Nonlinear Mathematical Modeling and Sensitivity Analysis of Hydraulic Drive Unit

The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.

Mathematical Constraints in Multiscale Subgrid-Scale Modeling of Nonlinear Systems

To shed light on the subgrid-seale （SGS） modeling methodology of nonlinear systems such as the Navier-Stokes turbulence, we define the concepts of assumption and restriction in the modeling procedure, which are shown by generalized derivation of three general mathematical constraints for different combinations of restrictions. These constraints are verified numerically in a one-dimensional nonlinear advection equation. This study is expected to inspire future research on the SGS modeling methodology of nonlinear systems.

Nonlinear stability of timber column strengthened with fiber reinforced polymer

By taking into account the effect of the bi-modulus for tension and compression of the fiber reinforced polymer （FRP） sheet in the reinforcement layer, a general mathematical model for the nonlinear bending of a slender timber beam strengthened with the FRP sheet is established under the hypothesis of the large deflection deformation of the beam. Nonlinear governing equations of the second order effect of the beam bending are derived. The nonlinear stability of a simply-supported slender timber column strengthened with the FRP sheet is then investigated. An expression of the critical load of the simply-supported FRP-strengthened timber beam is obtained. The existence of postbuckling solution of the timber column is proved theoretically, and an asymptotic analytical solution of the postbuckling state in the vicinity of the critical load is obtained using the perturbation method. Parameters are studied showing that the FRP reinforcement layer has great influence on the critical load of the timber column, and has little influence on the dimensionless postbuckling state.

COMPLEX NONLINEAR MATHEMATICAL MODEL FOR A KIND OF VEHICLE SHOCK ABSORBORS

A nonlinear mathematical model for the shock absorber in TJ7100 is developed. The oil compressibility and the entrapped gas in the oil are considered in the model. As a result, the hysteresis in the force velocity diagram is included. The results of computer simulation and the experiment are basically identical. The MATLAB/SIMULINK is used for the development of the simulation software. It is found that the pressure inside the cylinder is high if the inputs of velocity or displacement are big by simulation. This is certainly one of the main reasons for which the leak is appeared between the rod and the seal of the shock absorbers for a relatively short time in China.

Structure Identification of Nonlinearly Coupled Complex Networks with Non-Delayed and Delayed Coupling

Topology identification is an important problem for complex networks because much information about networks in practice such as the topological structure is uncertain. We propose an adaptive control method for identifying the topology of general nonlinearly-coupled complex network models that are either non-delayed or delayed coupled. Simulation results are also presented to illustrate the effectiveness of the method.

An Analysis of the Invariance and Conservation Laws of Some Classes of Nonlinear Ostrovsky Equations and Related Systems

A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties （through the Lie point symmetry generators） and construct classes of conservation laws for some of the models. In the latter case, the method involves finding the ＇multipliers＇ associated with the conservation laws with a stronger emphasis on the ＇higher-order＇ ones. The relationship between the symmetries and conservation laws is investigated by considering the invariance properties of the multipliers.

ANALYSIS OF THERMAL POST-BUCKLING OF HEATED ELASTIC RODS

Based on the nonlinear geometric theory of extensible rods, an exact mathematical model of thermal post_buckling behavior of uniformly heated elastic rods with axially immovable ends is developed, in which the arc length s(x) of axial line and the longitudinal displacement u(x) are taken as the basic unknown functions. This is a two point boundary value problem of first order ordinary differential equations with strong non_linearity. By using shooting method and analytical continuation, the nonlinear boundary value problems are numerically solved. The thermal post_buckled states of the rods with transversely simply supported and clamped ends are obtained respectively and the corresponding numerical data tables and characteristic curves are also given.

Transient Analysis of Steam Generator in PWR Nuclear Power Plant

The water level control system of steam generator in a pressurized water reactor of nuchear power plant plays an important role which effects the water level control of the steam generator are due the reverse dynamics behavior,so the transient analysis of the steam generator should firstly solve their mathematical models.For determination of dynamic behavior and design and testing of the control system, a nonlinear math model is developed using one dimensional conservation equations of mass,momentum and energy of primary and secondary sides of the steam generator. The nonlinear model is verified with standard power plant data available in the references, then the steady states and transient calculations are performed for full power to 5% power reactor operation of the steam generator of Chinese Qinshan Nuclear Power Plant.

Analysis of High Codimensional Bifurcation and Chaos for the Quad Bundle Conductor＇s Galloping

A two-degree-of-freedom model of iced, electrical quad bundle conductor is developed to comprehensively describe the different galloping behaviors observed. By applying centre manifold and invertible linear transformation, the co-dimension-2 bifurcation is analyzed. The relationships of parameters between this system and the original system are obtained to analyze and to control the galloping of the quad iced bundle conductor. The space trajectory, Lyapunov exponent and Lyapunov dimension are investigated via numerical simulation to present a rigorous proof of existence of chaos.

Fuzzy Modeling and Impulsive Control of a Memristor-Based Chaotic System

We mainly investigate the issues of fuzzy modeling and impulsive control of a memristor-based chaotic system and present a memristor-based chaotic system as the Takagi-Sugeno model-based fuzzy system. Then, based on the impulsive control theory of dynamical systems, a criterion ensuring impulsive stabilization of the memristorbased chaotic system is derived for the first time. An illustrative example is given to verify the effectiveness of the control scheme.

Bifurcation Control of Current-Mode Buck Converter via TDFC

Considering the TDFC controlled current-mode Buck converter featuring periodicity we propose a Fourier-decomposition based method for the bifurcation analysis of this system, hence the theoretical range of control gain of TDFC is determined. In addition, the power-stage experiment circuit is built and the control part is realized in a digital controller. The experimental results show that either bifurcation or chaos in the current-mode Buck converter can be controlled into the expectant period-1 orbit rapidly.

