Working Mechanism of a Kind of Non-resonant Linear Piezoelectric Motor with Flexible Driving End

A non-resonant piezoelectric linear motor with a flexible driving end,which has an extensive working frequency range and good operation stability,is studied theoretically and experimentally.Based on the microscopic vibration characteristics of the motor stator,the longitudinal vibration model is established for the whole motor system.According to the Coulomb friction model and the motor vibration model,the friction mechanism of the nonresonant piezoelectric linear motor is investigated by dynamical analysis of the whole motor system.Furthermore,the vibration characteristics and mechanical output characteristics of the stator are simulated and experimentally studied on the basis of the friction drive mechanism model.Finally,both the simulation and experimental results show that this kind of motor remain stable in the frequency domain from 2.2 kHz to 3.5 kHz and that when the pre-stress is 4 Nand the driving voltage is 90 V,the maximum velocity of the motor is above 4 mm/s and the maximum thrust is nearly 0.5 N.

The (3+1)-dimensional generalized mKdV-ZK equation for ion-acoustic waves in quantum plasmas as well as its non-resonant multiwave solution

The quantum hydrodynamic model for ion-acoustic waves in plasmas is studied.First,we design a new disturbance expansion to describe the ion fluid velocity and electric field potential.It should be emphasized that the piecewise function perturbation form is new with great difference from the previous perturbation.Then,based on the piecewise function perturbation,a(3+1)-dimensional generalized modified Korteweg–de Vries Zakharov–Kuznetsov(mKdV-ZK)equation is derived for the first time,which is an extended form of the classical mKdV equation and the ZK equation.The(3+1)-dimensional generalized time-space fractional mKdV-ZK equation is constructed using the semi-inverse method and the fractional variational principle.Obviously,it is more accurate to depict some complex plasma processes and phenomena.Further,the conservation laws of the generalized time-space fractional mKdV-ZK equation are discussed.Finally,using the multi-exponential function method,the non-resonant multiwave solutions are constructed,and the characteristics of ion-acoustic waves are well described.

Topographicaly Forced Thre-Wave Quasi-Resonant and Non-Resonant Interactions among Barotropic Rossby Waves on an Infinite Beta-Plane

In this paper, we first apply the assumption h=εh' of topographic variation ( h is the nondimensional topographic height and is a small parameter) to obtain nonlinear equations describing three-wave quasi-resonant and non-resonant interactions among Rossby waves for zonal wavenumbers 1—3 over a wavenumber-two bottom topography (WTBT). Some numerical calculations are made with the fourth-order Rung-Kutta Scheme. It is found that for the case without topographic forcing, the period of three-wave quasi-resonance (TWQR) is found to be independent of the zonal basic westerly wind, but dependent on the meridional wavenum ber and the initial amplitudes. For the fixed initial data, when the frequency mismatch is smaller and the meridional wavelength is moderate, its period will belong to the 30-60-day period band. However, when the wavenumber-two topography is included, the periods of the forced quasi-resonant Rossby waves are also found to be strongly dependent on the setting of the zonal basic westerly wind. Under the same conditions, only when the zonal basic westerly wind reaches a moderate extent, intraseasonal oscillations in the 30-60-day period band can be found for zonal wavenumbers 1-3. On the other hand, if three Rossby waves considered have the same meridional wavenumber, three-wave non-resonant interaction over a WTBT can occur in this case.When the WTBT vanishes, the amplitudes of these Rossby waves are conserved. But in the presence of a WTBT, the three Rossby waves oscillate with the identical period.The period, over a moderate range of the zonal basic westerly wind, is in the intraseasonal, 30-60-day range.

An mmWave Dual-Band Integrated Substrate Gap Waveguide Single Cavity Filter with Frequency Selectivity

A novel dual-band ISGW cavity filter with enhanced frequency selectivity is proposed in this paper by utilizing a multi-mode coupling topology.Its cavity is designed to control the number of modes,and then the ports are determined by analyzing the coupling relationship between these selected modes.By synthesizing the coupling matrix of the filter,a nonresonating node(NRN)structure is introduced to flexibly tune the frequency of modes,which gets a dualband and quad-band filtering response from a tri-band filter no the NRN.Furthermore,a frequency selective surface(FSS)has been newly designed as the upper surface of the cavity,which significantly improves the bad out-of-band suppression and frequency selectivity that often exists in most traditional cavity filter designs and measurements.The results show that its two center frequencies are f01=27.50 GHz and f02=32.92GHz,respectively.Compared with the dual-band filter that there is no the FSS metasurface,the out-of-band suppression level is improved from measured 5 dB to18 dB,and its finite transmission zero(FTZ)numbers is increased from measured 1 to 4 between the two designed bands.Compared with the tri-band and quadband filter,its passband bandwidth is expanded from measured 1.17%,1.14%,and 1.13% or 1.31%,1.50%,0.56%,and 0.57% to 1.71% and 1.87%.In addition,the filter has compact,small,and lightweight characteristics.

