Free wave propagation in binary gas mixtures

The problem concerning the propagation of free waves in binary mixtures of monatomic ideal gases is analyzed by using a kinetic model of the Boltzmann equation which is compatible with the two-fluid hydrodynamic theory. Comparison of the theoretical results with available experimental data shows that the two-fluid model equation can be used to describe the wave-vector dependence of the free sound waves in both continuum and kinetic regimes.     

Modeling and analysis of time-dependent processes in a chemically reactive mixture

In this paper, we study the propagation of sound waves and the dynamics of local wave disturbances induced by spontaneous internal fluctuations in a reactive mixture. We consider a non-diffusive, non-heat conducting and non-viscous mixture described by an Eulerian set of evolution equations. The model is derived from the kinetic theory in a hydrodynamic regime of a fast chemical reaction. The reactive source terms are explicitly computed from the kinetic theory and are built in the model in a proper way. For both time-dependent problems, we first derive the appropriate dispersion relation, which retains the main effects of the chemical process, and then investigate the influence of the chemical reaction on the properties of interest in the problems studied here. We complete our study by developing a rather detailed analysis using the Hydrogen–Chlorine system as reference. Several numerical computations are included illustrating the behavior of the phase velocity and attenuation coefficient in a low-frequency regime and describing the spectrum of the eigenmodes in the small wavenumber limit.     

功能梯度圆柱板中的周向衰逝导波

与传播波模态不同,衰逝波模态波数为纯虚数或复数,它们随传播距离呈指数或阻尼式衰减。复数根描述的衰逝波对结构缺陷形状和尺寸的导波检测具有重要作用,但其求解却是非常困难的,通常要借助于各种迭代技术。本文提出一种计算求解衰逝波问题的改进的Legendre正交多项式方法,该方法可将复杂的变系数微分方程组计算转换为特征值求解问题,无需迭代便能计算得到包含实波数域、虚波数域和复波数域的完整的频散曲线。通过具体算例验证了提出方法的正确性。应用提出方法计算了不同梯度圆柱板中的衰逝导波,绘制了三维频散曲线,研究了不同径厚比和梯度场对衰逝导波频散的影响,分析了衰逝导波的位移和应力分布,讨论了衰逝导波的传播特性。     

Symmetric and anti-symmetric Rayleigh–Lamb modes in sinusoidally corrugated waveguides: An analytical approach

The wave propagation analysis in corrugated waveguides is considered in this paper. Elastic wave propagation in a two-dimensional periodically corrugated plate is studied here analytically. The dispersion equation is obtained by applying the traction free boundary conditions. Solution of the dispersion equation gives both symmetric and anti-symmetric modes. In a periodically corrugated waveguide all possible spectral order of wave numbers are considered for the analytical solution. It has been observed that the truncation of the spectral order influences the results. Truncation number depends on the degree of corrugation and the frequency of the wave. Usually increasing frequency requires increasing number of terms in the series solution, or in other words, a higher truncation number. For different degrees of corrugation the Rayleigh–Lamb symmetric and anti-symmetric modes are investigated for their non-propagating ‘stop bands’ and propagating ‘pass bands’. To generate the dispersion equation for corrugated plates with a wide range of the degree of corrugation, appropriate truncation of the spectral orders has to be considered. Analytical results are given for three different degrees of corrugation in three plates. Resonance of symmetric and anti-symmetric modes in these plates, their ‘cut-off’, ‘cut-on’, ‘branch-point’, ‘change-place’, ‘mode conversion’ and ‘pinch points’ at various frequencies are also studied.     

桁架材料弹性波带隙特性分析

研究了弹性波在周期性桁架材料中的传播特性,并根据桁架材料的周期性特点和杆纵向振动模态,给出了基于单胞的桁架材料弹性波色散(dispersion)方程。分析了1维和2维问题的色散特性,研究了相应的弹性波带隙性质;以CAE分析软件为工具平台对桁架材料的带隙特性进行了数值仿真实验,给出了基于谐响应和特征频率变化特征的仿真实验方法。仿真实验确认了所分析的桁架材料的带隙特性,同时说明所用的仿真实验方法是可行的。     

考虑表面张力的非传播孤立波

本文考虑了表面张力,用多重尺度法导出了与立方 Schrodinger 方程相类似的非传播孤立波的基本方程,得到了非传播孤立波解。用毛细重力波理论解释了非传播孤立波横向谐振中波峰尖、波谷平的原因。在σ～kh 平面上首次给出了可产生非传播孤立波的二个参数区,但现有的实验点都在区域(1)中。     

A kinetic–hydrodynamic simulation of microstructure of liquid crystal polymers in plane shear flow

