Magneto-elastic combination resonances analysis of current-conducting thin plate

Based on the Maxwell equations, the nonlinear magneto-elastic vibration equations of a thin plate and the electrodynamic equations and expressions of electromagnetic forces are derived. In addition, the magneto-elastic combination resonances and stabilities of the thin beam-plate subjected to mechanical loadings in a constant transverse magnetic filed are studied. Using the Galerkin method, the corresponding nonlinear vibration differential equations are derived. The amplitude frequency response equation of the system in steady motion is obtained with the multiple scales method. The excitation condition of combination resonances is analyzed. Based on the Lyapunov stability theory, stabilities of steady solutions are analyzed, and critical conditions of stability are also obtained. By numerical calculation, curves of resonance-amplitudes changes with detuning parameters, excitation amplitudes and magnetic intensity in the first and the second order modality are obtained. Time history response plots, phase charts, the Poincare mapping charts and spectrum plots of vibrations are obtained. The effect of electro-magnetic and mechanical parameters for the stabilities of solutions and the bifurcation are further analyzed, Some complex dynamic performances such as perioddoubling motion and quasi-period motion are discussed.

Subharmonic and Combination Resonance of Rotating Pre-deformed Blades Subjected to High Gas Pressure

The present paper deals with the investigation of dynamic responses of a rotating pre-deformed blade in four cases of resonance,including two subharmonic resonances and two combination resonances.The dimensionless gas excitation amplitude is assumed to share the same order with the dimensionless vibration displacement.Four cases of resonance are confirmed by examining the secular terms.The theoretical analysis framework is established for each resonance case based on the method of multiple scales.The original dynamic system is integrated numerically by the Runge–Kutta method.The frequency components and phases obtained from fast Fourier transform of the numerical response are used to verify the theoretical results.For the purpose of contrast,modulation equations are also integrated numerically.In all four resonance cases,the theoretical results agree well with the numerical simulation.Parameter studies are conducted to clarify the effects of system parameters on the perturbation curves.Various results are obtained for the rotating blade.A quasi-saturation phenomenon occurs in both combination resonances of summed type and difference type,and the corresponding limit value of the second-mode response can be reduced by decreasing the external detuning parameter.The quasi-saturation phenomenon of rotating blade only appears with high gas pressure.The subharmonic resonance of second mode and the combination resonance of summed type are hard to excite in practice compared with the other two cases.

Combined resonance of low pressure cylinder-generator rotor system with bending-torsion coupling

A nonlinear model of a low pressure cylinder-generator rotor system is presented to study sub-synchronous resonance and combined resonance. Analytical results are obtained by an averaging method. Transition sets and bifurcation diagrams are obtained based on the singularity theory for the two-state variable system. The bifurcation characteristics are analyzed to provide a basis for the optimal design and fault diagnosis of the rotor system. Finally, the theoretical results are verified with the numerical results.

Combined Effect of Classical Chaos and Quantum Resonance on Entanglement Dynamics

We use linear entropy of an exact quantum state to study the entanglement between internal electronic states and external motional states for a two-level atom held in an amplitude-modulated and tilted optical lattice. Starting from an unentangled initial state associated with the regular ＇island＇ of classical phase space, it is demonstrated that the quantum resonance leads to entanglement generation, the chaotic parameter region results in the increase of the generation speed, and the symmetries of the initial probability distribution determine the final degree of entanglement. The entangled initial states are associated with the classical ＇chaotic sea＇, which do not affect the final entanglement degree for the same initial symmetry. The results may be useful in engineering quantum dynamics for quantum information processing.

ANALYSIS OF HUMAN PLACENTA BY ^(31)P NUCLEAR MAGNETIC RESONANCE AND THIN-LAYER CHROMATOGRAPHY SCANNING COMBINED WITH THE CORRECTIVE METHOD OF ABSORBANCE PROPORTIONAL COEFFICIENT

Five phospholipids in human placenta were determined by phosphorus 31 nuclear magnetic resonance(^(31)P NMR)spectroscopy and thin-layer chromatography(TLC) scanning combined with the corrective method of absorbance proportional coefficient. The NMR spectrometer used this investigation was a Bruker AM-500 spectrometer operating at 202.4 MHz for ^(31)P chemical shifts are relative to 85% phosphoric acid. TIC was carried out by silica gel H plate developed in chloroform-methanol-glacial acetic acid-ethanol-water(25:4:6:2:0.5),with Vaskovsky reagent as colour -developing agent of phospholipids.