On reducibility of a class of nonlinear quasi-periodic systems with small perturbational parameters near equilibrium

Consider the reducibility of a class of nonlinear quasi-periodic systems with multiple eigenvalues under perturbational hypothesis in the neighborhood of equilibrium. That is, consider the following system x = （A ＋ εQ（ t） ）x ＋ eg（t） ＋ h（x, t）, where A is a constant matrix with multiple eigenvalues; h = O（x2） （x-4）） ; and h（x, t）, Q（t）, and g（t） are analytic quasi-periodic with respect to t with the same frequencies. Under suitable hypotheses of non-resonance conditions and non-degeneracy conditions, for most sufficiently small ε, the system can be reducible to a nonlinear quasi-periodic system with an equilibrium point by means of a quasi-periodic transformation.

Resonant tunneling and quantum fluctuation in a driven triple-well system

The influence of parameters such as the strength and frequency of a periodic driving force on the tunneling dynamics is investigated in a symmetric triple-well potential. It is shown that for some special values of the parameters, tunneling could be enhanced considerably or suppressed completely. Quantum fluctuation during the tunneling is discussed as well and the numerical results are presented and analysed by virtue of Floquet formalism.

Interaction between energetic-ions and internal kink modes in a weak shear tokamak plasma

Based on the conventional tokamak HL-2 A-like parameters and profiles,the linear properties and the nonlinear dynamics of non-resonant kink mode(NRK)and non-resonant fishbone instability(NRFB)in reversed shear tokamak plasmas are investigated by using the global hybrid kinetic-magnetohydrodynamic nonlinear code M3 D-K.This work mainly focuses on the effect of passing energetic-ions on the NRK and NRFB instabilities,which is different from the previous works.It is demonstrated that the NRFB can be destabilized by the passing energeticions when the energetic-ion betaβ;exceeds a critical value.The transition from NRK to NRFB occurs when the energetic-ion betaβ;increases to above a critical value.The resonance condition responsible for the excitation of NRFB is interestingly found to be satisfied atω;+ω;≈ω,whereω;is the toroidal motion frequency,ω;is the poloidal motion frequency andωis the mode frequency.The nonlinear evolutions of NRFB’s mode structures and Poincaréplots are also analyzed in this work and it is found that the NRFB can induce evident energeticion loss/redistribution,which can degrade the performance of the plasmas.These findings are conducive to understanding the mechanisms of NRFB induced energetic-ion loss/redistribution through nonlinear wave-particle interaction.

Collective Excitations and Nonlinear Dynamics of 1D BEC with Two-and Three-body Interactions in Anharmonic Traps

The collective excitations of low-dimensional Bose-Einstein condensates with two- and three-body interactions in anharmonic potentials are investigated. Using the standard variational approach, the governing equations of motions for the low-energy excitations are obtained by solving time-dependent Gross-Pitaevskii-Ginzburg equation, and the excitation spectrums are calculated in small amplitude limit. The frequency shift and nonlinear mode coupling induced by the anharmonic distortion （adding cubic, quartic, or quintic terra to a harmonic trap） are studied.

THE INFLUENCE OF TOPOGRAPHY ON THE NONLINEAR INTERACTION OF ROSSBY WAVES iN THE BAROTROPIC ATMOSPHERE

In the frame of weak nonlinear theory,a set of equations depicting the nonlinear interactions of barotropic Rossby waves are derived,the topography and Ekman fric-tion are involved in the equations.Starting from the equations,we investigate the in -teraction of three Rossby wave packets with narrow-spread in wave vectors.When an intense primary pump Rossby wave with amplitude larger than a threshold propagates through the atmosphere ,the amplitude of one Rossby wave packet with scale greaterthan the primary one and one Rossby wave packet with scale smaller than the primaryone grow exponentially through three wave interactions,the intrinsic frequencies of the secondary waves can be varied,The threshold and the variation of the intrinsic frequ-encies of the secondary waves are related to the Ekman friction frequency dismatchtopography and spatial evolution of the secondary Rossby wave packets.

Codimension 3 Non-resonant Bifurcations of Rough Heteroclinic Loops with One Orbit Flip

Heteroclinic bifurcations in four dimensional vector fields are investigated by setting up a local coordinates near a rough heteroclinic loop. This heteroclinic loop has a principal heteroclinic orbit and a non-principal heteroclinic orbit that takes orbit flip. The existence, nonexistence, coexistence and uniqueness of the 1-heteroclinic loop, 1-homoclinic orbit and l-periodic orbit are studied. The existence of the two-fold or three-fold 1-periodic orbit is also obtained.

