active beams. The beam equations are validated with the previously reported results expressed in vector form. To transform passive beams to active beams, constitutive relations for internal actuation are presented in rate-form. Then, the resulting three-dimensional beam models are reduced to an active planar beam model. Finally, to illustrate the deformation due to internal actuation, an active Timoshenko-beam model is derived by linearizing the nonlinear planar equations. For an active, simply-supported Timoshenko-beam, the analytical solution is presented.

Nonlinear Time-Frequency Control of Permanent Magnet Synchronous Motors

Permanent magnet synchronous motors are essential components in a wide range of applications in which their unique benefits are explored. However, in order for a permanent magnet synchronous motor to achieve satisfactory performance, particular control frameworks are essential. After all, permanent magnet synchronous motor is an AC machine, which is characterized by its complex structure and strongly coupled system states. Therefore, in order for it to achieve satisfactory dynamic performance, advanced control techniques are the only solution. This paper presents a precise speed control of permanent magnet synchronous motors using the nonlinear time-frequency control concept. The novel aspect of this nonlinear time-frequency control, which is an integration of discrete wavelet transformation and adaptive control, is its ability in analyzing the fundamental temporal and spectral qualities inherent of a permanent magnet synchronous motor and exerting control signals accordingly. Simulation results verifies that the proposed nonlinear time-frequency control scheme is feasible for alleviating the nonlinear behavior of the permanent magnet synchronous motor which hampers the tracking of speed with desired precision.

Robustness Analysis of the Collective Dynamics of Nonlinear Periodic Structures Under Parametric Uncertainty

In order to ensure more realistic design of nonlinear periodic structures, the collective dynamics of a coupled pendulums system is investigated under parametric uncertainties. A generic discrete analytical model combining the multiple scales method, the perturbation theory and a standing-wave decomposition is proposed and adapted to the presence of uncertainties. These uncertainties are taken into account through a probabilistic modeling implying that the stochastic parameters vary according to random variables of chosen probability density functions. The proposed model leads to a set of coupled complex algebraic equations written according to the number and positions of the uncertainties in the structure and numerically solved using the time integration Runge-Kutta method. The uncertainty propagation through the established model is finally ensured using the Latin Hypercube Sampling method. The analysis of the dispersion, in term of variability of the frequency and amplitude intervals of the multistability domain shows the effects of uncertainties on the stability and nonlinearity of a three coupled pendulums structure. The nonlinear aspect is strengthened, the multistability domain is wider, more stable branches are obtained and thus the multimode solutions are enhanced.