SOLITARY WAVES IN FINITE DEFORMATION ELASTIC CIRCULAR ROD

A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes two nonlinear terms caused by finite deformation and double geometric dispersion effects caused by transverse inertia and transverse shearing strain. Nonlinear wave equation and corresponding truncated nonlinear wave equation were solved by the hyperbolic secant function finite expansion method. The solitary wave solutions of these nonlinear equations were obtained. The necessary condition of these solutions existence was given also.     

The Structure Functions of the Velocity and Temperature Fields from the Perspective of Dimensional Scaling

In this paper, dimensional scaling is used to describe the turbulence structure of the velocity and temperature fields in the inertial range and the far dissipation range as well as the intermediate transition range under locally isotropic conditions at sufficiently large Reynolds numbers. This kind of scaling is expressed in a strictly mathematical manner employing dimensional π -invariants analysis. It is shown that in the case of the asymptotic solutions for either the inertial range or the far dissipation range only one π number occurs that has to be considered as a non-dimensional universal constant. This π number may be determined theoretically or/and empirically. In the case of the transition range two π numbers occur. Consequently, a universal function is established that has to be derived theoretically or/and empirically, too. Here, Batchelor's [7] classical interpolation formula for the turbulence structure of the velocity field and the empirical one of Stolovitzky et al. [59], both may serve as universal functions, are compared with the results provided by numerical solutions of Kolmogorov′s [32] structure equation for the velocity field. It is shown that these interpolation formulae match not only the asymptotic solutions of the inertial range and the far dissipation range, respectively, but also these numerical results in an excellent manner. The former may be considered as necessary condition and the latter as sufficient condition. In the case of the temperature field results of the corresponding universal function are predicted using Yaglom's [63] structure equation. These results also match the corresponding asymptotic solutions of both the inertial range and the far dissipation range. However, in contrast to the case of the velocity field, the predicted universal function for the temperature field may notably overshoot its asymptotic solution for the inertial range. This overshooting occurs in the transition range and may be considered as an analogue to the so-called Hill ‘bump’ that usually occurs in the high-wave number portion of the temperature spectrum.     

各向同性和横观各向同性材料的统一点力解

本文根据横观各向同性弹性力学的通解获得了无限体的点力解，由它可以直接退化到各向同性情形的Ｋｅｌｖｉｎ解，利用这个点力解编制的边界元法程序，适用于横观各向同性材料也适用于各向同性材料，因此是真正的统一点力解。还用边界元法计算了两个数值例题。     

Plane waves in a semi-infinite fluid saturated porous medium

The field equations governing the propagation of waves in an incompressible liquid-saturated porous medium are investigated and a general solution is presented. It has been revealed that coupled longitudinal and transverse waves propagate in the porous medium. The propagation of transverse waves in the fluid phase is completely due to the interaction between the solid and fluid phases. The dispersion relationship and attenuation features are discussed. Unlike other investigations, all explicit forms of the arguments are derived. The reflection of the plane harmonic waves at the plane, traction-free boundary, which shows the influence of the dissipation on the velocity, and the attenuation coefficients of the reflected waves is studied. It is of interest that pore pressure is produced in the process of reflection, even in the case of the incidence of transverse waves.     

考虑畸变影响的箱梁横向弯矩计算方法

为研究偏心垂向荷载作用下梯形截面单室箱梁的横向弯矩,对框架分析法计算箱梁横向弯矩的方程进行优化,并在刚性支承法的基础上提出一种更加简单的横向弯矩计算方法;与框架分析法不同,横向弯矩可采用能量变分法求解,建立以箱梁顶板剪力差为未知量的四阶控制微分方程,采用比拟的弹性地基梁解法解出剪力差,得出梯形截面单室箱梁横向弯矩的能量变分法解。对几种箱梁横向弯矩计算方法用两个算例进行验证,结果表明,能量变分法解将箱梁底板上的弯矩误差绝对值由15.41%降到了9.68%;本文方法得出的横向弯矩结果和有限元结果吻合较好,弯矩误差绝对值最大不超过6.01%;本文方法和能量变分法可有效降低箱梁底板上的弯矩误差,计算精度得到提高。     

附加约束阻尼层对星箭系统动特性的影响分析

在星箭连接支架外表面附加约束阻尼层可抑制星箭对接界面的振动,从而降低卫星在发射过程中所承受的振动和噪声载荷.本文将有限元技术与矩阵特征值摄动分析方法相结合,就卫星支架局部修改(附加约束阻尼层)对星箭系统动态特性的影响进行了分析.以已有星箭系统结构的模态信息为基础,给出了支架部位附加约束阻尼层后星箭系统动态特性变化的定量计算方法,并证明了该减振技术能够不明显的改变原星箭系统的固有特性.     

