白车身耐疲劳结构6σ稳健优化参数的估算仿真

为提高车辆耐疲劳结构性能,降低零部件失效概率,提出白车身耐疲劳结构6σ稳健优化参数估算方法。首先分析白车身耐疲劳结构组成部分及稳健优化,利用运动微方程描述其在线性条件下的相关向量,完成耐疲劳结构平均损耗的表达方程,将6σ稳健优化参数计算分解成4个基本步骤,以降低计算过程中不确定因素的敏感性;其次,以耐疲劳可用时间安全性要求为宗旨,计算出稳健优化参数的最大波动范围,利用2阶响应面模型计算均值及方差,完成估算模型的构建,使用遗传算法寻取最优结果;最终,与传统稳健优化参数方法的仿真结果对比证明,6σ稳健优化参数估算方法稳健性更高、抗干扰能力强,能有效提高车辆耐疲劳结构性能,改善零部件失效情况。

Conserved quantities from Lie symmetries for nonholonomic systems

This paper presents a new method to seek the conserved quantity from a Lie symmetry without using either Lagrangians or Hamiltonians for nonholonomic systems. The differential equations of motion of the systems are established. The definition of the Lie symmetrical transformations of the systems is given, which only depends upon the infinitesimal transformations of groups for the generalized coordinates. The conserved quantity is directly constructed in terms of the Lie symmetry of the systems. The condition under which the Lie symmetry can lead to the conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.

Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations in Holonomic Systems with Unilateral Constraints

Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomie mechanic systems with unilateral constraints axe established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups axe also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results.

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.

Time Domain Calculation of Connector Loads of a Very Large Floating Structure

Loads generated after an air crash, ship collision, and other accidents may destroy very large floating structures （VLFSs） and create additional connector loads. In this study, the combined effects of ship collision and wave loads are considered to establish motion differential equations for a multi-body VLFS. A time domain calculation method is proposed to calculate the connector load of the VLFS in waves. The Longuet-Higgins model is employed to simulate the stochastic wave load. Fluid force and hydrodynamic coefficient are obtained with DNV Sesam software. The motion differential equation is calculated by applying the time domain method when the frequency domain hydrodynamic coefficient is converted into the memory function of the motion differential equation of the time domain. As a result of the combined action of wave and impact loads, high-frequency oscillation is observed in the time history curve of the connector load. At wave directions of 0° and 75°, the regularities of the time history curves of the connector loads in different directions are similar and the connector loads of C1 and C2 in the X direction are the largest. The oscillation load is observed in the connector in the Y direction at a wave direction of 75° and not at 0° This paper presents a time domain calculation method of connector load to provide a certain reference function for the future development of Chinese VLFS

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.

Vibration mechanism analysis and algorithm optimization of contactor contact system

In order to solve the problem of vibration bounce caused by the contact between moving and stationary contacts in the process of switching on,two-degree-of-freedom motion differential equation of the contact system is established.Genetic algorithm is used to optimize the pull in process of AC contactor.The whole process of contact bounce was observed and analyzed by high-speed photography experiment.The theory and experimental results were very similar.The iron core has collided before the contact is separated,which further aggravates the contact bounce.When the iron core bounces collided again,the bounce of the contact was not affected.During the operation of the contactor,the movement of the moving iron core will cause slight vibration of the system.The contact bounce time and the maximum amplitude are reduced.The research results provide a theoretical basis for further control and reduction of contact bounce.

Euler-Lagrangian Equations on Walker 4-Manifold with Walker Metric

The main purpose of the present paper is to study almost paracomplex structures Euler-Lagrangian Equations on Walker 4-manifold with Walker metric. In this study, routes of bodies moving in space will be modeled mathematically Euler-Lagrangian Equations on Walker 4-manifold with Walker metric that these are time-dependent partial differential equations. Here, we present paracomplex analogues of Euler-Lagrangian Equations on Walker 4-manifold with Walker metric. In addition, the geometrical-physical results related to paracomplex mechanical systems are discussed for Euler-Lagrangian Equations on Walker 4-manifold with Walker metric for dynamical systems. Finally, solution of the motion equations obtained as a result the study of using symbolic computational program is made.

