一种通用的复模态矩阵摄动法

对于非自伴随系统 ,提出了一种通用的复模态矩阵摄动法· 该法能同时适用于孤立特征值 ,重特征值及密集 (相近 )特征值三种复特征值情况· 由复特征子空间缩聚技术求解低阶摄动项 ,高阶摄动项则由逐次逼近过程求得· 三个计算实例表明 ,该通用方法合理可靠 。

万有D'Alembert原理的统一形式

本文给出万有D'Alembert原理的统一形式,包含了现有的各种形式.

Investigating the initiation and propagation processes of convection in heavy precipitation over the western Sichuan Basin

Heavy precipitation events occur often over the western Sichuan Basin in summer, near the transition zone between the Sichuan Basin and the steep terrain of the Tibetan Plateau. One such event -- a heavy precipitation process that occurred on 18-20 August 2010, with clear nocturnal peaks -- is chosen as a case to tentatively explore how the convection associated with convectivescale precipitation is initiated and propagated. By utilizing the vertical momentum equation from the viewpoint of separating perturbation pressure into dynamic and thermal parts, it is demonstrated that the vertical momentum is induced by the imbalance of several forces, including the dynamic/buoyant part of the perturbation pressure gradient force and the buoyancy force, with the latter dominating during the nocturnal-peak period. Although a negative value of the dynamic perturbation pressure gradient force partly offsets the positive buoyant forcing inside the strong updraft, the pattern of vertical motion tendency is largely attributable to its buoyancy because of its larger magnitude. Relative to the buoyancy component, the dynamic part of the vertical perturbation pressure gradient is also examined, revealing a smaller order of magnitude. Thus, it is the thermal effect that should be responsible for the initiation and propagation of convection. As for the convective-scale precipitation, it always presents a trailing morphology relative to the strong leading-side updraft. Furthermore, overlapping strong signals of vertical motion and its tendency point towards strong precipitation in the future.

Oscillation in a Class of Neutral Differential Equations with Positive and Negative Coefficients

The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.

Dynamic modeling and analysis of 3-■RS parallel manipulator with flexible links

The dynamic modeling and solution of the 3-RRS spatial parallel manipulators with flexible links were investigated. Firstly, a new model of spatial flexible beam element was proposed, and the dynamic equations of elements and branches of the parallel manipulator were derived. Secondly, according to the kinematic coupling relationship between the moving platform and flexible links, the kinematic constraints of the flexible parallel manipulator were proposed. Thirdly, using the kinematic constraint equations and dynamic model of the moving platform, the overall system dynamic equations of the parallel manipulator were obtained by assembling the dynamic equations of branches. FtLrthermore, a few commonly used effective solutions of second-order differential equation system with variable coefficients were discussed. Newmark numerical method was used to solve the dynamic equations of the flexible parallel manipulator. Finally, the dynamic responses of the moving platform and driving torques of the 3-RRS parallel mechanism with flexible links were analyzed through numerical simulation. The results provide important information for analysis of dynamic performance, dynamics optimization design, dynamic simulation and control of the 3-RRS flexible parallel manipulator.

Complete geometric nonlinear formulation for rigid-flexible coupling dynamics

A complete geometric nonlinear formulation for rigid-flexible coupling dynamics of a flexible beam undergoing large overall motion was proposed based on virtual work principle, in which all the high-order terms related to coupling deformation were included in dynamic equations. Simulation examples of the flexible beam with prescribed rotation and free rotation were investigated. Numerical results show that the use of the first-order approximation coupling (FOAC) model may lead to a significant error when the flexible beam experiences large deformation or large deformation velocity. However, the correct solutions can always be obtained by using the present complete model. The difference in essence between this model and the FOAC model is revealed. These coupling high-order terms, which are ignored in FOAC model, have a remarkable effect on the dynamic behavior of the flexible body. Therefore, these terms should be included for the rigid-flexible dynamic modeling and analysis of flexible body undergoing motions with high speed.

Dynamics and screening characteristics of a vibrating screen with variable elliptical trace

The ideal motion characteristics for the vibrating screen was presented according to the principle of screening process with constant bed thickness.A new vibrating screen with variable elliptical trace was proposed.An accurate mechanical model was constructed according to the required structural motion features.Applying multi-degree-of-freedom vibration theory,characteristics of the vibrating screen was analyzed.Kinematics parameters of the vibrating screen which motion traces were linear,circular or elliptical were obtained.The stable solutions of the dynamic equations gave the motions of the vibrating screen by means of computer simulations.Technological parameters,including amplitude,movement velocity and throwing index,of five specific points along the screen surface were gained by theoretical calculation.The results show that the traces of the new designed vibrating screen follow the ideal screening motion.The screening efficiency and processing capacity may thus be effectively improved.

