Interpretation of solar microwave C type burst spectra in terms of magnetic nonhomogeneity

The solar radio spectra of the gyro-synchrotron radiation without absorption from mildly relativistic non-thermal electron have been presented using the model with the spherical symmetric nonhomogeneity. These spectra have the following features: (i) Twists and turns of the spectra, which appear at the joint between the medium and high frequencies, (ii) Flux density drop at the lower frequencies. Even if there are no absorption in the radio sources, flux density drop at the lower frequencies is still present because of magnetic nonhomogeneity. (iii) These theoretical spectra belong to C type. This provides us a new interpretation for the observed solar burst C type spectra. Project supported by the National Natural Science Foundation of China.     

非均匀变厚度梁的动力响应的一般解

在本文中提出一个新方法——阶梯折算法来研究在任意载荷下任意非均匀和任意变厚度伯努利-欧拉梁的动力响应问题.研究了自由振动和强迫振动.新方法需要将区间离散为一定数目的元素,每个元素可看作是均匀和等厚度的.因此均匀、等厚度梁的一般解可在每个元素上应用.然后用初参数表示的整个梁的一般解使之满足相邻二元素间的物理和几何连续条件,这样就可以得到解析形式的自由振动的频率方程和解析形式的强迫振动的最终解,它化为求解二元线性代数方程,与离散元素的数目无关.现在的方法可推广应用至任意非均匀及任意变厚度有粘滞性和其他种类的梁以及其他结构元件问题上去.     

端面抽运板条介质抽运光束不均匀性及改善方法研究

 基于Zemax软件下的非序列模式(non-sequential mode)光线追迹法,分别模拟复合结构板条介质抽运端面和掺杂介质区工作端面上的光强度分布。由追迹结果可知,经过整形,在抽运面强度分布均匀的抽运光束经过非掺杂介质区传播到掺杂介质工作端面后光束分布均匀性大大降低。研究表明复合结构板条介质中非掺杂介质区影响了抽运光束,即抽运光在非掺杂介质区传播过程中发生全内反射,导致部分光束在实际工作端面的部分区域发生叠加,从而致使实际工作端面抽运光束分布不均匀。最后,依据平面波导匀化理论,从改变非掺杂介质区长度和入射光束发散角大小角度出发,提出改善抽运光束均匀性的思路,并进行了模拟验证。     

General analytic solution of dynamic response of beams with nonhomogeneity and variable cross-section

In this paper, a new method, the step-reduction method, is proposed to investigate the dynamic response of the Bernoulli-Euler beams with arbitrary nonhomogeneity and arbitrary variable cross-section under arbitrary loads. Both free vibration and forced vibration of such beams are studied. The new method requires to discretize the space domain into a number of elements. Each element can be treated as a homogeneous one with uniform thickness. Therefore, the general analytical solution of homogeneous beams with uniform cross-section can be used in each element. Then, the general analytic solution of the whole beam in terms of initial parameters can be obtained by satisfying the physical and geometric continuity conditions at the adjacent elements. In the case of free vibration, the frequency equation in analytic form can be obtained, and in the case of forced vibration, a final solution in analytical form can also be obtained which is involved in solving a set of simultaneous algebraic equations with only     

Thermal stress intensity factor for functionally gradient half space with an edge crack under thermal load

Summary The aim of this work is to investigate the thermal stress intensity factor of a functionally gradient half space with an edge crack under a steady heat flux. All material properties of the functionally gradient half space, except for the coefficient of linear thermal expansion, are exponentially dependent on the distance from the boundary of the plate. The coefficient of linear thermal expansion is assumed to be two-dimensionally dependent. The problem is reduced to a singular integral equation by using the Fourier transform. The thermal stress intensity factor versus the nonhomogeneous material parameters is calculated and represented in figures. The numerical results show that thermal stress intensity factor is dramatically decreased when the material nonhomogeneous parameters are appropriately selected.     

Light-induced nonhomogeneity and gradient bending in photochromic liquid crystal elastomers

The recently reported opto-mechanical effect of some photochromic liquid crystal elastomers (LCEs) is studied. It is found that in such LCEs, material parameters such as the Young’s modulus and the stress-free strains will become nonhomogeneous under light irradiations. One may call them the light-induced functionally gradient materials. Analytical expressions for the dependence of the material parameters on the space variable and possibly on the time variable are obtained. Exponential dependence can be derived under certain approximations. As an example, the light-induced bending of a beam is studied. Two neutral planes are found in the beam. Thus, along the thickness of the beam, there are extensions in the upper and lower parts and contractions in the middle.     

Estimation of the energetic nonhomogeneity of the surface of oxide and carbon materials

The molecular statistical method for evaluating the distribution of active sites of various adsorbents relative to their energies has been improved. This method is used not only for the treatment of experimental data on the adsorption of hydrocarbons on various adsorbents, which is the usual procedure, but also data on the adsorption of polar water and methanol molecules on the active sites of adsorbent surfaces. Two types of active sites differing in energy have been shown to exist on the surface of graphitized carbon black, the complex shungite carbon/mineral adsorbent, and modified Silochrom. Chromatographic, calorimetric, and structural adsorption data were used to establish the relationship between the observed maxima of the energy distribution function of the adsorption sites with concrete adsorption sites or pores of the surface, on which the molecules are adsorbed. Translated from Teoreticheskaya i éksperimental'naya Khimiya, Vol. 44, No. 5, pp. 315–320, September–October, 2008.     

Green functions for a compressible linearly non homogeneous half-space

Summary The paper presents a study of time-harmonic vibration of a half-space possessing a shear modulus linearly increasing with depth. Completing the previous paper [1], where the time-harmonic vibration of an incompressible half-space has been considered, the problem is now solved for a compressible as well as an incompressible material. The half-space is subjected to a vertical or horizontal surface load. The solution is represented in terms of Fourier-Bessel integrals containing functions of depth coordinate that are expressed through confluent hypergeometric functions. Numerical results concerning surface displacements due to a point force are given for a wide range of frequency variations and degree of non-homogeneity. The results show that, as compared to the homogeneous case, non-homogeneity can considerably increase vibration amplitudes at large distances from the applied force. Received 19 August 1996; accepted for publication 16, December 1996     

隧道洞口段非均质及各向异性土质裂缝仰坡稳定性上限解

针对忽略岩土体非均质和各向异性将导致边坡稳定性评价产生误差的问题，应用极限分析上限理论及抗剪强度系数折减法，推导土体强度非均质和各向异性影响下隧道洞口含裂缝仰坡稳定性解析式，探究土体强度非均质和各向异性对仰坡稳定性系数、坡顶裂缝位置、隧道拱顶失稳范围及仰坡安全系数的影响。结果表明，裂缝深度及坡角越大，仰坡稳定性系数越小；非均质系数越大和各向异性系数越小，维持仰坡稳定的临界坡高越大；非均质系数及各向异性系数越大，裂缝距坡顶边缘越远，隧道拱顶失稳范围越大；非均质系数增大有利于仰坡稳定，而各向异性系数越大仰坡越易失稳。