Nonlinear dynamics of axially moving viscoelastic Timoshenko beam under parametric and external excitations

This investigation focuses on the nonlinear dynamic behaviors in the trans- verse vibration of an axiMly accelerating viscoelastic Timoshenko beam with the external harmonic excitation. The parametric excitation is caused by the harmonic fluctuations of the axial moving speed. An integro-partial-differential equation governing the transverse vibration of the Timoshenko beam is established. Many factors are considered, such as viscoelasticity, the finite axial support rigidity, and the longitudinally varying tension due to the axial acceleration. With the Galerkin truncation method, a set of nonlinear ordinary differential equations are derived by discretizing the governing equation. Based on the numerical solutions, the bifurcation diagrams are presented to study the effect of the external transverse excitation. Moreover, the frequencies of the two excitations are assumed to be multiple. Further, five different tools, including the time history, the Poincaré map, and the sensitivity to initial conditions, are used to identify the motion form of the nonlinear vibration. Numerical results also show the characteristics of the quasiperiodic motion of the translating Timoshenko beam under an incommensurable re- lationship between the dual-frequency excitations.

LoLocalized Spatial Soliton Excitations in(2+1)-Dimensional Nonlinear Schrdinger Equation with Variable Nonlinearity and an External Potential

We report on the localized spatial soliton excitations in the multidimensional nonlinear Schrodinger equation with radially variable nonlinearity coefficient and an external potential. By using Hirota＇s binary differential operators, we determine a variety of external potentials and nonlinearity coefficients that can support nonlinear localized solutions of different but desired forms. For some specific external potentials and nonlinearity coefficients, we discuss features of the corresponding （2＋1）-dimensional multisolitonic solutions, including ring solitons, lump solitons, and soliton clusters.

EXACT SOLUTIONS FOR STATIONARY RESPONSES OF SEVERAL CLASSES OF NONLINEAR SYSTEMS TO PARAMETRIC AND/OR EXTERNAL WHITE NOISE EXCITATIONS

The exact solutions for stationary responses of one class of the second order and three classes of higher order nonlinear systems to parametric and/or external while noise excitations are constructed by using Fokkcr-Planck-Kolmogorov et/ualion approach. The conditions for the existence and uniqueness and the behavior of the solutions are discussed. All the systems under consideration are characterized by the dependence ofnonconservative fqrces on the first integrals of the corresponding conservative systems and arc catted generalized-energy-dependent f G.E.D.) systems. It is shown taht for each of the four classes of G.E.D. nonlinear stochastic systems there is a family of non-G.E.D. systems which are equivalent to the G.E.D. system in the sense of having identical stationary solution. The way to find the equivalent stochastic systems for a given G.E.D. system is indicated and. as an example, the equivalent stochastic systems for the second order G.E. D. nonlinear stochastic system are given. It is pointed out and illustrated with example that the exact stationary solutions for many non-G.E.D. nonlinear stochastic systems may he found by searching the equivalent G.E.D. systems.

Dependence of Nonlinear Optical Response of Anatase TiO2 on Shape and Excitation Intensity

Nonlinear optical （NLO） properties of anatase TiO2 with nanostructures of nanopaxticle （NP）, nanowire （NW） and annealed nanowire （NWA） are studied by open-aperture and closed-aperture Z-scan techniques with a fem- tosecond pulsed laser at wavelengths of 532 nm and 780 nm simultaneously. At 532 nm, when increasing excitation intensity, NLO absorption of TiO2 NPs transforms from saturable absorption to reverse-saturable absorption. However, NWs and NWAs exhibit the opposite change. At 780nm, all samples show reverse-saturable absorption, but have different sensitivities to excitation intensity. Due to the larger surface-to-volume ratio of NPs and less defects of NWAs by annealing, nonlinear optical absorption coet^icients follow the order NPs≥ NWs≥ NWAs. The results also show that these shape and annealing effects axe dominant at low excitation intensity, but do not exhibit at the high excitation intensity. The NLO refractive index of NPs shows a positive linear relationship with the excitation intensity, whereas NW and NWAs exhibit a negative linear relationship. The results could provide some foundational guidance to applications of anatase TiO2 in optoelectronic devices or other aspects.

