Soliton Solutions to the Coupled Gerdjikov-Ivanov Equation with Rogue-Wave-Like Phenomena

Bilinear forms of the coupled Gerdjikov–Ivanov equation are derived. The $N$-soliton solutions to the equation are obtained by Hirota＇s method. It is interesting that the two-soliton solutions can generate the rogue-wave-like phenomena by selecting special parameters. The equation can be reduced to the Gerdjikov–Ivanov equation as well as its bilinear forms and its solutions.

The Existence of Coupled Solutions for a Kind of Nonlinear Operator Equations in Partial Ordered Linear Topology Space

The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing the semi-order method. Some new existence results are obtained.

Painleve Integrability, Consistent Riccati Expansion Solvability and Interaction Solution for the Coupled mKdV-BLMP System

The integrability of the coupled, modified KdV equation and the potential Boiti-Leon-Manna-Pempinelli (mKdV-BLMP) system is investigated using the Painlevé analysis approach. It is shown that this coupled system possesses the Painlevé property in both the principal and secondary branches. Then, the consistent Riccati expansion (CRE) method is applied to the coupled mKdV-BLMP system. As a result, it is CRE solvable for the principal branch while non-CRE solvable for the secondary branch. Finally, starting from the last consistent differential equation in the CRE solvable case, soliton, multiple resonant soliton solutions and soliton-cnoidal wave interaction solutions are constructed explicitly.

Finite Element Harmonic Solution of the Coupled Rotor-bearing System

Fluid-solid interaction problems have been studied q uite extensively in the past years. Rotor-bearing system is a typical example. Fluid field is changed under the exciting of rotor vibration. On the same ti me, a net force caused by fluid pressure exerts on rotor, which will change roto r vibration. So, the fluid-solid coupled analysis method must be used. Traditionally, numerical difference method was used to solve fluid problems. The coupled fluid-solid equation could not be set up based on the method. It is no t until finite element method was used in fluid dynamics area then can the coupl ed dynamics be researched. Recently many experimental, analytical and numerical studies have been used in the area . But in these investigations, it is a ssumed that the solid vibration could not be influenced by fluid. In the other w ords, the force exerted on solid from fluid was neglected in the papers. So, the models built were some kinds of semi-coupled model only. In this paper, the Galerkin finite-element method, two-dimension vibration equ ation of rigid body and Navier-Stokes equations are used to build a full-coupl ed fluid-solid model in rotor-bearing system. Some assumptions are taken: 1) In fluid equation, the nonlinear terms are relatively small and neglected. 2) The gravity takes no effect on this system. 3) The bearing and the rotor are long. Flow and leakage along the axis is neglec ted. 4) The fluid is a kind of Newtonian incondensable viscous fluid. 5) The rotor is considered to be a rigid body. Using the model established, we calculated all the examples given by paper , results show the error are less than 7%. So the full-coupled model is built c orrectly. Examples are given in the end of the paper. After analyzing the examples, we get some conclusions: 1) In rotor-bearing system, while being taken under two conditions that whether coupled method is taken or not, difference of pressure and vibration amplitude could reach 76% and 120%. Therefore coupled method must be taken to investigate fluid-solid system. 1) Amplitude of fluid pressure can be more or less influenced by rotor unbalance , gap, eccentricity and other factors. 2) By using coupling method, results show that the amplitudes of vibration and p ressure are greater than ignoring the method. It should be paid more attention t o.

SOLUTION TO THE STRESS DISTRIBUTION ON THE SURFACE LAYER OF BUSHING ALLOY BY COUPLING BEM WITH ELASTICITY METHOD

In the design of the fatigue strength of dynamically loaded bearing in the equipmentssuch as internal combustion engines and roimg mun, the solution to the stress distribution on thebushing alloy layer is an important and difficult problem. In this paper, a new method has beenproposed by coupling BEM with etheticity method, The algorithm and its implementation were deseribed in details The calculation results verify that this up-dated method can provide us a moresimple and effective tool for solvingthe fatigue stress of the bushing alloy with tangible benefit oftime-saving and high computation accuraey. It may open a new vista in bearing fatigue strength design.

