On k-Error Linear Complexity of Some Explicit Nonlinear Pseudorandom Sequences

Combining with the research on the linear complexity of explicit nonlinear generators of pseudorandom sequences, we study the stability on linear complexity of two classes of explicit inversive generators and two classes of explicit nonlinear generators. We present some lower bounds in theory on the k-error linear complexity of these explicit generatol＇s, which further improve the cryptographic properties of the corresponding number generators and provide very useful information when they are applied to cryptography.

A Quantum-behaved Pigeon-Inspired Optimization approach to Explicit Nonlinear Model Predictive Controller for quadrotor

Purpose–The purpose of this paper is to simplify the Explicit Nonlinear Model Predictive Controller(ENMPC)by linearizing the trajectory with Quantum-behaved Pigeon-Inspired Optimization(QPIO).Design/methodology/approach–The paper deduces the nonlinear model of the quadrotor and uses the ENMPC to track the trajectory.Since the ENMPC has high demand for the state equation,the trajectory needed to be differentiated many times.When the trajectory is complicate or discontinuous,QPIO is proposed to linearize the trajectory.Then the linearized trajectory will be used in the ENMPC.Findings–Applying the QPIO algorithm allows the unequal distance sample points to be acquired to linearize the trajectory.Comparing with the equidistant linear interpolation,the linear interpolation error will be smaller.Practical implications–Small-sized quadrotors were adopted in this research to simplify the model.The model is supposed to be accurate and differentiable to meet the requirements of ENMPC.Originality/value–Traditionally,the quadrotor model was usually linearized in the research.In this paper,the quadrotormodel waskept nonlinear and the trajectorywill be linearizedinstead.Unequaldistance sample points were utilized to linearize the trajectory.In this way,the authors can get a smaller interpolation error.This method can also be applied to discrete systems to construct the interpolation for trajectory tracking.

Sign-invariant and Explicit Solutions of Nonlinear Reaction-Diffusion Systems

用症状不变的理论，我们学习非线性的反应散开系统。我们也获得一些新明确的解决方案到非线性的产生系统。

Explicit solutions to some nonlinear physical models by a two-step ansatz

Explicit solutions are derived for some nonlinear physical model equations by using a delicate way of two-step ansatz method.

Nonlinear evaluations of unconditionally stable explicit algorithms

Two explicit integration algorithms with unconditional stability for linear elastic systems have been successfully developed for pseudodynamic testing. Their numerical properties in the solution of a linear elastic system have been well explored and their applications to the pseudodynamic testing of a nonlinear system have been shown to be feasible. However, their numerical properties in the solution of a nonlinear system are not apparent. Therefore, the performance of both algorithms for use in the solution of a nonlinear system has been analytically evaluated after introducing an instantaneous degree of nonlinearity. The two algorithms have roughly the same accuracy for a small value of the product of the natural frequency and step size. Meanwhile, the first algorithm is unconditionally stable when the instantaneous degree of nonlinearity is less than or equal to 1, and it becomes conditionally stable when it is greater than 1. The second algorithm is conditionally stable as the instantaneous degree of nonlinearity is less than 1/9, and becomes unstable when it is greater than 1. It can have unconditional stability for the range between 1/9 and 1. Based on these evaluations, it was concluded that the first algorithm is superior to the second one. Also, both algorithms were found to require commensurate computational efforts, which are much less than needed for the Newmark explicit method in general structural dynamic problems.

Extensions of nonlinear error propagation analysis for explicit pseudodynamic testing

Two important extensions of a technique to perform a nonlinear error propagation analysis for an explicit pseudodynamic algorithm （Chang, 2003） are presented. One extends the stability study from a given time step to a complete step-by-step integration procedure. It is analytically proven that ensuring stability conditions in each time step leads to a stable computation of the entire step-by-step integration procedure. The other extension shows that the nonlinear error propagation results, which are derived for a nonlinear single degree of freedom （SDOF） system, can be applied to a nonlinear multiple degree of freedom （MDOF） system. This application is dependent upon the determination of the natural frequencies of the system in each time step, since all the numerical properties and error propagation properties in the time step are closely related to these frequencies. The results are derived from the step degree of nonlinearity. An instantaneous degree of nonlinearity is introduced to replace the step degree of nonlinearity and is shown to be easier to use in practice. The extensions can be also applied to the results derived from a SDOF system based on the instantaneous degree of nonlinearity, and hence a time step might be appropriately chosen to perform a pseudodynamic test prior to testing.

