求解完全强非线性自治系统周期解及其稳定性的三变量迭代法

本文提出用广义位移x,基波幅值变化率da/dt=A(a)和系统频率ω(a)进行迭代的一种解析方法——三变量迭代法,求解一般的二阶完全强非线性自治系统的周期解及其稳定性。通过若干实例计算,表明了该方法行之有效。     

强非线性问题的一类能量迭代方法

基于能量原理，引进迭代及最小二乘，研究完全强非线性自治系统的周期解及其稳定性，算例表明，该法精度较高。     

求解非线性动力学方程的分段直接积分法

针对n维未知向量v的一阶微分方程dv/dt=Hv f(v,t）进行求解。首先，将非线性部分f(v,t)在所论时刻tk处用t-tk=T的j次多项式来近似，然后借助分段直接积分法，导出了各段内的、用T的解析函数表达的求解公式，通过选取j值，可获得一系列具有不同精度的近似解，便于研究非线性动力学行为与其物理参数的依赖关系。为适应实际计算，还全面讨论了上述多项式的确定方法，其中包括避免求f(v,t)导数的算法。算例表明所提出的方法不仅可用于求解非线性动力响应问题，而且对研究解的形态和稳定性，如对吸引子、极限环、二次Hopf分岔等的分析也不失为一个有效的工具。     

一类强非线性机械基础系统的亚谐振动解析解

建立了机械基础动力系统的强非线性动力学模型，利用能量法对该系统的周期解进行了解析研究，确定了系统动态参数满足周期解的条件、系统的周期解以及解的稳定性判别式。发现了亚谐振动，并给出了系统在满足周期解条件下的一组参数对应的主振动、1／3亚谐振动和1／5亚谐振动。最后利用数值积分方法计算了系统在给定条件下的主振动及亚谐振动解，考察了解析解的正确性。     

非线性转子-轴承系统的周期解及近似解析表达式

通过对普通打靶方法进行改造提出一种确定非线性系统周期轨道及周期的新型打靶算法。首先通过改变系统的时间尺度，将非线性系统周期轨道的周期显式地出现在非线性系统的系统方程中，然后对传统打靶法进行改造，将周期也作为一个参数一起参与打靶法的迭代过程，迭代过程包含对周期轨道和周期的求解，迭代过程中的增量通过优化方法选择，从而能迅速确定出系统的周期轨道及其周期。应用所求的结果结合谐波平衡方法求得了非线性系统的周期轨道的近似解析表达式，理论上通过增加谐波的阶数任何精度的周期解都可以得到。最后将该方法应用于非线性转子轴承系统，求出了在某些参数下转子的周期解及其近似解析表达式，通过与四阶Runge-Kutta数值积分结果比较，验证了方法的有效性，计算结果对于转子系统运动的定量控制有重要理论指导意义。     

非线性Hill系统周期响应和分叉理论

本文首先给出并证明了解一类弱非线性问题的广义Ｇｒｅｅｅｎ法，利用这一方法求得非线性Ｈｉｌｌ振动系统在非共振和共振二种民政部下的周期响就以及描述周期响应特征的二次近似分叉方程应用具有Ｚ２对称的奇异性理论，建立了模参数与各物理参数之间的对应关系，通过对Ｚ２余维数≥３周期分叉解的普适性分类，全面分析了共振情况下物理参数对周期分叉解特征的影响。从而使二次近似分叉方程是否能够在拓扑意义下完全描述原系统的周期     

一种新的求解非线性系统周期解方法

本文利用切比雪夫多项式的若干良好性质,对非自治强非线性动力系统进行分析。将状态矢量在主周期上先展开谐波级数的形式,再将各谐波展开为切比雪夫多项式的形式,从而将求周期解的问题转变为非线性代数方程组的求解问题,得出一种可以方便、迅速地获得近似周期解的解析方法。此方法不依赖于小参数假设,可以用于分析强非线性问题和高维问题,而且对参数激励系统同样有效。以Duffing系统周期解的计算为例,通过与标准谐波平衡方法和四阶Runge-Kutta数值积分结果比较,说明此方法的有效性。     

分段线性耦合动力系统的周期解及稳定性分析

以某货车的主副钢板弹簧悬架为模型建立两自由度分段线性和轮胎非线性耦合动力学方程,采用打靶法求耦舍系统的周期解;将所得结果与近似解析法分析的结果进行比较,并利用Floquet理论判断周期解的稳定性。研究结果表明：当激励频率在等效固有频率附近时系统的周期解不稳定,其Floquet乘数的模大于1,系统振动剧烈,KBM法得到的周期解将产生较大误差;当路面工况突然发生改变或路面工况不变而载重发生较大变化时都有可能发生舅毡跃现象,造成系统的不稳定;周期解的长期时域图和Floquet理论验证了这一现象;     

用加权残值法求压杆的临界载荷

用加权残值法求压杆的临界载荷刘悦藏（河北工学院材料力学教研室，天津３００１３２）加权残值法是一种求解微分方程的方法。它不是严格地求微分方程的解析解，而是直接从微分方程得出问题的近似解。与其它数值法相比，它没有完全抛弃已有的理论解。由于此法原理简单、方...     