Nonlinear parametrically excited vibration and active control of gear pair system with time-varying characteristic

In the present work, we investigate the nonlinear parametrically excited vibration and active control of a gear pair system involving backlash, time-varying meshing stiffness and static transmission error. Firstly, a gear pair model is established in a strongly nonlinear form, and its nonlinear vibration characteristics are systematically investigated through different approaches. Several complicated phenomena such as period doubling bifurcation, anti period doubling bifurcation and chaos can be observed under the internal parametric excitation. Then, an active compensation controller is designed to suppress the vibration, including the chaos. Finally, the effectiveness of the proposed controller is verified numerically.

Wide-area nonlinear robust voltage control strategy for multi-machine power systems

This paper presented a novel wide-area nonlinear excitation control strategy for multi-machine power systems. A simple and effective model transformation method was proposed for the system's mathematical model in the COI (center of inertia) coordinate system. The system was transformed to an uncertain linear one where deviation of generator terminal voltage became one of the new state variables. Then a wide-area nonlinear robust voltage controller was designed utilizing a LMI (linear matrix inequality) based robust control theory. The proposed controller does not rely on any preselected system operating point, adapts to variations of network parameters and system operation conditions, and assures regulation accuracy of generator terminal voltages. Neither rotor angle nor any variable's differentiation needs to be measured for the proposed controller, and only terminal voltages, rotor speeds, active and reactive power outputs of generators are required. In addition, the proposed controller not only takes into account time delays of remote signals, but also eliminates the effect of wide-area information's incompleteness when not all generators are equipped with PMU (phase measurement unit). Detailed tests were conducted by PSCAD/EMTDC for a three-machine and four-machine power systems respectively, and simulation results illustrate high performance of the proposed controller.

Forced vibration control of an axially moving beam with an attached nonlinear energy sink

This paper investigates a highly efficient and promising control method for forced vibration control of an axially moving beam with an attached nonlinear energy sink（NES）.Because of the axial velocity,external force and external excitation frequency,the beam undergoes a high-amplitude vibration.The Galerkin method is applied to discretize the dynamic equations of the beam–NES system.The steady-state responses of the beams with an attached NES and with nothing attached are acquired by numerical simulation.Furthermore,the fast Fourier transform（FFT）is applied to get the amplitude–frequency responses.From the perspective of frequency domain analysis,it is explained that the NES has little effect on the natural frequency of the beam.Results confirm that NES has a great potential to control the excessive vibration.

Strong optical nonlinearities of self-assembled polymorphic microstructures of phenylethynyl functionalized fluorenones

Highly efficient nonlinear optical（NLO） materials with well-defined architectures in the wavelength and subwavelength length scales are of particular importance for next generation of integrated photonic circuits. Fluorenone analogues have been demonstrated to be promising candidates as building blocks for assembly of organic NLO materials thanks to their synergistic supramolecular interactions and brilliant optical properties. Here we have studied the polymorphs of a phenylethynyl functionalized fluorenone derivative, and their controlled self-assembly for microstructures with different morphologies. These polymorphic microcrystals exhibit very distinctive NLO properties, highly related to their supramolecular and electronic structures.

Observational linearization and tracking objective excitation control strategy based on phasor measurement unit

To improve the transient stability of multimachine power systems,observational linearization and tracking objective excitation control laws were derived from the phasor measurement unit(PMU),observational linearization,and tracking objective control theory based on synchronized coordinates and reference generator coordinates.The control strategies utilized real-time state variables obtained by PMU to linearize the state equations of the system,and then the linear optimal control strategy was used to design excitation controllers.The inaccuracy of the local linearization method and the complexity of the system models designed in the exact linearization method for nonlinear systems were avoided.Therefore,the control strategies were applied in real time.Simulation results show that the proposed method can improve the transient stability of power systems more efficiently than nonlinear optimal excitation control.