一类全对称周期Jacobi矩阵逆特征值问题

提出了关于全对称周期Ｊａｃｏｂｉ矩阵的一类逆特征值问题，导出了问题有唯一解的一个充分条件；在条件满足时给出了计算公式。     

风扇/压气机数值稳定性模型

本文给出了一种用于预测轴流压气机旋转失速发生的数值稳定性模型,并描述了模型的理论基础以及求解模型方程的方法。模型的建立基于线性稳定性理论的基础之上,通过特征值的虚部来判断系统的稳定性。一种全局性方法被用于求解离散系统的所有特征值。离散的方法包括二阶精度的有限差分方法以及切比雪夫谱配置的方法。计算结果表明,用这两种方法均可以得到准确的特征值,但是收敛的速度有所不同。另外,将文中的分析与实验进行了比较,结果表明实验中的失速点可以用这种模型进行合理的预测。     

Ni27+ 离子Kα和Kβ 型衰变的双电子复合速率系数的计算

用HFR波函数对低密度类氢Ni²⁷⁺等离子体与电子相互作用的KLn和KMn共振激发的双电子复合过程进行了细致的理论计算研究.根据可能的重要辐射衰变通道，分析了Ni²⁷⁺等离子体Kα 型和Kβ 型辐射衰变的双电子复合速率系数随旁观电子主量子数n和轨道角动量量子数l与电子温度的变化行为，计算了Ni²⁷⁺等离子体双电子复合过程的总速率系数.研究结果表明，在低密度条件下，Kα 型和Kβ型辐射衰变的分支双电子复合速率系数与旁观电子主量子数n和轨道角动量量子数l有重要关系，前者的分支速率系数远大于后者. 关键词： 27+离子')" href="#">Ni²⁷⁺离子 Kα型和Kβ型辐射衰变')" href="#">Kα型和Kβ型辐射衰变 双电子复合 速率系数     

电压型双频率控制开关变换器的动力学建模与多周期行为分析

在断续导电模式下, 建立了电压型双频率控制开关变换器的动力学模型, 并推导了相应的特征值方程. 根据动力学模型, 采用分岔图研究了电路参数变化时变换器存在的边界碰撞分岔行为和周期2, 周期3,周期4等多周期行为, 结果表明: 变换器经历了周期1态、多周期态、周期1态的分岔路由; 周期态的转变均是由边界碰撞分岔引起的. 根据特征值方程, 采用Lyapunov指数研究了变换器的稳定性, 结果表明: 随着电路参数的变化, Lyapunov指数始终小于零, 变换器一直工作于稳定的周期态, 验证了电压型双频率控制开关变换器的周期3行为并不意味着变换器会必然发生混沌. 通过电路仿真, 分析了负载变化时变换器的时域波形、相轨图和频谱图, 验证了动力学模型的可行性和理论分析的正确性. 实验结果验证了文中的仿真结果. 关键词： 开关变换器 双频率控制 边界碰撞分岔 多周期行为     

关于PCG迭代矩阵特征值近似计算

对于预处理共轭梯度法,本文给出其迭代矩阵AM^-1与三对角阵B_s之间的关系,并对B_s的特征值分布作了分析,进而得到关于AM^-1特征值的一些性质。通过算例对两者的特征值及条件数进行了探讨。     

超短超强激光与铜靶相互作用产生Kα源的蒙特卡罗模拟

超短超强激光打靶产生的超热电子，与固体靶相互作用时会产生Kα线辐射.由经典定标律给出了法线方向超热电子的温度.利用蒙特卡罗方法，对超热电子在固体靶中的传输进行了研究，模拟了不同靶厚度情况下Kα产额和角分布及不同电子温度下Kα光子的转化效率.计算结果与实验符合较好.结果表明：在一定电子温度下，随着靶厚度的增加Kα光子产额会达到饱和，并会使Kα光子发射的各向异性变得更加严重；存在最佳的电子温度，使Kα线转化效率最高. 关键词： 超短超强激光 超热电子 蒙特卡罗方法 Kα线')" href="#">Kα线     