Reliability of quasi integrable and non-resonant Hamiltonian systems under fractional Gaussian noise excitation

The reliability of quasi integrable and non-resonant Hamiltonian system under fractional Gaussian noise(fGn)excitation is studied.Noting rather flat fGn power spectral density(PSD)in most part of frequency band,the fGn is innovatively regarded as a wide-band process.Then,the stochastic averaging method for quasi integrable Hamiltonian systems under wide-band noise excitation is applied to reduce 2n-dimensional original system into n-dimensional averaged ltd stochastic differential equations(SDEs).Reliability function and mean first passage time are obtained by solving the associated backward Kolmogorov equation and Pontryagin equation.The validity of the proposed procedure is tested by applying it to an example and comparing the numerical results with those from Monte Carlo simulation.

An experimental investigation of dual-resonant and non-resonant responses for vortex-induced vibration of a long slender cylinder

Experimental results of the dual-resonant and non-resonant responses are presented for vortex-induced vibrations(VIV)of a long slender cylinder.The cylinder has a diameter of 10mm and a length of 3.31 m,giving an aspect ratio of 331.The cylinder was towed by a carriage with the velocity up to 1.5 m/s,with the Reynolds number varying from 2500 to 38000.Three different weights were used to provide the initial tension.Dual resonance means that resonance occurs simultaneously in both the cross-flow(CF)and in-line(IL)directions.The experiments were conducted in two stages.At the first stage,dual-resonant dynamic features of the cylinder subjected to vortex-induced excitation were investigated.The features of CF and IL vibration amplitude,motion orbits,phase angle differences,dominant frequencies and mode order numbers are presented.At the second stage of the experiments,particular emphasis was placed on non-resonant dynamic features.The variation of multi-mode modal displacement amplitudes was investigated in detail.

Analytical formula of free electron laser exponential gain for a non-resonant electron beam

The free electron laser （FEL） gain formulas for a non-resonant case are studied, and some new rigorous analytical formulas are given explicitly. For the mono-energetic and non-resonant electron beam, the exact expression of the solution of the FEL characteristic cubic equation is obtained with a form much more simple than that in the literatures, and the gain length as the function of the detuning parameter is explicitly given. Then the gain for different detuning parameters and from low to high can be easily calculated. A simplified approximation formula is also given for the exponential gain calculation in the non-resonant case. For the case of the electron beam with an energy spread, the solution of the characteristic cubic equation is given explicitly for rectangular energy distribution and Lorentz distribution, respectively. Moreover the explicit expression also can be used for the solution of the characteristic cubic equation including the impact of the space charge. The transition from the low gain to the high gain is analyzed. The variations of the gain bandwidth and of the detuning parameter for the maximum gain are demonstrated. The applicable ranges of the small signal gain formula and the exponential gain formula are analyzed.

Codimension 3 nonresonant bifurcations of homoclinic orbits with two inclination flips

Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take inclination flip. The existence, nonexistence, and uniqueness of the 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold 1-periodic orbit and three-fold 1 -periodic orbit are also obtained. It is indicated that the number of periodic orbits bifurcated from this kind of homoclinic orbits depends heavily on the strength of the inclination flip.

Eigenproblem for p-Laplacian and Nonlinear Elliptic Equation with Nonlinear Boundary Conditions

In this article, we study the solvability of nonlinear problem for p-Laplacian with nonlinear boundary conditions. We give some characterization of the first eigenvalue of an intermediary eigenvalne problem as simplicity, isolation and its strict monotonicity. Afterward, we character also the second eigenvalue and its strictly partial monotony. On the other hand, in some sense, we establish the non-resonance below the first and furthermore between the first and second eigenvalues of nonlinear Steklov-Robin.

Quasi Three-Body Decay of D Meson

The aim of this work is to provide a phenomenological analysis of the contribution of D^0 meson to K*(892)~0π^+π^-(K*(892)~0-→π^+K^-), K^-π^+ω(ω-→π^+π^-π~0) and K^-π^+?(?(1020)-→ K^+K^-) quasi-three-body decays. The analysis of mentioned multi-body decays is such as to factorize into the three-body decay and several channels observed. Hadronic three-body decays receive both resonant and non-resonant contribution. Based on the factorization method, there are tree and emission annihilation diagrams for these decay modes. In the case of D^0 to vector pseudoscalar states appeared in factored terms, the matrix elements of the vector and axial vector currents between the D^0 and PV mesons can be computed by using D^(*+)pole. Considering the non-resonant and resonant amplitude in our computation,the theoretical values of the branching ratio are(9.78 ± 0.46) × 10^(-3),(2.74 ± 0.17) × 10^(-2), and(3.53 ± 0.23) × 10^(-5), while the experimental results of them are(9.9 ±2.3) × 10^(-3),(2.7 ± 0.5) × 10^(-2), and(4 ± 1.7) × 10^(-5) respectively. Comparing computational analysis values with experimental values show that our results are in approximately agreement with them.