Internal resonance of an axially transporting beam with a two-frequency parametric excitation

This paper investigates the transverse 3:1 internal resonance of an axially transporting nonlinear viscoelastic Euler-Bernoulli beam with a two-frequency parametric excitation caused by a speed perturbation.The Kelvin-Voigt model is introduced to describe the viscoelastic characteristics of the axially transporting beam.The governing equation and the associated boundary conditions are obtained by Newton’s second law.The method of multiple scales is utilized to obtain the steady-state responses.The RouthHurwitz criterion is used to determine the stabilities and bifurcations of the steady-state responses.The effects of the material viscoelastic coefficient on the dynamics of the transporting beam are studied in detail by a series of numerical demonstrations.Interesting phenomena of the steady-state responses are revealed in the 3:1 internal resonance and two-frequency parametric excitation.The approximate analytical method is validated via a differential quadrature method.

Two-frequency amplification in a semiconductor tapered amplifier for cold atom experiments

Simultaneous two-frequency amplification is highly desirable in cold atom experiments. The nonlinear response would appear in the two-frequency amplification with a semiconductor tapered amplifier（TA） and has a direct influence on the experimental result. We investigated in detail the effects of frequency difference, total power, and power ratio of two seeding lasers on the output components based on a simplified theoretical model. The simulation results showed that the multiple sideband generation in the amplifier due to self-phase and amplitude modulation could be suppressed and the TA tended to linearly amplify the power ratio between two-frequency components, when the two seeding lasers had a large frequency difference. This was verified experimentally in the output power ratio measurement via a calibrated Fabry-Perot interferometer method with a good linearity and an uncertainty of 1%. We also discussed the consequences of power ratio responses in the amplification in light of cold atom experiments, especially in the ac Stark shift related phase error of Raman-type atom interferometers（AIs）. It was shown that the fluctuation of intensity ratio of Raman beams may induce significant systematic errors for an AI gyroscope.

New Two-Frequency Method and Devices for Electromagnetic Levitation Drip- and Leakage-Free Melting of Metals

A new method and devices for the electromagnetic levitation melting of metallic samples with greater weights and axisymmetrically stabilized positions is presented in this paper.The new method is applying two homogeneous magnetic fields of different frequencies,whose field lines are in absence of a charge horizontally and reciprocally normal in order to exert electromagnetic lift forces also on the axis of the levitated sample.Therefore the weight of the charge can be increased and the charge can be drip- and leakage-free melted.The method can be used in a melting furnace with or without a cold protective wall,as well as for the coreless induction valves applied for flow rate control,e.g.in the continuous casting of molten metals.The applicability of the method was experimentally examined and proved by tests conducted with three types of laboratory setups.

Photonic crystal fibre Brillouin laser based on Bragg grating Fabry-Perot cavity

A photonic crystal fibre Brillouin laser based on fibre Bragg grating Fabr-Perot cavity is presented. A highly nonlinear photonic crystal fibre 25 m in length is used as Brillouin gain medium and fibre Bragg grating Fabry-Perot cavity is chosen in order to enhance the laser conversion efficiency and suppress the higher-order Stokes waves. The laser reaches the threshold at input power of 35 mW, and the experimental laser conversion efficiency achieves 18% of the input power of 140 mW and does not show higher-order Stokes waves. A photonic crystal fibre Brillouin laser with shorter fibre length and lower threshold is experimentally realized.

Analysis of two-torus in a new four-dimensional autonomous system

In this paper, we report the dynamical behaviours of a four-dimenslonal autonomous continuous dissipative system analysed when the parameter is varied in the range we are interested in. The system changes its dynamical modes between periodic motion and quasiperiodic motion. Furthermore, the existence of two-torus is investigated numerically by means of Lyapunov exponents. By taking advantage of phase portraits and Poincaré sections, two types of the two-torus are observed and proved to have the structure of ring torus and horn torus, both of which are known to be the standard tori.