扣件刚度非线性对波磨区轮轨瞬态滚动接触行为的影响

WJ-8型扣件橡胶垫板刚度在长期服役过程中表现出非线性特征,静刚度随荷载增加而降低,为提高三维瞬态滚动接触有限元模型计算精确性,本文以LMA踏面车轮及CHN60型钢轨为基础,基于显式积分算法,将以往研究中线弹性扣件转化为非线性扣件,建立考虑扣件刚度非线性特征的三维轮轨瞬态滚动接触有限元模型,研究刚度非线性对车轮与钢轨波磨间高频动态响应及瞬态接触行为的影响,并重点分析了波磨工况下时频域内轮轨接触力、轴箱加速度的变化信息.结果表明:扣件非线性对轮轨接触力变化影响明显,主要表现为车轮行驶至扣件前端时强振动导致橡胶垫板表现为柔软特性使轮轨接触力减小,车轮行驶至扣件上方时在轴重作用下振动减弱表现为刚硬特性使轮轨接触力增大,轮轨力变化差异最大达到13.1%.

车辆-轨道非线性耦合系统显隐式求解算法的收敛性分析

针对车辆-轨道非线性耦合系统的动力学方程联立求解过程,将车辆和轨道分别考虑为2个子系统,通过2个子系统之间的位移协调和轮轨非线性接触力耦合,再结合显隐式积分格式,提出车辆-轨道非线性耦合系统的分离迭代和分离同步两种求解方法,通过算例验证了两种方法的正确性,并对两种求解方法的收敛性进行了对比分析。计算结果表明:显隐式分离迭代法和显隐式分离同步法的最大有效时间步长分别是0.5、0.1 ms;在时间步长较大时,采用Aitken加速法可以起到增强显隐式分离迭代法的计算稳定性的作用,但Aitken加速法的作用会随着时间步长的减小而变小;相同时间步长下显隐式分离同步法的计算效率要比显隐式分离迭代法高,但可以通过选用较大的时间步长来提高显隐式分离迭代法的计算效率。

分离变量法求解一些非线性发展方程的显式解

利用分离变量法求解一些非线性发展方程,如Harry-Dym方程,Hunter-Saxton方程,非线性扩散方程,半经典极限KdV方程等方程新的显式解析解.有意思的是,贝塞尔函数出现在部分解的表达式中,有些解可以预测解的爆破现象.

A Modified Form of Mild-Slope Equation with Weakly Nonlinear Effect

Nonlinear effect is of importance to waves propagating from deep water to shallow water. The non-linearity of waves is widely discussed due to its high precision in application. But there are still some problems in dealing with the nonlinear waves in practice. In this paper, a modified form of mild-slope equation with weakly nonlinear effect is derived by use of the nonlinear dispersion relation and the steady mild-slope equation containing energy dissipation. The modified form of mild-slope equation is convenient to solve nonlinear effect of waves. The model is tested against the laboratory measurement for the case of a submerged elliptical shoal on a slope beach given by Berkhoff et al. The present numerical results are also compared with those obtained through linear wave theory. Better agreement is obtained as the modified mild-slope equation is employed. And the modified mild-slope equation can reasonably simulate the weakly nonlinear effect of wave propagation from deep water to coast.

Nonlinear Dispersion Effect on Wave Transformation

A new nonlinear dispersion relation is given in this paper, which can overcome the limitation of the intermediate minimum value in the dispersion relation proposed by Kirby and Dalrymple (1986). and which has a better approximation to Hedges' empirical relation than the modified relations by Hedges (1987). Kirby and Dalrymple (1987) for shallow waters. The new dispersion relation is simple in form, thus it can be used easily in practice. Meanwhile, a general explicit approximation to the new dispersion and other and other nonlinear dispersion relations is given. By use of the explicit approximation to the new dispersion relation along with the mild slope equation taking into account weakly nonlinenr effect, a mathematical model is obtained, and it is applied to laboratory data. The results show that the model developed with the new dispersion relation predicts wave transformation over complicated topography quite well.

Comparison and assessment of time integration algorithms for nonlinear vibration systems

A corrected explicit method of double time steps(CEMDTS) was introduced to accurately simulate nonlinear vibration problems in engineering. The CEMDTS, the leapfrog central difference method, the Newmark method, the generalized-a method and the precise integration method were implemented in typical nonlinear examples for the purpose of comparison. Both conservative and non-conservative systems were examined. The results show that it isn't unconditionally stable for the precise integration method, the Newmark method and the generalized-a method in nonlinear systems. The stable interval of the three methods is less than that of the CEMDTS. When a small time step(?t≤T_(min)/20) is employed, the precise integration method is endowed with the highest accuracy while the CEMDTS possesses the smallest computation effort. However, the CEMDTS becomes the most accurate one when the time step is large(?t≥0.3T_(min)) or the system is strongly nonlinear. Therefore, the CEMDTS is more applicable to the nonlinear vibration systems.

Solitons for the cubic-quintic nonlinear Schrdinger equation with varying coefficients

In this paper,by means of similarity transfomations,we obtain explicit solutions to the cubic-quintic nonlinear Schr顜僤inger equation with varying coefficients,which involve four free functions of space.Four types of free functions are chosen to exhibit the corresponding nonlinear wave propagations.