多层横观各向同性圆柱壳的三维弹性理论解

本文从三维弹性理论出发,用特征函数法研究多层横观各向同性圆柱壳的轴对称问题.把位移和应力分量的齐次解表达成特征函数展开式,并把特解部分用Fourier级数表示.以多层圆柱壳的内、外柱面作为齐次边界,同时考虑层间的连续条件,推导出问题的特征方程并用Muller法求解.文中运用传递矩阵技术处理多层问题,并用边界型最小二乘配点法处理端部边界条件.作为实例,对双层圆柱壳作了数值计算.     

原位低场核磁共振弛豫法定量监测光催化Cr(Ⅵ)还原反应

本文利用原位低场核磁共振（LF-NMR）技术在真实固液反应环境中对光催化还原Cr（Ⅵ）反应进行了定量研究,并对Ag纳米颗粒负载量不同的Ag担载石墨相氮化碳复合光催化剂（Ag/g-C₃N₄）在可见光照射下催化Cr（Ⅵ）还原为Cr（Ⅲ）的性能进行了研究.研究发现,Ag纳米颗粒负载（负载量分别为1 wt.%、2 wt.%、5 wt.%和10 wt.%）可以有效提高g-C₃N₄的光催化性能;且负载量为5 wt.%时光催化性能最优,为无Ag负载的g-C₃N₄的4倍.此外,本文还通过横向弛豫时间（T₂）定量分析了反应体系中顺磁性Cr（Ⅲ）离子的浓度,证实了采用LF-NMR弛豫法评价光催化Cr（Ⅵ）还原反应性能的可行性.     

Monitoring dendrimer conformational transition using 19F and 1H2O NMR

The conformational transition of a fluorinated amphiphilic dendrimer is monitored by the ¹H signal from water, alongside the ¹⁹F signal from the dendrimer. High-field NMR data (chemical shift δ, self-diffusion coefficient D, longitudinal relaxation rate R₁, and transverse relaxation rate R₂) for both dendrimer (¹⁹F) and water (¹H) match each other in detecting the conformational transition. Among all parameters for both nuclei, the water proton transverse-relaxation rate R₂(¹H₂O) displays the highest relative scale of change upon conformational transition of the dendrimer. Hydrogen/deuterium-exchange mass spectrometry reveals that the compact form of the dendrimer has slower proton exchange with water than the extended form. This result suggests that the sensitivity of R₂(¹H₂O) toward dendrimer conformation originates, at least partially, from the difference in proton exchange efficiency between different dendrimer conformations. Finally, we also demonstrated that this conformational transition could be conveniently monitored using a low-field benchtop NMR spectrometer via R₂(¹H₂O). The ¹H₂O signal thus offers a simple way to monitor structural changes of macromolecules using benchtop time-domain NMR.     

Estimation of isotropic nuclear magnetic shieldings in the CCSD(T) and MP2 complete basis set limit using affordable correlation calculations

A linear correlation between isotropic nuclear magnetic shielding constants for seven model molecules (CH₂O, H₂O, HF, F₂, HCN, SiH₄ and H₂S) calculated with 37 methods (34 density functionals, RHF, MP2 and CCSD(T)), with affordable pcS‐2 basis set and corresponding complete basis set results, estimated from calculations with the family of polarization‐consistent pcS‐n basis sets is reported. This dependence was also supported by inspection of profiles of deviation between CBS estimated nuclear shieldings and shieldings obtained with the significantly smaller basis sets pcS‐2 and aug‐cc‐pVTZ‐J for the selected set of 37 calculation methods. It was possible to formulate a practical approach of estimating the values of isotropic nuclear magnetic shielding constants at the CCSD(T)/CBS and MP2/CBS levels from affordable CCSD(T)/pcS‐2, MP2/pcS‐2 and DFT/CBS calculations with pcS‐n basis sets. The proposed method leads to a fairly accurate estimation of nuclear magnetic shieldings and considerable saving of computational efforts. Copyright © 2013 John Wiley & Sons, Ltd.