声学超表面的非对称声分束特性研究

非对称声分束超表面是由人工微单元结构按照特定序列构建的二维平面结构,可将垂直入射的声波分成两束传播方向和分束比自由调控的透射波,在声功能器件设计及声通信领域具有广泛的应用前景。本文系统研究了一种实现非对称声分束的设计理论和实现方法,基于局域声功率守恒条件研究了声分束器的设计理论、阻抗矩阵分布、法向声强分布、声压场分布等。利用遗传算法对四串联共振腔结构进行参数优化实现了声分束器所需的阻抗矩阵分布,声压场分布表明声波入射到声分束器后在入射侧激发出两列传播方向相反且幅值和衰减系数均相同的表面波,实现了入射侧与透射侧的局域声功率相互匹配。声波经过声分束器后被分为两束透射波,两束透射波的折射角和透射系数与理论值十分吻合,证明了设计理论及实现方法的正确性和可行性。本文的研究工作可以为新型非对称声分束结构设计提供理论参考、设计方法和技术支持,并促进其在工程领域的实际应用。     

Hamiltonian and long paths in bipartite graphs with connectivity

Let G be a graph, $\nu (G)$ the order of G, $\kappa (G)$ the connectivity of G and k a positive integer such that $k\le (\nu (G)?2)/2$. Then G is said to be k-extendable if it has a matching of size k and every matching of size k extends to a perfect matching of G. A Hamiltonian path of a graph G is a spanning path of G. A bipartite graph G with vertex sets $V_1$ and $V_2$ is defined to be Hamiltonian-laceable if such that $|V_1|=|V_2|$ and for every pair of vertices $p\in V_1$ and $q\in V_2$, there exists a Hamiltonian path in G with endpoints p and q, or $|V_1|=|V_2|+1$ and for every pair of vertices $p,q\in V_1,p\ne q$, there exists a Hamiltonian path in G with endpoints p and q. Let G be a bipartite graph with bipartition $(X,Y)$. Define $bn(G)$ to be a maximum integer such that $0\le bn(G)<min\{|X|,|Y|\}$ and (1) for each non-empty subset S of X, if $|S|\le |X|?bn(G)$, then $|N(S)|\ge |S|+bn(G)$, and if $|X|?bn(G)<|S|\le |X|$, then $N(S)=Y$; and (2) for each non-empty subset S of Y, if $|S|\le |Y|?bn(G)$, then $|N(S)|\ge |S|+bn(G)$, and if $|Y|?bn(G)<|S|\le |Y|$, then $N(S)=X$; and (3) $bn(G)=0$ if there is no non-negative integer satisfying (1) and (2).Let G be a bipartite graph with bipartition $(X,Y)$ such that $|X|=|Y|$ and $bn(G)>0$. In this paper, we show that if $\nu (G)\le 2\kappa (G)+4bn(G)?4$, then G is Hamiltonian-laceable; or if $\nu (G)>6bn(G)?2$, then for every pair of vertices $x\in X$ and $y\in Y$, there is an $(x,y)$-path P in G with $|V(P)|\ge 6bn(G)?2$. We show some of its corollaries in k-extendable, bipartite graphs and a conjecture in k-extendable graphs.     

Stochastic sensitivity analysis of coupled acoustic-structural systems under non-stationary random excitations

This paper presents a new sensitivity analysis method for coupled acoustic–structural systems subjected to non-stationary random excitations. The integral of the response power spectrum density (PSD) of the coupled system is taken as the objective function. The thickness of each structural element is used as a design variable. A time-domain algorithm integrating the pseudo excitation method (PEM), direct differentiation method (DDM) and high precision direct (HPD) integration method is proposed for the sensitivity analysis of the objective function with respect to design variables. Firstly, the PEM is adopted to transform the sensitivity analysis under non-stationary random excitations into the sensitivity analysis under pseudo transient excitations. Then, the sensitivity analysis equation of the coupled system under pseudo transient excitations is derived based on the DDM. Moreover, the HPD integration method is used to efficiently solve the sensitivity analysis equation under pseudo transient excitations in a reduced-order modal space. Numerical examples are presented to demonstrate the validity of the proposed method.     

