Aeolian tones of a plate cascade

A model for the aeroacoustic resonance effects (aeolian tones) excited around a plate cascade in a gas flow is suggested. Methods of calculating the frequencies of natural acoustic oscillations near the cascade are developed. The effect of the cascade geometry and the Mach number of the main flow on the frequencies, abundance, and modes of the natural oscillations is investigated. Anomalous acoustic oscillations near a cyclic plate cascade are shown to exist and are studied. It is shown that there always exist no less than two natural oscillation frequencies in the gas flow near any nontrivial cyclic plate cascade. It has been found that the natural oscillation frequencies can be combined in bundles such that in the case where the number of plates in a period is large the frequencies pertaining to each bundle occupy a certain interval with arbitrary density. The natural oscillations are classified with respect to the form of the eigenfunctions; the classification is based on the theory of representations of groups of locally plane symmetries of the cyclic plate cascade in the solution space. The correctness of the proposed model of the aeroacoustic resonance effects (aeolian tones) excited near a plate cascade in a gas flow is supported by a comparison with the available experimental and theoretical data. On the basis of the investigation performed, some previously unknown physical phenomena are predicted. Thus, the existence of frequency zones or main-flow Mach number ranges on which aeroacoustic resonance phenomena exist near a cyclic cascade with a large number of plates in a period is proved; it is shown that for certain frequencies of the natural oscillations near the cyclic plate cascade the resonance oscillations may be localized in the vicinity of the source; and the existence of narrow-band wave packets slowly propagating along the cascade is demonstrated. Novosibirsk, e-mail: sukhinin@hydro.nsc.ru. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 171–186, March–April, 2000.     

Aeolian tones of a plate in a channel

The conditions of the onset of aeroacoustic resonance phenomena near a plate in a gas flow in a rectangular channel are studied theoretically and experimentally in a two-dimensional formulation. The eigenfrequency as a function of the plate's chord and its position in the channel, the shape of the eigenfunctions, and the effect of the Mach number of the basic gas flow versus the eigenfrequencies and eigenfunctions and the mechanism of self-excited oscillations are determined. A mathematical model by means of which the dependence of the resonance phenomena on the geometrical parameters of the structure were performed is proposed and substantiated. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 69–77, March–April, 1998.     

Elastodynamic Behaviour of Honeycomb Cellular Media

The aim of this contribution is twofold. First, we formulate a continuum model of the elastic cellular medium having a plane periodic structure of an arbitrary lay-out. Second, we apply this model to the analysis of wave propagation and vibration problems in a regular hexagonal (honeycomb) structure. The proposed approach makes it possible to investigate the cell size effect on the global dynamic behaviour of the medium under consideration. It is shown that the overall response of a honeycomb structure is transversaly isotropic and that two special kinds of long waves can propagate in the unbounded medium. The physical correctness and the scope of applicability of the obtained results are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Energy Absorption Characteristics of a Novel Asymmetric and Rotatable Re-entrant Honeycomb Structure

Based on the symmetric re-entrant honeycomb(S-RH)structure with negative Poisson's ratios,a novel asymmetric and rotatable re-entrant honeycomb(AR-RH)structure ...     

Kinetic Relations for a Lattice Model of Phase Transitions

The aim of this article is to analyse travelling waves for a lattice model of phase transitions, specifically the Fermi–Pasta–Ulam chain with piecewise quadratic interaction potential. First, for fixed, sufficiently large subsonic wave speeds, we rigorously prove the existence of a family of travelling wave solutions. Second, it is shown that this family of solutions gives rise to a kinetic relation which depends on the jump in the oscillatory energy in the solution tails. Third, our constructive approach provides a very good approximate travelling wave solution.     