We study the microstructure formation and defects dynamics arising in liquid crystalline polymers (LCPs) in plane shear flow by a kinetic–hydrodynamic coupled model. The kinetic model is an extension of the Doi theory with a non-local intermolecular potential, including translational diffusion and density variation. LCP molecules are ensured anchoring at the boundary by an additional boundary potential, meanwhile mass conservation of LCPs holds in the whole flow region. Plane Couette flow and Poiseuille flow are studied using the kinetic–hydrodynamic model and the molecular director is restricted in the shear plane. In plane Couette flow, the numerical results predict seven in-plane flow modes, including four in-plane modes reported by Rey and Tsuji [Macromol. Theory Simul. 7 (1998) 623–639] and three new complicated in-plane modes with inner defects. Furthermore, some significant scaling properties were verified, such as the thickness of the boundary layer is proportional to molecular length, the tumbling period is proportional to the inverse of shear rate. In plane Poiseuille flow, the micro-morph is quasi-periodic in time when flow viscosity and molecular elasticity are comparable. Different local states, such as flow-aligning, tumbling or wagging, arise in different flow region. The difference of the local states, or difference of the tumbling rates in near-by regions causes defects and form branch pattern in director spatial–temporal configuration figure.     

Non-propagating solitary waves with the consideration of surface tension

In this paper, the governing equation for the non-propagating solitary waves, similar to the cubic Schrödinger equation, is derived by the multiple scales with the consideration of surface tension. The non-propagating solitary wave solution is given. It is explained by the capillary-gravity wave theory that the crests are sharpened and the troughs are flattened in the transversal harmonic of the non-propagating solitary waves. On σ～kh plane, two parameter regions are obtained in which the non-propagating solitary wave can occur, but all existing experimental parameters are in region 1 (Fig. 1).     

Temporal and spatial instability of an inviscid compound jet

This paper examines the linear hydrodynamic stability of an inviscid compound jet. We perform the temporal and the spatial analyses in a unified framework in terms of transforms. The two analyses agree in the limit of large jet velocity. The dispersion equation is explicit in the growth rate, affording an analytical solution. In the temporal analysis, there are two growing modes, stretching and squeezing. Thin film asymptotic expressions provide insight into the instability mechanism. The spatial analysis shows that the compound jet is absolutely unstable for small jet velocities and admits a convectively growing instability for larger velocities. We study the effect of the system parameters on the temporal growth rate and that of the jet velocity on the spatial growth rate. Predictions of both the temporal and the spatial theories compare well with experiment.Dedicated to the memory of Professor Tasos C. Papanastasiou     

The theory of relativistic analytical mechanics of the rotational systems

I'IntroductionThespinningmotionisintrinsicattributeofmicroscopicparticle.In1979,R.BengtssonandS.Frauendorfaccuratlymeasuredthemaximumvolumesofthespinningrotativevelocityof14kindsofnucleons,andtheresultsshowedthatthemaximumvolumesofthespinningrotativevelocityofeachnucleonaredifferent[ll.Withthede\'elopingofmodernscienceandtechnology,moreandmoreexperimentalfactsrelatedtothehighspeedrotationquestions,theEinstein'srelativitytheoryandtherotationaltheoryofclassicalmechanicsarenotsuitabletothesepro…     

On beams made of a phase-transforming material

This paper presents a theory for the mechanics of beams made of single crystals of shape memory alloys. The behavior of such beams can be quite unexpected and complicated due to the presence and propagation of phase boundaries. It is shown that the usual laws of mechanics do not fully determine the propagation of phase boundaries and that there is a need for additional constitutive information in the form of a kinetic relation. A simple experiment to measure this kinetic relation is proposed. Finally, a strategy to use such beams for propulsion at small scales is presented.     

Coupled radially symmetric linear thermoelasticity

In this study we consider linear thermoelastic wave propagation with second sound. We consider two theories; a theory based on the Maxwell-Cataneo relation and a linearized theory based on a simplified form of a generalization of classical thermoelasticity. We consider cylindrically and spherically symmetric longitudinal waves, and for both problems we obtain expressions for the initial discontinuities, and also the time rate of decay of propagating discontinuities. Numerical solutions are obtained from the application of the method of characteristics, and further, a technique is proposed which allows numerical solutions, valid for times large compared with the relaxation time, to be efficiently generated.     

圆管型局域共振声子晶体三维构型振动带隙研究

采用多重多级子结构方法计算具有一定刚度的圆管型局域共振声子晶体三维构型振动带隙特性。考察包裹方向对带隙特性的影响,并对第一带隙上下边界点的单胞振动形式进行分析。结果表明,两种包裹形式都可以得到较低较宽的第一带隙,并且带隙特性相似,因而其周期结构都可以大幅减弱带隙范围内弹性波的传播。但两种构型带隙上下边界点对应振动形式不同,此外带隙特性还受单胞尺寸的影响。通过给定评价指标得到相关材料参数与带隙特性关系的相图,由此分析包裹层材料属性对带隙特性的影响。     

Wave propagation in a transversely isotropic solid cylinder of arbitrary cross-sections immersed in fluid

The wave propagation in an infinite, transversely isotropic solid cylinder of arbitrary cross-section immersed in fluid is studied using the Fourier expansion collocation method, within the framework of the linearized, three-dimensional theory of elasticity. The equations of motion of solid and fluid are respectively formulated using the constitutive equations of a transversely isotropic cylinder and the constitutive equation of an inviscid fluid. Three displacement potential functions are introduced to uncouple the equations of motion along the radial, circumferential and axial directions. The frequency equations of longitudinal and flexural (symmetric and antisymmetric) modes are analyzed numerically for an elliptic and cardioidal cross-sectional transversely isotropic solid cylinder of arbitrary cross-section immersed in fluid. The computed non-dimensional wavenumbers are presented in the form of dispersion curves for the material zinc. The general theory can be used to study any kind of cylinder with proper geometric relations.     