Optimization of Five-Freedom Comfort Model of Vehicle

In this paper, a planar five-freedom model of whole vehicle is set up and its corresponding sport differential equation is founded. The square root of the driver＇ s acceleration is selected as the estimate index by the estimate way of vehicle＇ s comfort. The estimate index is minimized by optimization of fore-and-aft suspension＇ s stiffness and written with corresponding program. In the end, a model of comfort simulation by soitware of Simulink is found, and a temporal simulation for the upper example is applied to guessing the comfort of vehicle.

Experimental and Analytical Study of Torsional Vibration under Multiaxial Loading in Time Domain

The torsional vibration of power transmission shaft is a phenomenon whose analytical modeling can be represented by a differential equation of motion proposed by technical literature. The solutions of these equations need coefficients and parameters that, usually, must be experimentally estimated. This work uses a resistive electric SG （strain gage） to dynamically determine strains produced in the shaft due to harmonic oscillatory motion under multiaxial loading. This movement is simulated on a prototype specially developed for this purpose. It comprises a pulley attached to the end of a stepped cantilevered shaft, which is clamped at the opposite end. In this configuration, a cam generates a torque to the system, springs regulate the stiffness and the damping coefficient of the assembly, as well as they can be suitably adjusted to produce an underdamped condition. The main advantage, highlighted in this study, refers to a major simplification. Although the system under study shows multiple degrees of freedom （torsion and bending）, the shape and the positioning of linking SGs with the resistor bridge （Wheatstone Bridge）, allow ＂to evaluate the loading effects independently, as if only one degree of freedom of the system exists at a time domain. Strains graphs for two forms of cyclic torsional oscillation, analytical and experimental, were successfully generated.

Free radical reaction model for n-pentane pyrolysis

A mathematical mechanism of the n-pentane pyrolysis process based on free radical reaction model was presented.The kinetic parameters of n-pentane pyrolysis are obtained by quantum chemistry and the reaction network is established. The solution of the stiff ordinary differential equations in the n-pentane pyrolysis model is completed by semi implicit Eular algorithm. Then the pyrolysis mechanism based on free radical reaction model is built,and the computational efficiency increases 10 times by algorithm optimization. The validity of this model and its solution method is confirmed by the experimental results of n-pentane pyrolysis.

Comparative analysis of residence and diffusion times in rotating bed used for biogas upgrading

Rotating bed can be used in desorption operation of biogas upgrading as a new technology. For enough time to desorb, it is important to study the relationship between the residence time of liquid in rotating bed and the material diffusion time of liquid droplet in desorption process. By theoretical deduction, the exponential relation between residence time and liquid flow rate and rotational speed and kinematic viscosity is obtained. By analyzing the solution of nonlinear partial differential equation, the time law of material diffusion in the droplet is obtained. Moreover, by comparing the residence and diffusion times, the diffusion time can be within or out of residence time range, which has a direct relationship to rotational speed and liquid flow. By experiment, the comparison between residence and diffusion times is more realistic when the rotational speed is higher.

On General Mller Transformation

We give a study on the general Moiler transformation and emphatically introduce its differential form. In this paper, a definition of acceleration is given in spacetime language and the inertial reference frame is also settled. With a discussion of the geodesic equations of motion, the differential form of the general MФller transformation at arbitrary direction is presented.

Stability of Linear Stochastic Differential Equations with Respect to Fractional Brownian Motion

This paper is concerned with the stochastically stability for the m-dimensional linear stochastic differential equations with respect to fractional Brownian motion （FBM） with Hurst parameter H ∈ （1/2, 1）. On the basis of the pioneering work of Duncan and Hu, a Ito＇s formula is given. An improved derivative operator to Lyapunov functions is constructed, and the sufficient conditions for the stochastically stability of linear stochastic differential equations driven by FBM are established. These extend the stochastic Lyapunov stability theories.