Exact Solutions for Two Equation Hierarchies

Bilinear forms and double-Wronskian solutions are given for two hierarchies, the （2＋1）-dimensional breaking Ablowitz-Kaup-Newell-Segur （AKNS） hierarchy and the negative order AKNS hierarchy. According to some choices of the coefficient matrix in the Wronskian condition equation set, we obtain some kinds of solutions for these two hierarchies, such as solitons, 3ordan block solutions, rational solutions, complexitons and mixed solutions.

Effects of simulated on-fire processing conditions on the microstructure and mechanical performance of Q345R steel

A series of simulated on-fire processing experiments on Q345R steel plates was conducted, and the plates＇ Brinell hardness, ten- sile strength, and impact energy were tested. Microstructure morphologies were systematically analyzed using a scanning electron micro- scope with the aim of investigating the effect of the steel＇s microstructure on its performance. All examined performance parameters exhib- ited a substantial decrease in the cases of samples heat-treated at temperatures near 700℃. However, although the banded structure decreased with increasing treatment temperature and holding time, it had little effect on the performance decline in fact. Further analysis revealed that pearlite degeneration near 700℃, which was induced by the interaction of both subcritical annealing and conventional spherical annealing, was the primary reason for the degradation behavior. Consequently, some nonlinear mathematical models of different mechanical perform- ances were established to facilitate processing adjustments.

Stochastic Investigations for the Fractional Vector-Host Diseased Based Saturated Function of Treatment Model

The goal of this research is to introduce the simulation studies of the vector-host disease nonlinear system(VHDNS)along with the numerical treatment of artificial neural networks(ANNs)techniques supported by Levenberg-Marquardt backpropagation(LMQBP),known as ANNs-LMQBP.This mechanism is physically appropriate,where the number of infected people is increasing along with the limited health services.Furthermore,the biological effects have fadingmemories and exhibit transition behavior.Initially,the model is developed by considering the two and three categories for the humans and the vector species.The VHDNS is constructed with five classes,susceptible humans Sh(t),infected humans Ih(t),recovered humans Rh(t),infected vectors Iv(t),and susceptible vector Sv(t)based system of the fractional-order nonlinear ordinary differential equations.To solve the number of variations of the VHDNS,the numerical simulations are performed using the stochastic ANNs-LMQBP.The achieved numerical solutions for solving the VHDNS using the stochastic ANNs-LMQBP have been described for training,verifying,and testing data to decrease the mean square error(MSE).An extensive analysis is provided using the correlation studies,MSE,error histograms(EHs),state transitions(STs),and regression to observe the accuracy,efficiency,expertise,and aptitude of the computing ANNs-LMQBP.

PARAMETRIC QUADRATIC PROGRAMMING METHOD FOR VISCOPLASTICITY

Perzyna model in viscoplasticity has been studied by the parametric variational principle, which could be transformed into solving the parametric quadratic programming problem. The FEM form of this problem and its implementation have also been discussed in the paper.

Ground State Energy for Fermions in a 1D Harmonic Trap with Delta Function Interaction

Conjectures are made for the ground state energy of a large spin 1/2 Fermion system trapped in a 1D harmonic trap with delta function interaction. States with different spin J are separately studied. The Thomas-Fermi method is used as an effective test for the conjecture.

Ground State Density Distribution of Bose-Fermi Mixture in a One-Dimensional Harmonic Trap

By the density-functional calculation we investigate the ground-state properties of Bose-Fermi mixture confined in one-dimensional harmonic traps. The homogeneous mixture of bosons and polarized fermions with contact interaction can be exactly solved by the Bethe-ansatz method. After giving the exact formula of ground state en- ergy density, we employ the local-density approximation to determine the density distribution of each component. It is shown that with the increase in interaction, the total density distribution evolves to Fermi-like distribution and the system exhibits phase separation between finite. While in the infinite interaction limit both distributions and phase separation disappears. two components when the interaction is strong enough but bosons and fermions display the completely same Fermi-like

A Simple Method for Generating Discrete Multi-Component Integrable Hierarchy

For M×N spectral matrix, a kind of operation ？ which satisfies combination law （a？b）？c=a？（b？c） is introduced. The discrete multi？component zero-curvature equation is deduced by using the new operation ？, and a simple method for constructing discrete multi-component integrable hierarchy is proposed. As its application, the multi-component Toda hierarchy and its two kinds of integrable couplings are worked out.

Modulational Instability and Variable Separation Solution for a Generalized （2＋1）-Dimensional Hirota Equation

It is demonstrated by the linear modulational instability analysis that a generalized （2＋1）-dimensional Hirota equation is modulationally stable. Then, a B？cklund transformation （BT） is obtained by means of the truncated Painlevé approach. Using the BT, the model is transformed to a system of equations, which finally leads to a special variable separation solution with arbitrary functions.

Generalized Lorenz Equation Derived from Thermal Convection of Viscoelastic Fluids in a Loop

A new generalized Lorenz system is presented based on the thermal convection of Oldroyd-B fluids in a circular loop. Two non-dimensional parameters De1 （a measure of the fluid relaxation） and De2 （a measure of the fluid retardation） appear in the equation. Then we study this generalized Lorenz equation numerically and find that the values of De1 and De2 can greatly influence the behavior of the solution. The fluid relaxation De1 is found to precipitate the onset of periodic solution （limit cycle） in the system and impedes the onset of chaos while the fluid retardation （De2） tends to delay the onset of the periodic solution and precipitate the onset of chaos in the system.