Bifurcation and chaos study on transverse-torsional coupled 2K-H planetary gear train with multiple clearances

A new non-linear transverse-torsional coupled model was proposed for 2K-H planetary gear train, and gear's geometric eccentricity error, comprehensive transmission error, time-varying meshing stiffness, sun-planet and planet-ring gear pair's backlashes and sun gear's bearing clearance were taken into consideration. The solution of differential governing equation of motion was solved by applying variable step-size Runge-Kutta numerical integration method. The system motion state was investigated systematically and qualitatively, and exhibited diverse characteristics of bifurcation and chaos as well as non-linear behavior under different bifurcation parameters including meshing frequency, sun-planet backlash, planet-ring backlash and sun gear's bearing clearance. Analysis results show that the increasing damping could suppress the region of chaotic motion and improve the system's stability significantly. The route of crisis to chaotic motion was observed under the bifurcation parameter of meshing frequency. However, the routes of period doubling and crisis to chaos were identified under the bifurcation parameter of sun-planet backlash; besides, several different types of routes to chaos were observed and coexisted under the bifurcation parameter of planet-ring backlash including period doubling, Hopf bifurcation, 3T-periodic channel and crisis. Additionally, planet-ring backlash generated a strong coupling effect to system's non-linear behavior while the sun gear's bearing clearance produced weak coupling effect. Finally, quasi-periodic motion could be found under all above–mentioned bifurcation parameters and closely associated with the 3T-periodic motion.

3D Dynamic Response of Layered Unsaturated Soils to Harmonic Loads

Considering compression of solid grain and pore fluids,viscous-coupling interactions and inertial force of fluids,dynamic governing equations for unsaturated soils are established by adopting an exact constitutive formula of saturation.These equations are highly versatile and completely compatible with Biot's wave equations for the special case of fully saturated soils.The governing equations in Cartesian coordinates are firstly transformed into a group of state differential equations by introducing the state vector.Then the transfer matrix for layered media are derived by means of a double Fourier transform.Using the transfer matrix followed by boundary and continuity conditions between strata,solutions of steady-state dynamic response for multi-layered unsaturated soils are obtained.Numerical examples show that the echoes generated by boundary and stratum interfaces make the displacement amplitude of the ground surface fluctuate with distance;the relative position of soft and hard strata has a significant influence on displacement.

Classification and Approximate Solutions to a Class of Perturbed Nonlinear Wave Equations

A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutions of the equations based on the Lie group method are constructed.

Envelope Solitons Perturbed by Stochastic Noise

We perform langevin dynamics simulation for envelope solitons in an FPU-β lattice,with the nearestneighborinteraction and quartic anharmonicity.We get the motion equations of our discrete system by adding noiseand damping to the set of deterministic motion equations.We define'half-time'as the time when the amplitude of theenvelope soliton decreases by half due to damping.And then the mass,center and half-time of the perturbed envelopesoliton are numerically simulated,beginning with the discrete envelope soliton at rest.Results show successfully hownoise affects behavior of the envelope soliton.

Self-Trapping of Two Weakly Coupled Bose-Einstein Condensates with Oscillating Atomic Scattering Length

We investigate the self-tapping phenomena for two weakly coupled Bose-Einstein condensates with a rapid periodic modulation of the atomic scattering length. By using an averaging method, the equations of motion of the slow dynamics are derived to analyze the self-trapping behavior. It is shown numerically that under certain conditions, an alternative self-trapping in either well appears.

Dynamics of mechanical system for electromechanical integrated toroidal drive under electric disturbance

Based on electromagnetics and mechanics, electromechanical coupled dynamic equations for the drive were developed. Using method of perturbation, free vibrations of the mechanical system under electric disturbance were investigated. The forced responses of the mechanical system to mechanical excitation under electric disturbance were also presented. It is known that for the system with electric disturbance, as time grows, beat occurs. When electric disturbing frequency is near to the natural frequencies of the mechanical system or their integer multiple, resonance vibrations occur. The forced responses of the mechanical system to mechanical excitation under electric disturbance are compound vibrations decided by mechanical excitation, electric disturbance and parameters of the system. The coupled resonance vibration caused by electric disturbance and mechanical excitation was discussed as well. The conditions under which above coupled resonance occurs were presented. The results show that when the difference of the excitation frequency and the perturbation frequency is equal to some order of natural frequency, coupled resonance vibrations occur.

