Effect of Shot Peening on Surface Damage Evolution Behavior of Cu-19Ni Alloy

Shot peening is a surface modification technology with the metal surface nano machine(SNC),which can modify the surface microstructure and extend the fatigue life of Cu-19Ni alloy.The hardness,damage evolution and mechanical properties were investigated and characterized by scanning electron microscope(SEM),laser confocal microscope(LSM)and material surface performance tester(CFT).The results showed that the surface roughness and friction coefficient of Cu-19Ni alloy decreased with the increase of shot peening duration and diameter,while the microhardness and strength increased.Moreover,with the increase in shot peening duration and diameter,SEM observation showed that the fracture dimples became smaller,meanwhile,with the increase of small cleavage planes,shear tearing ridges and the thickness of the surface nano layer,the fracture mode gradually evolved from plastic to brittle fracture.The uniaxial tensile test of shot peened Cu-19Ni alloy was carried out by MTS testing machine combined with digital image correlation technology(DIC).The evolution of Cu-19Ni surface damage was analyzed,and the evolution equations describing the damage of large deformation zone and small deformation zone were established.The effect of shot peening on the damage evolution behavior of Cu-19Ni alloy was revealed.

Classical and nonclassical symmetry classifications of nonlinear wave equation with dissipation

A complete classical symmetry classification and a nonclassical symmetry classification of a class of nonlinear wave equations are given with three arbitrary parameter functions. The obtained results show that such nonlinear wave equations admit richer classical and nonclassical symmetries, leading to the conservation laws and the reduction of the wave equations. Some exact solutions of the considered wave equations for particular cases are derived.

Symmetry analysis of modified 2D Burgers vortex equation for unsteady case

In this paper, a symmetry analysis of the modified 2D Burgers vortex equation with a flow parameter is presented. A general form of classical and non-classical symmetries of the equation is derived. These are fundamental tools for obtaining exact solutions to the equation. In several physical cases of the parameter, the specific classical and non-classical symmetries of the equation are then obtained. In addition to rediscovering the existing solutions given by different methods, some new exact solutions are obtained with the symmetry method, showing that the symmetry method is powerful and more general for solving partial differential equations(PDEs).

The development of real time data driving multi-axis linkage and synergic movement control system of 3D variable cross-section roll forming machine

The three dimensional variable cross-section roll forming is a kind of new metal forming technology which combines large forming force,multi-axis linkage movement and space synergic movement,and the sequential synergic movement of the ganged roller group is used to complete the metal sheet forming according to the shape of the complicated and variable forming part data.The control system should meet the demands of quick response to the test requirements of the product part.A new kind of real time data driving multi-axis linkage and synergic movement control strategy of 3D roll forming is put forward in the paper.In the new control strategy,the forming data are automatically generated according to the shape of the parts,and the multi-axis linkage movement together with cooperative motion among the six stands of the 3D roll forming machine is driven by the real-time information,and the control nodes are also driven by the forming data.The new control strategy is applied to a 48axis 3D roll forming machine developed by our research center,and the control servo period is less than 10ms.A forming experiment of variable cross section part is carried out,and the forming precision is better than±0.5mm by the control strategy.The result of the experiment proves that the control strategy has significant potentiality for the development of 3D roll forming production line with large scale,multi-axis ganged and synergic movement.

On the completeness of eigen and root vector systems for fourth-order operator matrices and their applications

In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechan- ics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenvalue, the symplectic orthogonality, and completeness of eigen and root vector systems. The obtained results are applied to the plate bending problem.

Completeness of system of root vectors of upper triangular infinitedimensional Hamiltonian operators appearing in elasticity theory

This paper deals with a class of upper triangular infinite-dimensional Hamilto- nian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Furthermore, the algebraic multiplicity of the eigenvalue is obtained. Based on these properties, the concrete completeness formulation of the system of eigenvectors or root vectors of the Hamiltonian operator is proposed. It is shown that the completeness is determined by the system of eigenvectors of the operator entries. Finally, the applications of the results to some problems in the elasticity theory are presented.