“碰撞-辐射”模型在Z箍缩等离子体K壳层线辐射谱分析中的应用

介绍了由K壳层谱线强度比估算等离子体状态参数的"碰撞-辐射"模型的基本原理.详细描述了自行研制的基于该模型的Z箍缩等离子体K壳层线辐射谱分析程序——ZSPEC的基本情况.给出了氖等离子体的计算结果,包括不同电离态离子的相对含量随电子温度的变化曲线和K壳层谱线强度比在"电子密度-电子温度"平面内的等高线分布图.该程序已在"阳"加速器Z箍缩实验结果分析中得到应用,将椭圆晶体谱仪测得的氖等离子体K壳层谱线强度比与ZSPEC程序计算结果相比较,得出在该发实验 关键词： 碰撞-辐射模型 K壳层线辐射谱')" href="#">K壳层线辐射谱 氖气喷气Z箍缩 阳加速器     

Gruhn-Hess两体势修正模型向列相液晶微滴的Monte Carlo模拟

基于Gruhn-Hess两体势修正模型,用Monte Carlo方法模拟向列相液晶微滴.Gruhn-Hess两体势是空间各向异性的,修正模型的势参数依赖于液晶的弹性常数K₁₁、K₂₂、K₃₃及表面弹性常数K₁₃.假设向列相液晶微滴具有自由表面,在低温下计算分子二阶序参数和切向内禀强度在微滴内不同区域的变化,并与Gruhn-Hess两体势模型一作对比分析.结果表明:附加K₁₃项的修正模型在微滴表面产生内禀锚定,其大小决定了内禀易取向方向及内禀锚定强度的大小,且内禀强度的大小与K₃₃/K₁₁值有关;空间不完整的向列相液晶微滴由内层到外层有序度逐渐降低.     

甲烷-煤尘爆炸物火焰传播特性

 在10 m³的爆炸罐中对体积分数为8%的甲烷和75 g/m³煤尘的混合物进行了系统的燃烧爆炸实验。分别利用光测方法和压力方法得到了爆炸物的层流燃烧速度、火焰传播速度、火焰厚度、马克斯坦长度以及爆炸特征值的变化规律。结果表明,在常温常压下,当点火能为40 J时：利用光测法得到的8%甲烷与75 g/m³煤尘混合物的燃烧速度为0.437 m/s,而根据压力-时间关系得到的混合物燃烧速度为0.459 m/s,两者符合较好;用火焰厚度与马克斯坦长度判定的火焰发展趋势相同,即向外传播的火焰趋于稳定;爆炸物的爆炸特征值最大值出现在0.5 m处,壁面的爆炸特征值偏小。     

谷值V~2控制Boost变换器的精确建模与动力学分析

建立了谷值V2控制Boost变换器的离散迭代映射模型,在此基础上得到了输入电压、输出电容及其等效串联电阻(equivalent series resistance,ESR)变化时的分岔图,推导了不动点处的雅可比矩阵,利用特征值和最大Lyapunov指数对系统进行了稳定性分析,并验证了分岔图的正确性.重点研究了输入电压和输出电容及其ESR对谷值V2控制Boost变换器的动力学特性的影响.研究结果表明,输入电压增大时,变换器从周期1态经历1次倍周期分岔和边界碰撞分岔进入混沌状态;输出电容及其ESR具有相同的分岔路由,随着输出电容及其ESR的逐渐减小,变换器具有从周期1态经历周期2态、周期4态、周期8态、逐渐演变到混沌态的动力学行为.最后,用仿真和实验结果验证了本文理论分析的正确性.     