非线性动力学方程的一种级数解

本文针对n维未知向量v的一阶微分议程v=Hv f(v,t)进行求解,其中Hv和f(v,t)分别是右端项的线性剂次部分和非线性部分,首先,将非线性部分f(v,t)在所论时刻tk处展成t-tk=τ的泰勒级数,并通过求原函数的方法直接给出每一项的积分,从而获得了待求微分方程在级数形式下的闭合争,它的具有不同精度的各次静似解可表示成τ的分段解析函数,便于研究非线性动力学行为与其物理参数的依赖关系。本文还用算例验证了各次近似解之间的数值关系,并和解析解等作了比较。     

The 7th International Conference on Fluid Mechanics May 24-27,2015,Qingdao,China

正http://www.icfm7.org First Announcement and Call for PapersThe objective of International Conference on Fluid Mechanics(ICFM)is to provide a forum for researchers to exchange new ideas and recent advances in the fields of theoretical,experimental,computational Fluid Mechanics as well as interdisciplinary subjects.It was successfully convened by the Chinese Society of Theoretical and Applied Mechanics(CSTAM)in Beijing(1987,     

INFORMATION FOR CONTRIBUTORS

Contributions： The Journal, Acta Mechanica Solida Sinica, is pleased to receive papers from engineers and scientists working in various aspects of solid mechanics. All contributions are subject to critical review prior to acceptance and publication.     

Preface

This special issue of PARTICUOLOGY is devoted to the first UK-China Particle Technology Forum taking place in Leeds, UK, on 1-3 April 2007. The forum was initiated by a number of UK and Chinese leading academics and organised by the University of Leeds in collaboration with Chinese Society of Particuology, Particle Technology Subject Group （PTSG） of the Institution of Chemical Engineers （IChemE）, Particle Characterisation Interest Group （PCIG） of the Royal Society of Chemistry （RSC） and International Fine Particle Research Institute （IFPRI）. The forum was supported financially by the Engineering and Physics Sciences Research Council （EPSRC） of United Kingdom,     

基于鲁棒滤波的捷联导引头视线角速度估计方法

针对捷联导引头无法直接获取视线角速度等信息的问题,研究了鲁棒滤波在大气层外飞行器捷联导引头视线角速度估计中的应用。为了建立非线性滤波估计模型,考虑目标视线角速度的慢变特性,采用一阶马尔科夫模型建立了状态方程;推导了视线角速度的解耦模型,并建立了量测方程;考虑到实际应用中存在系统噪声统计特性失准的问题,基于Huber-Based鲁棒滤波方法,设计了视线角速度滤波器,并完成了基于Huber-Based滤波方法和扩展卡尔曼滤波方法的数学仿真。仿真结果表明Huber-Based滤波方法的视线角、视线角速度及视线角加速度估计精度分别达到0.1140'、0.1423'/s、0.0203'/s2,而扩展卡尔曼滤波方法的视线角、视线角速度及视线角加速度估计精度仅分别为0.6577'、0.6415'/s、0.0979'/s~2。仿真结果证明了该方法可以有效地估计出相对视线角速度等信息,并且在非高斯噪声的条件下,依然可获得较高的估计精度,具有一定的鲁棒性。     

Guide for authors

正Each of the sections below provides essential information for authors.We recommend that you take the time to read them before submitting a contribution to Acta Mechanica Sinica.We hope our guide to authors may help you navigate to the appropriate section.How to prepare a submission This document provides an outline of the editorial process involved in publishing a scientific paper in Acta Mechanica     

Use specification of multiscale materials for life spanned over macro-, micro-, nano-, and pico-scale

Multiscale material intends to enhance the strength and life of mechanical systems by matching the transmitted spatiotemporal energy distribution to the constituents at the different scale, say—macro, micro, nano, and pico,—, depending on the needs. Lower scale entities are, particularly, critical to small size systems. Large structures are less sensitive to microscopic effects. Scale shifting laws will be developed for relating test data from nano-, micro-, and macro-specimens. The benefit of reinforcement at the lower scale constituents needs to be justified at the macroscopic scale. Filling the void and space in regions of high energy density is considered.Material inhomogeneity interacts with specimen size. Their combined effect is non-equilibrium. Energy exchange between the environment and specimen becomes increasingly more significant as the specimen size is reduced. Perturbation of the operational conditions can further aggravate the situation. Scale transitional functions and/or f_j/j+1 are introduced to quantify these characteristics. They are represented, respectively, by , and (f_mi/ma,f_na/mi,f_pi/na). The abbreviations pi, na, mi, and ma refer to pico, nano, micro and macro.Local damage is assumed to initiate at a small scale, grows to a larger scale, and terminate at an even larger scale. The mechanism of energy absorption and dissipation will be introduced to develop a consistent book keeping system. Compaction of mass density for constituents of size 10⁻¹², 10⁻⁹, 10⁻⁶, 10⁻³ m, will be considered. Energy dissipation at all scales must be accounted for. Dissipations at the smaller scale must not only be included but they must abide by the same physical and mathematical interpretation, in order to avoid inconsistencies when making connections with those at the larger scale where dissipations are eminent.Three fundamental Problems I, II, and III are stated. They correspond to the commonly used service conditions. Reference is made to a Representative Tip (RT), the location where energy absorption and dissipation takes place. The RT can be a crack tip or a particle. At the larger size scales, RT can refer to a region. Scale shifting of results from the very small to the very large is needed to identify the benefit of using multiscale materials.