Differentiability of stochastic differential equations driven by the G-Brownian motion

In this paper,we study the differentiability of the solutions of stochastic differential equations driven by the G-Brownian motion with respect to the initial data and the parameter.

BSDE,path-dependent PDE and nonlinear Feynman-Kac formula

We introduce a new type of path-dependent quasi-linear parabolic PDEs in which the continuous paths on an interval [0, t] become the basic variables in the place of classical variables （t, x） ∈[0, T]× R^d. This new type of PDEs are formulated through a classical BSDE in which the terminal values and the generators are allowed to be general function of Brownian motion paths. In this way, we establish the nonlinear Feynman- Kac formula for a general non-Markoviau BSDE. Some main properties of solutions of this new PDEs are also obtained.

The stability analysis of rolling motion of hypersonic vehicles and its validations

The stability of the rolling motion of near space hypersonic vehicles with rudder control is studied using method of qualitative analysis of nonlinear differential equations, and the stability criteria of the deflected rolling motions are improved. The out- comes can serve as the basis for further study regarding the influence of pitching and lateral motion on the stability of rolling motion. To validate the theoretical results, numerical simulations were do^e for the rolling motion of two hypersonic vehicles with typical configurations. Also, wind tunnel experiments for four aircraft models with typical configurations have been done. The results show that： 1） there exist two dynamic patterns of the rolling motion under statically stable condition. The first one is point attractor, for which the motion of aircraft returns to the original state. The second is periodic attractor, for which the aircraft rolls periodically. 2） Under statically unstable condition, there exist three dynamic patterns of rolling motion, namely, the point attractor, periodic attractor around deflected state of rolling motion, and double periodic attractors or chaotic attrac- tors.

Moving collocation methods for time fractional differential equations and simulation of blowup

A moving collocation method is proposed and implemented to solve time fractional differential equations. The method is derived by writing the fractional differential equation into a form of time difference equation. The method is stable and has a third-order convergence in space and first-order convergence in time for either linear or nonlinear equations. In addition, the method is used to simulate the blowup in the nonlinear equations.

Breather Dynamics of the Sine-Gordon Equation

This paper studies the adiabatic dynamics of the breather soliton of the sine-Gordon equation. The integrals of motion are found and then used in soliton perturbation theory to derive the differential equation governing the soliton velocity. Time-dependent functions arise and their properties are studied. These functions are found to be bounded and periodic and affect the soliton velocity. The soliton velocity is numerically plotted against time for different combinations of initial velocities and perturbation terms.

An effective genetic algorithm to VDA with discontinuous “on-off” switches

With more and more improvements of atmosphere or ocean models,a growing number of physical processes in the form of parameterization are incorporated into the models,which,on the one hand,makes the models capable of describing the at-mospheric or oceanic movement more precisely,and on the other hand,introduces non-smoothness in the form of "on-off" switches into the models."On-off" switches enhance the nonlinearity of the models and finally result in the loss of the effec-tiveness of variational data assimilation(VDA) based on the conventional adjoint method(ADJ).This study,in virtue of the optimization ability of a genetic algorithm(GA) for non-smooth problems,presents a new GA(referred to as GA NEW) to solve the problems of the VDA with discontinuous "on-off" processes.In the GA-NEW,adaptive selection and mutation oper-ators,blend crossover operator,and elitist strategy are combined in application.In order to verify the effectiveness and feasi-bility of the GA NEW in VDA,an idealized model of partial differential equation with discontinuous "on-off" switches in the forcing term is adopted as the governing equation.By comparison with the ADJ,it is shown that the GA NEW in VDA is more effective and can yield better assimilation retrievals.In addition,VDA experiments demonstrate that the performance of a GA is greatly related to the configuration of genetic operators(selection,crossover and mutation operators) and much better results may be attained with more proper genetic operations.Furthermore,the robustness of the GA NEW to observational noise,model errors and observation density is investigated,and the results show that the GA NEW has stronger robustness than the ADJ with respect to all the three observation noises,model errors,and sparse observation.