Free wave propagation in two-dimensional periodic plates

The propagation of flexural waves in a two-dimensional periodic plate which rests on an orthogonal array of equi-spaced simple line supports has been investigated. A type of plane wave motion has been considered. An energy method has been developed to predict the frequency of wave propagation in terms of the propagation constants. A Galerkin type of analysis has been used, incorporating assumed complex modes of wave motion for the identical rectangular elements of the periodic plate. Expressions for the frequency have been obtained firstly by using simple polynomial modes for the plate displacements, and then (alternatively) by using characteristics beam function modes. The use of these different modes has first been demonstrated by applying them to the analysis of wave propagation in periodic beams. A single polynomial mode which satisfies the geometric and wave-boundary conditions of the periodic plate element leads to an elegant expression relating the frequency and the wave propagation constants in the first propagation band. The frequencies so obtained compare well with those found from a multi-mode, characteristic beam function analysis. The latter involves much more algebra, is solved as an eigenvalue problem, and yields the frequencies in as many propagation bands as are desired. The bounding frequencies and corresponding wave motions in the first and higher propagation bands have been identified, and it has been shown that the propagation bands can overlap. Consideration has been given to one-dimensional “strip” structures which are equivalent to the two-dimensional plate when a plane wave in a general direction is propagating. Furthermore, it is shown that the natural frequencies of finite rectangular periodic plates can be obtained very simply from the results of the wave propagation analysis.     

Propagation of guided elastic waves in 2D phononic crystals

The phononic band structure of two-dimensional phononic guides is numerically studied. A plane wave expansion method is used to calculate the dispersion relations of guided elastic waves in these periodic media, including 2D phononic plates and thin layered periodic arrangements. We show that, for any guided elastic wave, Lamb or generalised Lamb modes, stop bands appear in the dispersion curves, displaying a phononic band structure in both cases.     

Low-frequency band gaps in one-dimensional thin phononic crystal plate with periodic stubbed surface

Using supercell plane wave expansion method, the Lamb wave band structure of one-dimensional thin plate with periodic stubs is investigated. The numerical results show that flat bands will appear and band gap can exist in a low-frequency domain. The position of the flat bands and width of the low-frequency Lamb wave band gap can be tuned by the stub height, plate thickness and filling fraction. The band gap is obtained by opening the folding points of the same plate modes not the crossing point of different plate mode when the stub height is small.     

A study of modal characteristics and the control mechanism of finite periodic and irregular ribbed plates

An analytical solution is presented in this paper to investigate the control mechanism and modal characteristics of finite periodic and irregular ribbed plates. Peak responses of a finite periodic ribbed plate were examined where they were grouped into two sets of propagation zones according to the coupling mechanism at beam/plate interfaces. Details of modal characteristics in pass bands of the periodic ribbed plate were elucidated and the control mechanism was discussed. Modes in each pass band that are governed by shear force couplings were characterized by one of the beam flexural modes whose modal responses could be represented approximately by those of the corresponding orthotropic plate modes. Modes in the second set of pass bands were found to retain the resonance frequencies of the corresponding modes of the unribbed base plate. Higher order orthotropic plate modes were also identified, which could not be grouped into any pass bands defined by the classical periodic theory. The control mechanism leading to vibration confinement in disordered and irregular ribbed plates was also discussed. It was found that beam spacing irregularity attributes to localization of the group of modes associated with flexural wave couplings but not the group of modes associated with moment couplings.     

Localisation of elastic waves in two-dimensional randomly disordered solid phononic crystals

Combined with the supercell technique, the plane wave expansion method is used to calculate the band structures of the two-dimensional solid–solid phononic crystals with the random disorders in either radius or location of the scatterers. Phononic systems with plumbum scatterers embedded in an epoxy matrix are calculated in detail. The influences of the disorder degree on the band structures for both anti-plane and in-plane wave modes are investigated. It is found that, with increase of the disorder degree, the band gaps become narrower with more flat bands appearing in the gaps. Both displacement distribution and response spectra show that at the flat bands, elastic waves are localised due to the presence of the disorder. Wave localisation is more pronounced at the flat bands near the lower/upper edge for the radius/location disorder. Wave propagation and localisation in a randomly disordered system with a point defect is also studied. The influence of the disorder on the point-defect state is discussed. The results show that the disorder can tune the frequencies of the defect states. It is particularly noticed that the double degenerate mode appearing within the gap of the mixed in-plane waves is split up into two separated ones when the random disorder is introduced into the system. Generally, the influence of the disorder is more pronounced for the mixed in-plane modes than the anti-plane modes. The analysis of this paper is relevant to the assessment of the influences of manufacture errors on wave behaviours in phononic crystals as well as the possible control of wave propagation by intentionally introducing disorders into periodic systems.     