Freeting fatigue strength of mechanical joints

An analytical approach to the calculation of fretting fatigue strength of mechanical joints based on a stress model of the fretting fatigue damage mechanism has been presented. The fretting fatigue limit has been defined as a stress (expressed by the threshold stress intensity factor) required for further propagation of the non-propagating main fatigue crack appearing in a cyclically loaded member. Some practical recommendations resulting from the theory have been suggested.     

Linear stability analysis of supersonic axisymmetric jets

Stabilities of supersonic jets are examined with different velocities, momentum thicknesses, and core temperatures. Amplification rates of instability waves at inlet are evaluated by linear stability theory (LST). It is found that increased velocity and core temperature would increase amplification rates substantially and such influence varies for different azimuthal wavenumbers. The most unstable modes in thin momentum thickness cases usually have higher frequencies and azimuthal wavenumbers. Mode switching is observed for low azimuthal wavenumbers, but it appears merely in high velocity cases. In addition, the results provided by linear parabolized stability equations show that the mean-flow divergence affects the spatial evolution of instability waves greatly. The most amplified instability waves globally are sometimes found to be different from that given by LST.     

The modes of an open resonator with plane circular mirrors

Summary A new method is developed to calculate the frequencies, amplitudes, and energy losses of the modes of an open resonator consisting of two plane circular mirrors.The present theory does not suffer from some of the disadvantages of earlier theories. Numerical results are given for a resonator with a small Fresnel number.     

Electromagnetism in steadily rotating matter

Several writers have proposed quasistatic theories of moving magnetized bodies, neglecting the induced electric fields. Obviously, this excludes the possibility of analyzing radiation, which I can tolerate. However, time independent fields have been observed in some steadily rotating magnetized bodies, in particular. I will review experimental evidence for such cases, paying attention to the observed induced electric fields. It turns out that these tend to be very small in dielectrics, but not in conductors. For the latter, I will suggest a rather simple way of modifying theories to account for them. Also, for more general theories of electromagnetism, I will compare two old schemes, a non-relativistic one due to Maxwell and Lorentz and a relativistic scheme proposed by Minkowski. Among workers interested in continuum theory, the former seems to be more popular, but experimental evidence favors the latter over the former and one modern theory.     

桁架结构稳定分析的几何非线性欧拉稳定理论

目前,桁架结构稳定分析有两个理论:经典的特征值理论和几何非线性临界点理论。前者发展较早,在许多结构力学书中都有叙述。但是经过工程应用检验,它过高地估计了结构抗稳定的能力。后者是20年前提出的,提出者认为适用于所有的扁桁架。经过几年的研究,作者连续提出三个稳定理论:线性与非线性欧拉理论;非线性临界点-欧拉理论和两个计算方法,进行桁架结构的线性和非线性截面优化设计。经过理论研究和对前人文献中数值例题的计算和比较,发现特征值理论不符合实际,临界点理论只适用于大扁度的桁架,而不适用于一切扁桁架。研究结果提供了若干有用的结论,给出了各种稳定理论的适用范围,指出了国际文献中若干例题的正确和错误,补充了桁架结构的稳定分析理论,使之更为完整和实用了。     

Folding beam-type piezoelectric phononic crystal with low-frequency and broad band gap

A folding beam-type piezoelectric phononic crystal model is proposed to isolate vibration. Two piezoelectric bimorphs are joined by two masses as a folding structure to comprise each unit cell of the piezoelectric phononic crystal. Each bimorph is connected independently by a resistive-inductive resonant shunting circuit. The folding structure extends the propagation path of elastic waves, while its structure size remains quite small. Propagation of coupled extension-flexural elastic waves is studied by the classical laminated beam theory and transfer matrix method. The theoretical model is further verified with the finite element method(FEM). The effects of geometrical and circuit parameters on the band gaps are analyzed. With only 4 unit cells, the folding beam-type piezoelectric phononic crystal generates two Bragg band gaps of 369 Hz to1 687 Hz and 2 127 Hz to 4 000 Hz. In addition, between these two Bragg band gaps, a locally resonant band gap is induced by resonant shunting circuits. Appropriate circuit parameters are used to join these two Bragg band gaps by the locally resonant band gap.Thus, a low-frequency and broad band gap of 369 Hz to 4 000 Hz is obtained.