Analysis of telescopic beam structure using couple of DOF technique and its application

Couple of DOF technique in FEM and the algorithm for equation group solution in the whole stiffness matrix is studied in this paper. A new procedure is developed for the analysis of telescope beam structure. This method can solve most of the complex structural problems in engineering practice. This method has been used in the FEM analysis of pile frame of muhifunetion drilling machine, which is designed and manufactured by our research group. The right analysis result can improves the design efficiency and the reliability of the structure and reduce the design cost.

A GENERAL SOLUTION AND THE APPLICATION OF SPACE AXISYMMETRIC PROBLEM IN PIEZOELECTRIC MATERIAL

According to the structure feature of the governing equations of spaceaxisymmetric problem in transversely, isotropic piezoelectric material. using the methodof introducing potential .function one by. one, in this paper we obtain the so-calledgeneral solution of displacement and eleclric potential function denoied by uniquepoiential.function which satisfies specific partiality equations. As an applying exampleof the general solution, we solve problem of semi-infinile boodt. made of piezoelectricmaterial, on the surface of the semi-infinite body a concentrative .force is applied, andget the analytic .formulations of stress and electric displacement comiponenis. Thegeneral solution provided by this paper can be used as a tool to analyse the mechanical-electrical coupling behavior of piezoelecrtic material which conlains defects such ascavity inclusion. penny-shape crack. and so on. The result of the solved problem canbe used directly to analyse contact problems which take place between twopiezoelectric bodies or piezoelectric body. and elastic body .

Existence Results for Systems of Nonlinear Caputo Fractional Differential Equations

We aim, in this work, to demonstrate the existence of minimal and maximal coupled quasi-solutions for nonlinear Caputo fractional differential systems with order q ∈ (1,2). Our approach is based on mixed monotone iterative techniques developed under the concept of lower and upper quasi-solutions. Our results extend those obtained for ordinary differential equations and fractional ones.

Numerical Investigation on Fluid Structure Interaction Considering Rotor Deformation for a Centrifugal Pump

The existing research for unsteady flow field and the corresponding flow induced vibration analysis of centrifugal pump are mainly carried out respectively without considering the interaction between fluid and structure. The ignorance of fluid structure interaction （FSI） means that the energy transfer between fluid and structure is neglected. To some extent, the accuracy and reliability of unsteady flow and rotor deflection analysis should be affected by this interaction mechanism. In this paper, a combined calculation between two executables for turbulent flow and vibrating structure was established using two-way coupling method to study the effect of FSI. Pressure distributions, radial forces, rotor deflection and equivalent stress are analyzed. The results show that the FSI effect to pressure distribution in flow field is complex. The pressure distribution is affected not only around impeller outlet where different variation trends of pressure values with and without FSI appear according to different relative positions between blade and cutwater, but also in the diffusion section of volute. Variation trends of peak values of radial force amplitude calculated with and without FSI are nearly same under high flow rate and designed conditions while the peak value with FSI is slightly smaller, and differently, the peak value with FSI is larger with low flow rate. In addition, the effect of FSI on the angle of radial force is quite complex, especially under 0.5Q condition. Fluctuation of radial deflection of the rotor has obvious four periods, of which the extent is relatively small under design condition and is relatively large under off-design condition. Finally, fluctuations of equivalent stress with time are obvious under different conditions, and stress value is small. The proposed research establishes the FSI calculation method for centrifugal pump analysis, and ensures the existing affect by fluid structure interaction.

BIFURCATIONS AND NEW EXACT TRAVELLING WAVE SOLUTIONS OF THE COUPLED NONLINEAR SCHRDINGER-KdV EQUATIONS

By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrdinger-KdV equations are studied. Based on this method, all phase portraits of the system in the parametric space are given. All possible bounded travelling wave solutions such as solitary wave solutions and periodic travelling wave solutions are obtained. With the aid of Maple software, the numerical simulations are conducted for solitary wave solutions and periodic travelling wave solutions to the coupled nonlinear Schrdinger-KdV equations. The results show that the presented findings improve the related previous conclusions.

Multiply Kink and Anti-Kink Solutions for a Coupled Camassa–Holm Type Equation

This article amis at revealing dynamical behavior of a coupled Camassa–Holm type equation, which was proposed by Geng and Wang based on a 4×4 matrix spectral problem with two potentials. Its kink and anti-kink solutions are presented explicitly. In particular, some exact multi-kink and anti-kink wave solutions are discussed and under some conditions, the kink and anti-kinks look like hat-shape solitons. The dynamic characters of the obtained solutions are investigated by figures. The method used in this paper can be widely applied to looking for the multi-kinks for Camassa–Holm type equations possessing cubic nonlinearity.