金属蜂窝材料的弹塑性屈曲临界应力值

本文参考Hexcel公司生产的各种规格的金属蜂窝芯,讨论了金属蜂窝芯夹层板承受单轴面外压力时的屈曲模式,发现大多数商用金属蜂窝夹层板受到面外压力作用时发生弹塑性屈曲。基于二维蜂窝结构的代表性单元,建立了金属蜂窝材料弹塑性屈曲的力学模型,进而推导出其临界应力显式公式。该公式反映了蜂窝材料的几何特征及其母材的力学性能,并通过单参数表征金属蜂窝材料的弹塑性屈曲特性。本文还探讨了相对密度和开度角对金属蜂窝材料弹塑性屈曲值的影响规律。最后,通过与已有理论结果和实验结果的比较证实：本文采用的屈曲模式合理,与实验测定值符合较好表明理论预测公式有一定应用价值。     

蜂窝锥壳卫星适配器约束阻尼层振动抑制分析

主要研究在蜂窝锥壳卫星适配器上附加约束阻尼来抑制锥壳传递振动。尽管约束阻尼方面的研究很多，但是大多数都是针对简单的梁或者板结构，而对复杂蜂窝锥壳结构的振动抑制问题研究还很少；为此，通过对蜂窝壳的等效化处理和约束阻尼结构的有限元建模理论分析，建立起卫星一适配器结构在有无附加约束阻尼情况下的有限元模型，进一步通过模态分析和频响分析，得到不同约束阻尼层设计参数对结构振动抑制影响规律。分析结果对于经济有效的设计约束阻尼层和结构减振减重具有较好的参考价值。     

Spatial Dynamics of a Discrete-Time Population Model in a Periodic Lattice Habitat

This paper is devoted to the study of spatial dynamics of a class of discrete-time population models in a periodic lattice habitat. In the general case of recruitment functions, we obtain the existence and computation formula of spreading speeds and show that they coincide with the minimal wave speeds for periodic traveling waves in the positive and negative directions.     

Diffusivity of Lattice Gases

We consider one-component lattice gases with local dynamics and a stationary product Bernoulli measure on ${\mathbb{Z}^d}$ . We study the scaling exponents of the space-time correlations of the system in equilibrium at a given density. We consider a variance-like quantity computed from the correlations called the diffusivity (connected to the Green–Kubo formula) and give rigorous upper and lower bounds on it that depend on the dimension and the local behavior of the macroscopic flux function. Our results identify the cases in which the system scales superdiffusively; these cases have been predicted before, using non-rigorous scaling arguments. Our main tool is the resolvent method: the estimates are the result of a careful analysis of a complicated variational problem.     

Lattice modelling of nematodynamics

The microstructures of textured nematics under shear are investigated by means of a director lattice model incorporating linear shear response as well as elastic interactions between neighbouring directors. The model can be understood as a lattice implementation of the so-called nematodynamics equation for a constant uniaxial order parameter. The dimensionless number governing the model is found to be a mesoscale Ericksen number, which scales with the square of the lattice cell size. It is shown that the predicted microstructure depends strongly on the scale of that number. In particular, disclination loops are found to grow for a range of mesoscale Ericksen numbers, while below or above that they disappear. We apply the model to investigate the director profiles of tumbling nematics. If the orientations are restricted to lying in the vorticity plane, we reproduce the director wind-up layers and distortion saturation predicted theoretically. In the full three-dimensional case an initially polydomain director field evolves to a vorticity-aligned state up to a critical Ericksen number, above which in-plane orientations with distortion saturation are found. The simulations hence reproduce the transition from log-rolling to flow aligning with increasing shear rate observed experimentally. Received: 9 March 1999 /Accepted: 26 July 1999     

Admissible Steady-State Regimes of Crack Propagation in a Square-Cell Lattice

In this paper, the authors return to the classical problem of crack propagation in a lattice. The authors study the problems concerned with the possible regimes of stable steady-state crack propagation in an anisotropic lattice. They show that the steady-state crack propagation is impossible for some relations between the strength and elastic properties of the lattice. The authors also discuss the possibility of stable crack propagation at low speeds.     

关于蜂窝结构面内剪切模量的注记

本文指出Gibson等提出的等壁厚峰窝结构在面内剪力作用下的单元分析不满足平衡条件.本文建立了等壁厚与非等壁厚峰窝结构在面内剪力作用下的合理的单元分析,导出了蜂窝结构面内折合剪切模量G_(xy)的计算公式.本文结果与实验数据符合得很好.     