PARAMETRIC SHIMMY ANALYSIS

A more reliable parametric shimmy analysis model taking the elasticity of strut, the elasticity of damper linkage system and the influence of shimmy damping into consideration is set up in this paper. The Multiple Scales Method is utilized to obtain the expressions of stability condition and transition curve under the conditions of non resonant case, principal parametric resonance and combination resonance respectively. The parametric shimmy analysis for a real type of aircraft is carried out based on the perturbation analysis results, and the stability chart and critical taxiing velocities of two types of aircraft in the case of principal parametric resonance are given. It is indicated that there exist two critical taxiing velocities near which parametric shimmy is susceptible to occur, while the landing gear system is stable when taxiing velocity is far from them. This characteristic makes the parametric shimmy distinct from the shimmy in general case. Because few previous studies of nose gear shimmy have dealt with parametric shimmy problem, the results given in this paper provide useful reference for aircraft design and maintenance.

Nonlinear resonance characteristics of a dual-rotor system with a local defect on the inner ring of the inter-shaft bearing

In this paper,the nonlinear resonance characteristics of a dual-rotor system are investigated with the consideration of a local defect on the inter-shaft bearing of the system.A simplified model of the dual-rotor system is proposed by considering that there is a local defect on the inner ring of inter-shaft bearing.The local defect is modelled as an inverted isosceles trapezoidal groove,which can make great influence on the inter-shaft bearing force due to the change of radial clearance of the inter-shaft bearing.The motion equations of the dual-rotor system are formulated by using the Lagrange equation.The Runge-Kutta method is employed to solve the motion equation.The amplitude-frequency response curve of the dual-rotor system is obtained,the abnormal resonance characteristics are analyzed.In addition,the influence of defect parameters,rotors and support parameters and inter-shaft bearing parameters on the amplitude-frequency characteristics of the system are discussed.The results show that there are two main resonance peaks and four abnormal resonance peaks on the amplitude-frequency response curve of the dual-rotor with a local defect on the inner ring of the inter-shaft bearing.Through analyzing the vibration response of the abnormal resonance peaks,it is found that the first two abnormal resonances are caused by the combined resonance,which are related to the inner ring fault and the rotational speed of high or low pressure rotors,and the last two resonances are caused by the induced resonance of the inner ring fault.At the same time,when the parameters of defect,rotors and support and inter-shaft bearing change,the resonance of the system also shows the corresponding change law.

Energy dependence of resonance production in relativistic heavy ion collisions

The production of the hadronic resonances K^＊0（892）,φ（1020）,∑^＊（1385）,and Ξ^＊（1530） in central AA collisions at √SNN=17.3,200,and 2760 GeV is systematically studied.The direct production of these resonances at system hadronization is described by the quark combination model and the effects of hadron multiple-scattering stage are dealt with by a ultra-relativistic quantum molecular dynamics model（UrQMD）.We study the contribution of these two production sources to final observation and compare the final spectra with the available experimental data.The pT spectra of K^＊0（892） calculated directly by quark combination model are explicitly higher than the data at low pT≤1.5 GeV,and taking into account the modification of rescattering effects,the resulting final spectra well agree with the data at all three collision energies.The rescattering effect on φ（1020） production is weak and including it can slightly improve our description at low p_T on the basis of overall agreement with the data.We also predict the pT spectra of ∑^＊（1385） and Ξ^＊（1530）,to be tested by the future experimental data.

Multifrequency excitation of a clamped–clamped microbeam:Analytical and experimental investigation

Using partial electrodes and a multifrequency electrical source,we present a large-bandwidth,large-amplitude clamped–clamped microbeam resonator excited near the higher order modes of vibration.We analytically and experimentally investigate the nonlinear dynamics of the microbeam under a two-source harmonic excitation.The first-frequency source is swept around the first three modes of vibration,whereas the second source frequency remains fixed.New additive and subtractive resonances are demonstrated.We illustrated that by properly tuning the frequency and amplitude of the excitation force,the frequency bandwidth of the resonator is controlled.The microbeam is fabricated using polyimide as a structural layer coated with nickel from the top and chromium and gold layers from the bottom.Using the Galerkin method,a reduced order model is derived to simulate the static and dynamic response of the device.A good agreement between the theoretical and experimental data are reported.