水下对转螺旋桨流致辐射噪声机理与预报方法*

水下对转螺旋桨流致辐射噪声的预报对于水下目标的特征提取和分类识别具有重要意义。由桨叶的旋转引起的湍流场是水下对转螺旋桨流致辐射噪声的源场。分述了水下对转螺旋桨湍流边界层脉动、旋转干涉效应和空化效应引发的水动力噪声机制和研究进展,比较了目前工程应用中的3种对转螺旋桨流致辐射噪声预报方法的特点。在分析对转螺旋桨流致辐射噪声数值预报难点的基础上,综述了对转螺旋桨流致辐射噪声计算方法的研究进展,指出间接数值模拟方法是工程中进行对转螺旋桨流致辐射噪声预报的有效方法。     

单颗金刚石切削无氧铜的声发射关联维特征*

声发射技术可以实现无氧铜切削加工特征的监测与评价。采用声发射技术监测单颗金刚石磨粒旋转切削无氧铜，利用G-P算法重构出声发射时域信号相空间，采用自相关函数法计算出相空间时间延迟参数，通过相空间双对数曲线的计算，得到不同切削工况下的关联维数。研究结果表明，进给速度和切削速度对声发射信号影响较不显著，切深与声发射信号振幅呈正效应关系；声发射信号双对数曲线呈现阶段性增加趋势，并逐渐收敛于饱和状态，关联维数随着嵌入维数的增加先快速下降后趋于平稳；金刚石切削无氧铜的声发射信号具有混沌运动变化特性，在较小嵌入维数时，关联维数与切深和切削速度呈现线性负效应关系，与进给速度呈现线性正效应关系。该研究为无氧铜的切削加工提供理论参考。     

Monochromatic k-edge-connection colorings of graphs

A path in an edge-colored graph $G$ is called monochromatic if any two edges on the path have the same color. For $k\ge 2$, an edge-colored graph $G$ is said to be monochromatic $k$-edge-connected if every two distinct vertices of $G$ are connected by at least $k$ edge-disjoint monochromatic paths, and $G$ is said to be uniformly monochromatic $k$-edge-connected if every two distinct vertices are connected by at least $k$ edge-disjoint monochromatic paths such that all edges of these $k$ paths are colored with a same color. We use $m{c}_k\left(G\right)$ and $um{c}_k\left(G\right)$ to denote the maximum number of colors that ensures $G$ to be monochromatic $k$-edge-connected and, respectively, $G$ to be uniformly monochromatic $k$-edge-connected. In this paper, we first conjecture that for any $k$-edge-connected graph $G$, $m{c}_k\left(G\right)=e\left(G\right)-e\left(H\right)+\lfloor \frac{k}{2}\rfloor$, where $H$ is a minimum $k$-edge-connected spanning subgraph of $G$. We verify the conjecture for $k=2$. We also prove the conjecture for $G=K_{k+1}$ and $G=K_{k,n}$ with $n\ge k\ge 3$. When $G$ is a minimal $k$-edge-connected graph, we give an upper bound of $m{c}_k\left(G\right)$, i.e., $m{c}_k\left(G\right)\le k-1$. For the uniformly monochromatic $k$-edge-connectivity, we prove that for all $k$, $um{c}_k\left(G\right)=e\left(G\right)-e\left(H\right)+1$, where $H$ is a minimum $k$-edge-connected spanning subgraph of $G$.     

Meshless acoustic analysis using a weakly singular Burton-Miller boundary integral formulation

The Burton-Miller boundary integral formulation is solved by a complex variable boundary element-free method (CVBEFM) for the boundary-only meshless analysis of acoustic problems with arbitrary wavenumbers. To regularize both strongly singular and hypersingular integrals and to avoid the computation of the solid angle and its normal derivative, a weakly singular Burton-Miller formulation is derived by considering the normal derivative of the solid angle and adopting the singularity subtraction procedures. To facilitate the implementation of the CVBEFM and the approximation of gradients of the boundary variables, a stabilized complex variable moving least-square approximation is selected in the meshless discretization procedure. The results show the accuracy and efficiency of the present CVBEFM and reveal that the method can produce satisfactory results for all wavenumbers, even for extremely large wavenumbers such as k = 10 000.     

Elastic,dielectric, and piezoelectric characterization of 0.92Pb(Zn1/3Nb2/3)O3-0.08PbTiO3 single crystal by Brillouin scattering

In this paper,a complete set of elastic,piezoelectric,and dielectric constants of high-quality tetragonal poled0.92Pb(Zn_(1/3)Nb_(2/3))O_3-0.08PbTiO_3 single crystal grown by the modified flux method is determined using high-resolution Brillouin scattering.A comparison is made between the results obtained by a hybrid method combining ultrasonic and resonant techniques and the results obtained by the Brillouin scattering.The elastic,piezoelectric,and dielectric constants obtained by the two methods are similar.The Brillouin spectrum consists of one longitudinal and two transverse acoustic phonon modes,and the variations of the Brillouin shifts,the full widths at half maximum,and the scattering intensities of these modes with scattering angle 9 are investigated.In particular,the transverse acoustic phonon mode at the lowfrequency becomes markedly soft from 28.2 GHz to 18.4 GHz and broadens gradually with the increase of θ,while its intensity decreases gradually as compared with that of the original one.The possible origins of the results are discussed.