二维色散和各向异性磁化等离子体光子晶体色散特性研究

采用平面波展开法和时域有限差分法研究了二维色散和各向异性磁化等离子体光子晶体的色散特性.当波矢在周期平面时,由于外加磁场的作用使TE模的色散曲线出现两个不同区域的平带,改变磁场的大小不但可以控制平带的位置,而且可以控制光子带隙的位置和大小.增大背景材料的介电常数,可以形成全方向光子带隙,随着背景材料介电常数的增加,带隙的中心位置降低但带隙宽度增加.当波矢偏离周期平面时,色散曲线不再分为TE和TM模,随着非周期平面波矢的增加,带隙位置上移,带隙宽度先增加随后基本保持不变.     

Hybrid phononic crystal plates for lowering and widening acoustic band gaps

We propose hybrid phononic-crystal plates which are composed of periodic stepped pillars and periodic holes to lower and widen acoustic band gaps. The acoustic waves scattered simultaneously by the pillars and holes in a relevant frequency range can generate low and wide acoustic forbidden bands. We introduce an alternative double-sided arrangement of the periodic stepped pillars for an enlarged pillars’ head diameter in the hybrid structure and optimize the hole diameter to further lower and widen the acoustic band gaps. The lowering and widening effects are simultaneously achieved by reducing the frequencies of locally resonant pillar modes and prohibiting suitable frequency bands of propagating plate modes.     

Band gap behaviours of periodic magnetoelectroelastic composite structures with Kagome lattices

In this paper, the elastic wave propagation in periodic cylinder magnetoelectroelastic composite structures is studied using the plane wave expansion method. The band structure characteristics of magnetoelectroelastic rods embedded in polymer matrix and the reverse case are investigated taking the electric, magnetic and mechanical coupling effects into account. The generalised eigenvalue equation is derived to analyse the in-plane and out-of-plane modes, respectively. The numerical calculations for both the cases with Kagome lattices are performed. The relation between the gap widths and filling fractions are discussed in detail. The effects of the magnetoelectricity on the band structures and widths of band gaps are analysed. The band gap characteristics are illustrated further and the results will be helpful to design such kind of composite structures.     

Reflection-free one-way edge modes in a gyromagnetic photonic crystal

We point out that electromagnetic one-way edge modes analogous to quantum Hall edge states, originally predicted by Raghu and Haldane in 2D photonic crystals possessing Dirac point-derived band gaps, can appear in more general settings. We show that the TM modes in a gyromagnetic photonic crystal can be formally mapped to electronic wave functions in a periodic electromagnetic field, so that the only requirement for the existence of one-way edge modes is that the Chern number for all bands below a gap is nonzero. In a square-lattice yttrium-iron-garnet crystal operating at microwave frequencies, which lacks Dirac points, time-reversal breaking is strong enough that the effect should be easily observable. For realistic material parameters, the edge modes occupy a 10% band gap. Numerical simulations of a one-way waveguide incorporating this crystal show 100% transmission across strong defects.     

基于波传播法的周期复合板振动带隙衰减特性研究

运用波传播法对有限和无限周期对边简支复合板的振动带隙衰减特性进行了研究.在建立相邻板结构边界连续方程的基础上, 分别运用传递矩阵和Bloch定理建立了有限和无限周期复合板的耦合运动方程, 并详细对比分析了有限和无限周期复合板带隙衰减特性的关联关系.研究表明: 周期板结构的振动带隙频率范围与激励方式和激励位置是相关的, 若周期复合板在宽度方向按某阶模态进行线激励, 则该激励下的振动带隙与无限周期复合板在该阶模态下的振动带隙是一致的; 若周期板在点激励作用, 则该点激励下的振动带隙是参与振动的各阶模态振动带隙的交集. 此外, 还进一步研究了结构阻尼对振动衰减带隙的影响. 关键词： 周期复合板 带隙衰减特性 波传播法 结构阻尼