CALCULATING ACCURATE PERIODIC MOTIONS OF HARMONICALLY FORCED PIECEWISE LINEAR OSCILLATORS

This paper presents an efficient numerical scheme for calculating the periodic motion of a harmonically forced piecewise linear oscillator very accurately. The scheme is based on the shooting technique with the traditional numerical Poincare mapping and its Jacobian replaced by the piecewise analytic ones. Thus, the scheme gets rid of the requirement of the current schemes for an assumed order of the oscillator trajectory passing through different linear regions. The numerical examples in the paper demonstrate that the new scheme, compared with the current schemes, enables one to cope with more complicated dynamics of harmonically forced piecewise linear oscillators.

The construction of conserved quantities for linearly coupled oscillators and study of symmetries about the conserved quantities

In this paper, the conserved quantities are constructed using two methods. The first method is by making an ansatz of the conserved quantity and then using the definition of Poisson bracket to obtain the coefficients in the ansatz. The main procedure for the second method is given as follows. Firstly, the coupled terms in Lagrangian are eliminated by changing the coordinate scales and rotating the coordinate axes, secondly, the conserved quantities are obtain in new coordinate directly, and at last, the conserved quantities are expressed in the original coordinates by using the inverse transform of the coordinates. The Noether symmetry and Lie symmetry of the infinitesimal transformations about the conserved quantities are also studied in this paper.

Stochastic Multiresonance for a Fractional Linear Oscillator with Quadratic Trichotomous Noise

The stochastic multiresonance behavior for a fractional linear oscillator with random system frequency is investigated. The fluctuation of the system frequency is a quadratic trichotomous noise, the memory kernel of the fractional oscillator is modeled as a Mittag Lemer function. Based on linear system theory, applying Laplace transform and the definition of fractional derivative, the expression of the system output amplitude （SPA） is obtained. Stochastic multiresonanee phenomenon is found on the curves of SPA versus the memory time and the memory exponent of the fractional oscillator, as well as versus the trichotomous noise amplitude. The SPA depends non-monotonically on the stationary probability of the trichotomous noise, on the viscous damping coefficient and system characteristic frequency of the oscillator, as well as on the driving frequency of external force.

Coherent States and a Path Integral for the Relativistic Linear Singular Oscillator

The SU（1,1） coherent states for a relativistic model of the linear singular oscillator are considered. The corresponding partition function is evaluated. The path integral for the transition amplitude between SU（1,1） coherent states is given. Classical equations of the motion in the generalized curved phase space are obtained. It is shown that the use of quasiclassical Bohr Sommerfeld quantization rule yields the exact expression for the energy spectrum.

Nonstandard Numerical Schemes for a Linear Stochastic Oscillator with Additive Noise

In order to simulate a linear stochastic oscillator with additive noise,improved nonstandard optimal(INSOPT) schemes are derived utilizing the nonstandard finite difference(NSFD)technique and the improvement technique.These proposed schemes reproduce long time features of the oscillator solution exactly.Their abilities in preserving the symplecticity,the linear growth property of the second moment and the oscillation property of the solution of the stochastic oscillator system on long time interval are studied.It can be shown that the component { x_n}_(n≥1) of the INSOPT schemes switch signs infinitely many times as n →∞,almost surely.Further,the mean-square convergence order of 1 is obtained for these INSOPT schemes.Finally,numerical experiments illustrate intuitively the results obtained in this paper.

A Novel Resonant Frequency Tracking Control for Linear Compressor Based on MRAS Method

To optimize the efficiency of the linear compressor,its operating frequency must be controlled equal to the system resonant frequency.The traditional resonant frequency tracking control algorithm relies on the steady state characteristics of the system,which suffers from slow convergence speed,low accuracy and slow system response.In order to solve these problems,a novel resonant frequency tracking control for linear compressor based on model reference adaptive system(MRAS)is proposed in this paper,and the parameter adaptive rate is derived by the Popov's hyperstability theory,so that the system resonant frequency can be directly calculated through the parameter adaptive rate.Furthermore,the traditional algorithm needs to calculate the piston stroke signal by integrating the back-EMF,which has the problem of integral drift.The algorithm proposed in this paper only needs the velocity signal,and the accuracy of the velocity calculation can be ensured by utilizing the self-adaptive band-pass filter(SABPF),thereby greatly improving the accuracy of the resonance frequency calculation.Simulation results verify the effectiveness of the proposed algorithm.

ANALYSIS OF CRITERIA PREDICTING THE TENDENCY OF PILOT INDUCED OSCILLATION FOR LINEAR NON-LINEAR SYSTEM

Some problems encountered in applying Smith's technique to predict the PIO tendency for non-linear pilot-vehicle loop, are thoroughly analyzed. Subsequently, modified PIO predictable criteria are developed, in addition, to make also a certain improvement on Smith's PIO definition and PIO types. These modified criteria are applied to predict PIO tendency of various different configurations on the variable stability aircraft NT-33 in case of supposed non-linearity, and predicted results are compared with the flight tests and analytical results in the case of linear hypothesis given in Ref. (4)

AN ANALYSIS OF AXISYMMETRIC MAGNETIC FIELD OF LINEAR OSCILLATION MOTOR

In this paper, using axial field finite analysis method, the field of a movable core type linear oscillation motor is analyzed. The program of axial field finite analysis is worked out. Using this program, we analyze various fields, including the field excited by permanent magnet materials, the field by two coils respectively, and the fields with the core moving to various positions.

Modeling and analysis of mover gaps in tubular moving-magnet linear oscillating motors

A tubular moving-magnet linear oscillating motor（TMMLOM） has merits of high efficiency and excellent dynamic capability. To enhance the thrust performance, quasi-Halbach permanent magnet（PM） arrays are arranged on its mover in the application of a linear electro-hydrostatic actuator in more electric aircraft. The arrays are assembled by several individual segments, which lead to gaps between them inevitably. To investigate the effects of the gaps on the radial magnetic flux density and the machine thrust in this paper, an analytical model is built considering both axial and radial gaps. The model is validated by finite element simulations and experimental results.Distributions of the magnetic flux are described in condition of different sizes of radial and axial gaps. Besides, the output force is also discussed in normal and end windings. Finally, the model has demonstrated that both kinds of gaps have a negative effect on the thrust, and the linear motor is more sensitive to radial ones.

A New Prediction Model for Grain Yield in Northeast China Based on Spring North Atlantic Oscillation and Late-Winter Bering Sea Ice Cover

Accurate estimations of grain output in the agriculturally important region of Northeast China are of great strategic significance for guaranteeing food security.New prediction models for maize and rice yields are built in this paper based on the spring North Atlantic Oscillation index and the Bering Sea ice cover index.The year-to-year increment is first forecasted and then the original yield value is obtained by adding the historical yield of the previous year.The multivariate linear prediction model of maize shows good predictive ability,with a low normalized root-mean-square error（NRMSE）of 13.9%,and the simulated yield accounts for 81%of the total variance of the observation.To improve the performance of the multivariate linear model,a combined forecasting model of rice is built by considering the weight of the predictors.The NRMSE of the model is 12.9%and the predicted rice yield explains 71%of the total variance.The corresponding cross-validation test and independent samples test further demonstrate the efficiency of the models.It is inferred that the statistical models established here by applying year-to-year increment approach could make rational prediction for the maize and rice yield in Northeast China before harvest.The present study may shed new light on yield prediction in advance by use of antecedent large-scale climate signals adequately.