带有双线性非线性全动舵面气动弹性的数值与试验研究

基于结构刚度非耦合,设计了在扭转方向存在双线性非线性的全动舵面,并对其开展了数值仿真与风洞试验研究。用接触对模拟双线性非线性,基于CFD/CSD耦合建立了该舵面数值仿真模型,考虑了初始接触刚度、触点震颤和接触摩擦力等因素。结果表明:初始接触刚度变化,对数值模拟所得极限环幅值几乎没有影响;采用接触时间控制能够有效解决触点震颤,使流固耦合模拟过程数值稳定;接触摩擦力增大,数值模拟所得极限环幅值减小;数值计算所得极限环幅值随动压的变化规律与风洞试验吻合。

Double-Parameter Solutions of Projective Riccati Equations and Their Applications

The purpose of the present paper is twofold. First, the projective Riccati equations （PREs for short） are resolved by means of a linearized theorem, which was known in the literature. Based on the signs and values of coeffcients of PREs, the solutions with two arbitrary parameters of PREs can be expressed by the hyperbolic functions, the trigonometric functions, and the rational functions respectively, at the same time the relation between the components of each solution to PREs is also implemented. Second, more new travelling wave solutions for some nonlinear PDEs, such as the Burgers equation, the mKdV equation, the NLS^＋ equation, new Hamilton amplitude equation, and so on, are obtained by using Sub-ODE method, in which PREs are taken as the Sub-ODEs. The key idea of this method is that the travelling wave solutions of nonlinear PDE can be expressed by a polynomial in two variables, which are the components of each solution to PREs, provided that the homogeneous balance between the higher order derivatives and nonlinear terms in the equation is considered.

Painleve Analysis and Determinant Solutions of a (3+1)-Dimensional Variable-Coefficient Kadomtsev-Petviashvili Equation in Wronskian and Grammian Form

In this paper, the investigation is focused on a （3＋1）-dimensional variable-coefficient Kadomtsev- Petviashvili （vcKP） equation, which can describe the realistic nonlinear phenomena in the fluid dynamics and plasma in three spatial dimensions. In order to study the integrability property of such an equation, the Painlevé analysis is performed on it. And then, based on the truncated Painlevé expansion, the bilinear form of the （3＋1）-dimensionaJ vcKP equation is obtained under certain coefficients constraint, and its solution in the Wronskian determinant form is constructed and verified by virtue of the Wronskian technique. Besides the Wronskian determinant solution, it is shown that the （3＋1）-dimensional vcKP equation also possesses a solution in the form of the Grammian determinant.

HBFTrans2: A Maple Package to Construct Hirota Bilinear Form for Nonlinear Equations

An improved algorithm for symbolic computation of Hirota bilinear form of nonlinear equations by a logarithm transformation is presented. The improved algorithm is more efficient by using the property of Hirota-D operator. The software package HBFTrans2 is written in Maple and its running efficiency is tested by a variety of soliton equations.

A Maple Package on Symbolic Computation of Hirota Bilinear Form for Nonlinear Equations

An improved algorithm for symbolic computation of Hirota bilinear forms of KdV-type equations withlogarithmic transformations is presented.In the algorithm,the general assumption of Hirota bilinear form is successfullyreduced based on the property of uniformity in rank.Furthermore,we discard the integral operation in the traditionalalgorithm.The software package HBFTrans is written in Maple and its running effectiveness is tested by a variety solitonequations.

Free Surface Flow Generated by Submerged Twin-cylinders in Forward Motion Using a Fully Nonlinear Method

The free surface flow generated by twin-cylinders in forced motion submerged beneath the free surface is studied based on the boundary element method. Two relative locations, namely, horizontal and vertical, are examined for the twin cylinders. In both cases, the twin cylinders are starting from rest and ultimately moving with the same constant speed through an accelerating process. Assuming that the fluid is inviscid and incompressible and the flow to be irrotational, the integral Laplace equation can be discretized based on the boundary element method. Fully-nonlinear boundary conditions are satisfied on the unknown free surface and the moving body surface. The free surface is traced by a Lagrangian technique. Regriding and remeshing are applied, which is crucial to quality of the numerical results. Single circular cylinder and elliptical cylinder are calculated by linear method and fully nonlinear method for accuracy checking and then fully nonlinear method is conducted on the twin cylinder cases, respectively. The generated wave elevation and the resultant force are analysed to discuss the influence of the gap between the two cylinders as well as the water depth. It is found that no matter the kind of distribution, when the moving cylinders are close to each other, they suffer hydrodynamic force with large absolute value in the direction of motion. The trend of force varying with the increase of gap can be clearly seen from numerical analysis. The vertically distributed twin cylinders seem to attract with each other while the horizontally distributed twin cylinders are opposite when they are close to each other.

Soliton Solutions and Bilinear Bcklund Transformation for Generalized Nonlinear Schrdinger Equation with Radial Symmetry

Investigated in this paper is the generalized nonlinear Schrodinger equation with radial symmetry. With the help of symbolic computation, the one-, two-, and N-soliton solutions are obtained through the bilinear method. B^cklund transformation in the bilinear form is presented, through which a new solution is constructed. Graphically, we have found that the solitons are symmetric about x = O, while the soliton pulse width and amplitude will change along with the distance and time during the propagation.

ＬＯＣＡＬＥＸＡＣＴＢＯＵＮＤＡＲＹＣＯＮＴＲＯＬＬＡＢＩＬＩＴＹＦＯＲＡＣＬＡＳＳＯＦＱＵＡＳＩＬＩＮＥＡＲＨＹＰＥＲＢＯＬＩＣＳＹＳＴＥＭＳ

For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an application, the authors show the local exact boundary controllability for a kind of nonlinear vibrating string problem.

Breather-Type Periodic Soliton Solutions for (1+1)-Dimensional Sinh-Poisson Equation

In this paper,by using bilinear form and extended homoclinic test approach,we obtain new breather-type periodic soliton solutions of the (1+1)-dimensional Sinh-Poisson equation.These results demonstrate that the nonlinear evolution equation has rich dynamical behavior even if it is (1+1)-dimensional.

Bilinear Forms and Soliton Solutions for the Reduced Maxwell-Bloch Equations with Variable Coefficients in Nonlinear Optics

Investigation in this paper is given to the reduced Maxwell-Bloeh equations with variable coetcients, describing the propagation of the intense ultra-short optical pulses through an inhomogeneous two-level dielectric medium. We apply the Hirota method and symbolic computation to study such equations. With the help of the dependent variable transformations, we present the variable-coetteient-dependent bilinear forms. Then, we construct the one-, two- and N- soliton solutions in analytic forms for them.

Explicit Traveling Wave Solutions to Nonlinear Evolution Equations

First of all,some technical tools are developed.Then the author studies explicit traveling wave solutions to nonlinear dispersive wave equations,nonlinear dissipative dispersive wave equations,nonlinear convection equations,nonlinear reaction diffusion equations and nonlinear hyperbolic equations,respectively.

A novel two-stage spectral compression structure em-ploying a logarithmic DIF interconnected with an HNLF- NOLM

A novel two-stage spectral compression structure which employs a logarithmic dispersion increasing fiber （DIF） in- terconnected with a highly nonlinear linear fiber-nonlinear optical loop mirror （HNLF-NOLM） is proposed and dem- onstrated by numerical simulation. The numerical simulation is implemented by solving the generalized nonlinear SchrOdinger equation using split-step Fourier method, where the soliton number is in the range of 0.5≤N≤1.4. The re- suits show that the spectra are well-compressed and low-pedestal, and the maximum spectral compression ratio （SCR） can reach 10.93 when N=l.4.