Viscosity Solutions of Monotonic Functional Parabolic PDE

In this paper,by the technique of coupled solutions,the notion of viscosity solution is ex- tended to quasi-monotonic fully nonlinear parabolic equations with delay,which involves many models arising from optimal control theory,economy and finance,biology etc.The comparison,existence and uniqueness are proved.And the results are applied to the retarded Bellman equations.

Assumed stress quasi-conforming triangular element for couple stress theory

In this paper, a 3-node triangular element for couple stress theory is proposed based on the assumed stress quasi-conforming method. The formulation starts from polynomial approx- imation of stresses. Then the stress-function matrix is treated as the weighted function to weaken the strain-displacement equations. Finally, the string-net functions are introduced to calculate strain integration and the stress smooth technique is adopted to improve the stress accuracy. Numerical results show that the proposed new model can pass the Co- 1 patch test with excellent precision, does not exhibit extra zero energy modes and can cap- ture the scale effects of microstructure.

Infrared radiation signature of exhaust plume from solid propellants with different energy characteristics

The infrared radiation signature of the plume from solid propellants with different energy characteristics is not the same. Three kinds of double-base propellants of different energy characteristics are chosen to measure the infrared spectral radiance from 1000 cm 1 to 4500 cm 1 of their plumes. The radiative spectrum is obtained in the tests. The experimental results indicate that the infrared radiation of the plume is determined by the energy characteristics of the propellant. The radiative transfer calculation models of the exhaust plume for the solid propellants are established. By including the chemical reaction source term and the radiation source term into the energy equation, the plume field and the radiative transfer are solved in a coupled way. The calculated results are consistent with the experimental data, so the reliability of the models is confirmed. The temperature distribution and the extent of the afterburning of the plume are distinct for the propellants of different energy characteristics, therefore the plume radiation varies for different propellants. The temperature of the fluid cell in the plume will increase or decrease to some extent by the influence of the radiation term.

Inhibition Effect of Water Injection on Afterburning of Rocket Motor Exhaust Plume

One of the most important characteristic signatures of the exhaust plume from rocket motor is the aflerbuming phenomenon, and the injected water into the plume could inhibit the afterburning. The calculation model for the gas-liquid multiphase flow field with chemical reaction in the plume is built. By inducing the energy source terms caused by the vaporization of liquid water, condensation of the vapor and chemical reaction in the energy equation, the gas-liquid multiphase flow field and the afterburning phenomenon are calculated in a coupling way. Mixture multiphase flow model is used to calculate the gas-liquid flow field, and the vaporization mechanism is used to investigate the water vaporization process. The temperature contours are obtained and accord well with the experimental photos. The mass fraction contours of primary species are obtained, which can indicate the extent of inhibition effect of water injection on the afterburning phenomenon in the plume. When water is injected into the plume, the region of aflerburning reduces a lot, and temperature on the ground wall declines rapidly, which can decrease the ablation of the combustion gas to the launch ground.

Steady thermal-solutal capillary convection in a shallow annular pool with the radial temperature and concentration gradients

Using asymptotical analysis,we investigate the characteristics of the coupled thermal and solutal capillary convection with the radial temperature and solute concentration gradients in a shallow annular pool with the free surface.The pool is heated from the outer cylinder with high solutal concentration and cooled at the inner cylinder with low solutal concentration.The asymptotic solution is obtained in the core region in the limit as the aspect ratio,which is defined as the ratio of the depth to the width of the pool,goes to zero.The comparison with the previous work certifies that the asymptotic solution is right and believable.The influences of the solutal capillary force,the buoyant force,the Soret effect and the geometric parameters on the fluid flow are analyzed.

A Fast Stable Marching Scheme for Calculating Mixed Convection in a Vertical Rotating Annulus

An iterative simultanous solution method is developed to efficiently solve the Newton-Raphson linear equation set for velocity in three dimensions, pressure amd temperature. The proposed method is demonstrated for several cases of the thermal drive in a vertical rotating annulus, and is shown to be insensitive to dimensionless time step, requiring significantly less computational effort to converge to the desired accuracy than SIMPLEC, even for low Prandtl number fluid flows.