Eigenvalue problem of a class of fourth-order Hamiltonian operators

The eigenvalue problem of a class of fourth-order Hamiltonian operators is studied. We first obtain the geometric multiplicity, the algebraic index and the algebraic multiplicity of each eigenvalue of the Hamiltonian operators. Then, some necessary and sufficient conditions for the completeness of the eigen or root vector system of the Hamiltonian operators are given, which is characterized by that of the vector system consisting of the first components of all eigenvectors. Moreover, the results are applied to the plate bending problem.

mKdV Equation for the Amplitude of Solitary Rossby Waves in Stratified Shear Flows with a Zonal Shear Flow

In this paper,modified Korteweg-de Vries (mKdV) equations for the amplitude of solitary Rossby waves in stratified fluids with a zonal shear flow are derived by using a weakly nonlinear method.It is found that the coefficients of mKdV equations depend not only on the β effect and the Visl-Brunt frequency,but also on the basic shear flow.

Symplectic eigenvector expansion theorem of a class of operator matrices arising from elasticity theory

This paper deals with the completeness of the eigenvector system of a class of operator matrices arising from elasticity theory, i.e., symplectic eigenvector expansion theorem. Under certain conditions, the symplectic orthogonality of eigenvectors of the operator matrix is demonstrated. Based on this, a necessary and sufficient condition for the completeness of the eigenvector system of the operator matrix is given. Furthermore, the obtained results are tested for the free vibration of rectangular thin plates.

Electrokinetic energy conversion of electro-magneto-hydro-dynamic nanofluids through a microannulus under the time-periodic excitation

In this work,the effects of externally applied axial pressure gradients and transverse magnetic fields on the electrokinetic energy conversion(EKEC)efficiency and the streaming potential of nanofluids through a microannulus are studied.The analytical solution for electro-magneto-hydro-dynamic(EMHD)flow is obtained under the condition of the Debye-Huuckel linearization.Especially,Green’s function method is used to obtain the analytical solutions of the velocity field.The result shows that the velocity distribution is characterized by the dimensionless frequency?,the Hartmann number Ha,the volume fraction of the nanoparticlesφ,the geometric radius ratio a,and the wallζpotential ratio b.Moreover,the effects of three kinds of periodic excitations are compared and discussed.The results also show that the periodic excitation of the square waveform is more effective in increasing the streaming potential and the EKEC efficiency.It is worth noting that adjusting the wallζpotential ratio and the geometric radius ratio can affect the streaming potential and the EKEC efficiency.

Trajectory analysis of the propagation of Rossby waves on the Earth's δ-surface

本文通过迹线分析δ-平面近似下Rossby波传播的物理机制,结果表明:一方面,在正压大气和斜压大气模式下,通过位涡方程研究发现δ效应对Rossby波传播起到稳定的作用,特别在中高纬度其作用尤为明显;另外,利用WKB方法得到δ-平面近似下正压和斜压Rossby波色散关系说明了δ效应使Rossby波的移动速度增加。另一方面,在行波变换下通过迹线分析发现δ效应对正压和斜压Rossby波传播有着重要的影响。这些结果从理论上揭示了δ-平面近似下不论正压大气模式还是斜压大气模式δ效应对Rossby波作用的重要性不能忽视,为有助于进一步认识和探究Rossby波的演变提供详实的理论依据。

Application of the Generalized Simplest Equation Method to the Burgers Equation

We successfully constructed wide classes of exact solutions for the Burgers equation by using the generalized simplest equation method. This method yielded a B&aumlcklund transformation between the Burgers equation and a related constraint equation. By dealing with the constraint equation, we obtained the traveling wave solutions and non-traveling wave solutions of the Burgers equation.