Design of dead reckoning system for mobile robot

A dead reckoning system for a wheeled mobile robot was designed, and the method for robot’s pose estimation in the 3D environments was presented on the basis of its rigid-body kinematic equations. After analyzing the locomotion architecture of mobile robot and the principle of proprioceptive sensors, the kinematics model of mobile robot was built to realize the relative localization. Considering that the research on dead reckoning of mobile robot was confined to the 2 dimensional planes, the locomotion of mobile robot in the 3 coordinate axis direction was thought over in order to estimate its pose on uneven terrain. Because the computing method in a plane is rather mature, the calculation in height direction is emphatically represented as a key issue. With experimental results obtained by simulation program and robot platform, the position of mobile robot can be reliably estimated and the localization precision can be effectively improved, so the effectiveness of this dead reckoning system is demonstrated.

Fractional Fourier Transformation for Quantum Mechanical Wave Functions Studied by Virtue of IWOP Technique

Starting from the optical fractional Fourier transform (FFT) and using the technique of integration withinan ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing so, theessence of FFT can be seen more clearly, and the FFT of some wave functions can be derived more directly and concisely.We also point out that different FFT integral kernels correspond to different quantum mechanical representations. Theyare generalized FFT. The relationship between the FFT and the rotated Wigner operator is studied by virtue of theWeyl ordered form of the Wigner operator.

Similarities and Differences Between Freundlich Kinetic Equation and Two-Constant Equation

A mathematical expression of Freundlich kinetic equation, 1nS=A'+B'1nt, is presented, and the physical meanings of its parameters are indicated. Although the Freundlich kinetic equation and the two-constant equation are the same in the form, the derivation of the Freundlich kinetic equation is precise, while the deriVation of the two-constant equation has some contradictions and is unreasonable. And it is suggested that the Freundlich kinetic equation should have priority over the two-constant equation to be used.

Prevention of wing rock motion for lightly damped aircraft in lateral-directional dynamics

Based on the Ricatti technique, the methodology for preventing the limit cycle accomplished by adding a control function to the original equation of wing rock motion is presented in this paper. To analyze the state variables of the system, the complete set of nonlinear equations of motion including an effective linear control function was solved for A-4D and Mig-21 Aircraft. The roll angle responding to the linear control function for both models was estimated when the systems were tested under different damping ratios. The numerical re- suits show that a linear control function including both the roll attitude and the roll rate is sufficient to suppress the wing rock motion with an acceptable error in desired time. A good agreement between the numerical results and the published work is obtained for the limit cycle oscillation existence at different damping ratios.

Analysis of Relation Between Binding and Magnetic Force in Generators in Extreme Conditions

Because of the action of strong magnetic forces, it's difficult to avoid end winding vibration in the large turbo-generator stator. Sometimes it leads to the occurrence of accidents and affects the normal operation of the generator. This paper firstly lays out the calculation method for end winding magnetic force. Second, based on the structure of large machines, the natural vibration frequency equation and forced oscillation equation is set up. Third, through the analysis of magnetic force calculation and vibration on the end winding of turbo-generator, it will be shown that the end winding vibration is related to the magnetic force and the position of winding binds as well as binding tightness. We can ease the winding vibration by distributing binding position appropriately or add more bindings, and test the concept through experimental data.

SA METHOD FOR PREDICTING THE PERFORMANCE OF DASH STOP MANEUVER OF HELICOPTER

The Dash Stop flight at the extreme condition is the primary interest of this study. This paper describes some research on the flight characteristics of helicopter in Dash Stop. A set of equations which govern the Dash Stop is developed. A method which determines the acceleration and deceleration is proposed. Formulas are then developed which relate the aircraft angular rates and attitudes to flight speed, angle of attack and acceleration or deceleration. Finally the DOLPHIN helicopter is taken as an example to calculate its acceleration/deceleration capability, pilot control and aircraft attitudes in space. It is found that the results are reasonable.

Nonlinear dynamic behaviors of ball bearing rotor system

Nonlinear forces and moments caused by ball bearing were calculated based on relationship of displacement and deflection and quasi-dynamic model of bearing.Five-DOF dynamic equations of rotor supported by ball bearings were estimated.The Newmark-β method and Newton-Laphson method were used to solve the equations.The dynamic characteristics of rotor system were studied through the time response,the phase portrait,the Poincar?maps and the bifurcation diagrams.The results show that the system goes through the quasi-periodic bifurcation route to chaos as rotate speed increases and there are several quasi-periodic regions and chaos regions.The amplitude decreases and the dynamic behaviors change as the axial load of ball bearing increases;the initial contact angle of ball bearing affects dynamic behaviors of the system obviously.The system can avoid non-periodic vibration by choosing structural parameters and operating parameters reasonably.