Study of Two-Frequency Excitation of Turbulent Jets by Fundamental and Subharmonic Tones

The possibility of enhancing or attenuating the mixing in a turbulent jet excited by a two-frequency acoustic signal consisting of fundamental and subharmonic tones is investigated experimentally. It is shown that two-frequency acoustic excitation of the jet is effective only at low frequencies, whereas at high frequencies the effect of two-frequency and single-frequency forcing is almost the same.     

Lattice Boltzmann simulation of flow past a circular cylinder near a moving wall

The two‐dimensional flows past a circular cylinder near a moving wall are simulated by lattice Boltzmann method. The wall moves at the inlet velocity and the Reynolds number ranges from 300 to 500. The influence of the moving wall on the flow patterns is demonstrated and the corresponding mechanism is illustrated by using instability theory. The correlations among flow features based on gap ratio are interpreted. Force coefficients, velocity profile and vortex structure are analyzed to determine the critical gap ratio. Copyright © 2011 John Wiley & Sons, Ltd.     

Lattice Boltzmann simulation of two-sided lid-driven flow in a staggered cavity

In this article, the lattice Boltzmann method is employed in order to explore incompressible fluid flow inside a two-sided lid-driven staggered cavity. Results of the lattice Boltzmann simulation for antiparallel motion of lids are compared with the data from existing literature. For parallel motion of lids, the characteristics of flow pattern for a variety of Re numbers (50–3200) are presented. An asymmetric steady-state flow pattern for parallel motion of lids is obtained.     

安装蜂窝板动力学特性分析及主动控制试验研究

通过对蜂窝芯的等效化处理,建立了ANSYS的壳单元模型,并作有限元模态分析,然后与其试验模态分析结果比较,有限元分析结果和试验结果基本一致。通过ANSYS的PSD随机功率谱分析和模态分析所得振型确定了贴片位置,对蜂窝板进行了压电智能结构振动主动控制试验研究,得到了较好的振动抑制效果。分析结果为仪器安装蜂窝板的设计和实现智能结构控制提供了重要参考依据。     

考虑面层约束时蜂窝芯弹性常数的确定

本文研究了面板约束效应对蜂窝芯弹性性能的影响并基于六边形蜂窝芯夹层板的代表性体单元建立了考虑面板约束效应的蜂窝芯位移模式.根据真实蜂窝芯代表性单元与其等效材料的代表性单元在宏观均匀应变作用下的总弹性应变能相等,导出了蜂窝芯材料等效弹性常数的公式,进一步探讨了蜂窝几何参数对其弹性常数的影响规律.通过与现有理论结果、有限元结果和实验数据进行对比证实本文导出的弹性常数公式具有较好的预报精度.结果表明面板约束对蜂窝芯等效弹性常数有显著影响.     

低速冲击下蜂窝铝板的表面变形检测及其吸能特性研究

铝质蜂窝结构由于其优良的物理和机械性能被广泛地应用于工程结构,因而对其力学性能的研究也成为越来越重要的课题。本文通过摆锤冲击实验,研究了蜂窝铝的动态压缩性能及低速冲击吸能特性。结果表明,在球形摆锤冲击下,蜂窝铝结构具有很好的冲击吸能特性,其变形特征与准静态变形类似。研究中通过高速摄像系统和加速度传感器记录摆锤的加速度衰减过程,通过投影光载波技术获得受冲击蜂窝铝板表面的压缩行为和三维变形形貌。最后利用有限元方法进一步分析了蜂窝铝结构中内部损伤形式等实验中无法观测的现象,并对蜂窝铝结构参数对其吸能行为的影响进行了详细的讨论。     

Lattice Boltzmann simulation of a fluid flow around a triangular unit of three isothermal cylinders

The lattice Boltzmann method is employed to simulate heat transfer in the flow past three arrangements of elliptical and circular cylinders under an isothermal boundary condition. The lattice Boltzmann equations and the Bhatnagar–Gross–Krook model are used to simulate two-dimensional forced convection at 30 ≤ Re ≤ 100 and Pr = 0.71. Pressure distributions, isotherms, and streamlines are obtained. Vortex shedding maps are observed in detail for several cases. The present results are in good agreement with available experimental and numerical data.