Spectrum of a Class of Difference Operators with Indefinite Weights

In this study, we use analytical methods and Sylvester inertia theorem to research a class of second order difference operators with indefinite weights and coupled boundary conditions. The eigenvalue problem with sign-changing weight has lasted a long time. The number of eigenvalues and the number of sign changes of the corresponding eigenfunctions of discrete equations under different boundary conditions are mainly studied. For the discrete Sturm-Liouville problems, similar conclusions about the properties of eigenvalues and the number of sign changes of the corresponding eigenfunctions are obtained under different boundary conditions, such as periodic boundary conditions, antiperiodic boundary conditions and separated boundary conditions etc. The purpose of this paper is to extend the similar conclusion to the coupled boundary conditions, which is of great significance to the perfection of the theory of the discrete Sturm-Liouville problems. We came to the following conclusions: first, the eigenvalues of the problem are real and single, the number of the positive eigenvalues is equal to the number of positive elements in the weight function, and the number of negative eigenvalues is equal to the number of negative elements in the weight function. Second, under some conditions, we obtain the sign change of the eigenfunction corresponding to the j-th positive/negative eigenvalue.

Potential Symmetries, One-Dimensional Optimal System and Invariant Solutions of the Coupled Burgers’ Equations

In this paper, we discuss one-dimensional optimal system and the invariant solutions of Coupled Burgers’ equations. By using Wu-differential characteristic set algorithm with the aid of Mathematica software, the classical symmetries of the Coupled Burgers’ equations are calculated, and the one-dimensional optimal system of Lie algebra is constructed. And we obtain the invariant solution of the Coupled Burgers’ equations corresponding to one element in one dimensional optimal system by using the invariant method. The results generalize the exact solutions of the Coupled Burgers’ equations.

Triple reverse order law for the Drazin inverse

In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.

Inverse Spectral Problem for Sturm-Liouville Operator with Boundary and Jump Conditions Dependent on the Spectral Parameter

In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem and the eigenvalue properties are given, then the asymptotic formulas of eigenvalues and eigenfunctions are presented. Finally, the uniqueness theorems of the corresponding inverse problems are given by Weyl function theory and inverse spectral data approach.

Approximate solutions to fractional differential equations

In this paper, the time-fractional coupled viscous Burgers' equation(CVBE)and Drinfeld-Sokolov-Wilson equation(DSWE) are solved by the Sawi transform coupled homotopy perturbation method(HPM). The approximate series solutions to these two equations are obtained. Meanwhile, the absolute error between the approximate solution given in this paper and the exact solution given in the literature is analyzed. By comparison of the graphs of the function when the fractional order α takes different values, the properties of the equations are given as a conclusion.

Modified KdV equation for solitary Rossby waves with β effect in barotropic fluids

This paper uses the weakly nonlinear method and perturbation method to deal with the quasi-geostrophic vorticity equation,and the modified Korteweg-de Vries（mKdV） equations describing the evolution of the amplitude of solitary Rossby waves as the change of Rossby parameter β（у） with latitude у is obtained.

Binding energies of shallow impurities in asymmetric strained wurtzite Al_x Ga_(1-x)N/GaN/AIy Ga1-y N quantum wells

The ground state binding energies of hydrogenic impurities in strained wurtzite AlGaN/GaN/AlGaN quantum wells are calculated numerically by a variational method.The dependence of the binding energy on well width,impurity location and Al concentrations of the left and right barriers is discussed,including the effect of the built-in electric field induced by spontaneous and piezoelectric polarizations.The results show that the change in binding energy with well width is more sensitive to the impurity position and barrier heights than the barrier widths,especially in asymmetric well structures where the barrier widths and/or barrier heights differ.The binding energy as a function of the impurity position in symmetric and asymmetric structures behaves like a map of the spatial distribution of the ground state wave function of the electron.It is also found that the influence on the binding energy from the Al concentration of the left barrier is more obvious than that of the right barrier.

Symmetry of the Point Spectrum of Infinite Dimensional Hamiltonian Operators and Its Applications

This paper studies the symmetry, with respect to the real axis, of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H. Note that the point spectrum of H can be described as σp（H） = σp （A） U σp1 （-A＊）. Using the characteristic of the set σp1（-A＊）, we divide the point spectrum σp （d） of A into three disjoint parts. Then, a necessary and sufficient condition is obtained under which σp1（-A＊） and one part of σp（A） are symmetric with respect to the real axis each other. Based on this result, the symmetry of σp（H） is completely given. Moreover, the above result is applied to thin plates on elastic foundation, plane elasticity problems and harmonic equations.