A family of explicit algorithms for general pseudodynamic testing

A new family of explicit pseudodynamic algorithms is proposed for general pseudodynamic testing. One particular subfamily seems very promising for use in general pseudodynamic testing since the stability problem for a structure does not need to be considered. This is because this subfamily is unconditionally stable for any instantaneous stiffness softening system, linear elastic system and instantaneous stiffness hardening system that might occur in the pseudodynamic testing of a real structure. In addition, it also offers good accuracy when compared to a general second-order accurate method for both linear elastic and nonlinear systems.

Bcklund Transformations and Explicit Solutions of (2+1)-Dimensional Barotropic and Quasi-Geostrophic Potential Vorticity Equation

By the Bcklund transformation method, an important (2+1)-dimensional nonlinear barotropic and quasigeostrophicpotential vorticity (BQGPV) equation is investigated. Some simple special Bcklund transformation theoremsare proposed and used to get explicit solutions of the BQGPV equation. Futhermore, all solutions of a secondorder linear ordinary differential equation including an arbitrary function can be used to construct explicit solutions ofthe (2+1)-dimensional BQGPV equation. Some figures are also given out to describe these solutions.

钢纤维混凝土栓钉-橡胶组合连接件抗剪刚度分析

为建立钢纤维混凝土(steel fiber reinforced concrete,SFRC)栓钉-橡胶组合连接件抗剪刚度设计计算方法,结合已有文献推出试验,采用ABAQUS显式准静态求解技术进行非线性有限元分析,仿真计算结果与文献推出试验结果基本吻合。以橡胶套高度、橡胶套厚度、混凝土强度和栓钉直径为影响参数,分析组合连接件抗剪刚度变化规律,并结合现有栓钉抗剪刚度计算式拟合出SFRC栓钉-橡胶组合连接件抗剪刚度设计计算公式。结果表明:ABAQUS显式准静态求解技术能较好地实现组合连接件推出试验数值模拟;采用橡胶套包裹栓钉后会大幅降低连接件抗剪刚度,抗剪刚度最大降幅约为60%;当橡胶套高度为25 mm、厚度为2.5 mm时,即可显著降低连接件抗剪刚度;钢纤维混凝土强度对抗剪刚度影响较小;组合连接件抗剪刚度与栓钉直径近似呈正比关系;提出的抗剪刚度设计计算式能较准确预测钢纤维混凝土栓钉-橡胶组合连接件抗剪刚度,为工程设计提供参考与借鉴。

应用构型一致的显式方法预测结构冲击动响应

目的 发展构型一致的显式方法,以提高拉格朗日有限元对冲击、碰撞及侵彻问题计算的精度和健壮性。方法 为更准确地描述和计算结构大变形,基于任意参考构型理论,建立构型一致的动量方程拉格朗日有限元格式。为避免网格间侵入现象,通过结合前增量位移的时间积分方法和共轭梯度算法,使得显式增量步更新后,仍满足接触非侵入条件。结果 通过对大变形碰撞及侵彻问题的模拟,并与LS-DYNA软件结果对比,验证了计算方法的可靠性。结论 基于构型一致的显式算法可有效抑制大变形碰撞过程的单元畸变,提高计算程序的健壮性和预测准确度,使该算法在模拟大变形碰撞问题方面具有优势。

建筑减震结构分析的层间剪力校准系数法

我国《建筑抗震设计规范》(GB 50011-2010)推荐采用考虑附加阻尼比和附加刚度的振型分解反应谱法进行建筑减震结构地震作用效应分析。但附加阻尼比和附加刚度的确定存在近似性,亟待发展高效准确的减震结构分析方法。以减震结构为研究对象,建立了减震结构地震响应的时域显式表达式,实现了非线性减震装置恢复力(阻尼力)的快速迭代计算。结合蒙特卡罗模拟,通过地震响应平均峰值的计算获得了统计上准确的结构层间剪力,并将其与规范反应谱法得到的层间剪力进行对比,进而获得了各楼层的层间剪力校准系数,采用该校准系数对规范反应谱法计算得到的各楼层构件内力进行了调整。最后,针对三个建筑减震结构,分别采用层间剪力校准系数法和规范反应谱法进行地震响应分析,验证了层间剪力校准系数法在减震结构地震作用效应计算方面的高效性和准确性。

基于LS-DYNA的包带式星箭连接装置分离过程和冲击响应分析

采用显式非线性动力学分析方法来研究包带式星箭连接装置的分离过程和冲击响应,给出了有限元建模和预紧力施加方法,采用LS-DYNA软件计算得到某包带式星箭连接装置的包带动态包络和冲击响应;分析了对接框刚度、抗剪凸台、分离弹簧和拉伸弹簧刚度系数等参数对分离冲击的影响,并采用单自由度"弹簧-质量"系统模拟缓释过程,讨论了缓释过程对分离冲击的影响。结果表明:①采用显式非线性动力学分析方法能够同时解决星箭分离过程仿真和冲击响应分析问题;②增加对接框刚度,合理设计抗剪凸台高度,适当减小分离弹簧推力和拉伸弹簧拉力均可降低分离冲击响应;③延长解锁装置释放时间能够同时降低最大冲击响应峰值及其对应频率。