Calculation of force constants and mean amplitudes of vibration of octahedral XY6 molecules using frequencies and zeta constants

Expressions involving vibrational frequencies, Coriolis coupling constants and masses of the atoms of the molecule that are invariant under symmetrical isotopic substitutions are derived for octahedral XY₆ molecules following the method given by Jagannathan and others. These invariants are used to calculate the force constants, compliance constants and mean amplitudes of vibration of 13 molecules of XY₆-type.     

Averaging Anisotropic Elastic Constant Data

A method of averaging the data on the anisotropic elastic constants of a material is presented. The anisotropic elastic constants are represented by the elasticity tensor which is expressed as a second rank tensor in a space of six dimensions. The method consists of averaging eigenbases of different measurements of the elasticity tensor, then averaging the eigenvalues referred to the average eigenbasis. The eigenvalues and eigenvectors are obtained by using a representation of the stress-strain relations due, in principle, to Kelvin [17, 18]. The formulas for the representation of the averaged elasticity tensor are simple and concise. The applications of these formulas are illustrated using previously reported data, and are contrasted with the traditional analysis of the same data by Hearmon [9]. An interesting result that emerges from this analysis is a method dealing with variable composition anisotropic elastic materials whose elastic constants depend upon the particular composition. In the case of porous isotropic materials, for example, it is customary to regress the Young's modulus against porosity. The results of this paper suggest a structure or paradigm for extending to anisotropic materials this empirical method of regressing elastic constant data against composition or porosity.     

Two results on solution uniqueness and multiplicity for the linear elastic friction problem with normal compliance

This study is concerned with the frictional contact problem governed by the normal compliance law in linear elasticity. The paper presents two contributions dealing with the stationary problem: we first obtain improved bounds ensuring the uniqueness of a solution. Second we exhibit examples in which infinitely many solutions to the problem exist.     

纤维沥青混凝土FRA黏弹性预测模型

纤维沥青混凝土FRA(Fiber reinforced asphalt concrete)的力学行为取决于沥青混合料和纤维的物理属性及几何特征。通过三参数固体模型,考虑纤维的几何特性,构造了一种预测FRA黏弹性行为模型,推导出该模型的本构方程、蠕变柔量和松弛模量表达式。采用该模型研究了纤维体积分、比半径和弹性模量等对FRA松弛模量和蠕变柔量的影响。结果表明,纤维掺入量和比半径对FRA的松弛模量和蠕变柔量影响较大,而弹性模量影响较小。通过试验,验证了FRA预测模型具有较高的精度。在研究试验范围内,SMA-13沥青混凝土的聚丙烯腈纤维(PAN)最佳掺入量和长径比分别为0.3%～0.4%和600～900。     

裂隙挤喷流对孔隙介质排水体积模量的影响

实际岩石比如沉积形成的岩石往往是裂隙和孔隙并存的孔隙介质. 由于扁状的裂隙与近似球形或圆管形的孔隙具有不同的可压缩性,当孔隙介质受压时,液体会从易压缩的裂隙中挤出流入不易压缩的孔隙中,这种挤喷流会引起弹性模量的频散和能量的耗散. 着重研究了裂隙挤喷流和液体可压缩性对孔道变形的影响,推导出了动载荷作用下排水体积模量的表达式. 与挤喷流相关的裂隙附加柔度会引起排水体积模量随频率变化,使得孔隙介质呈现黏弹性. 频率越高,模量的实部越大,岩石抵抗变形的能力越强. 而模量的虚部体现了挤喷流对能量的耗散. 裂隙密度主要决定模量频散的幅度以及能量耗散的强度,且裂隙密度越大,模量频散幅度越大,能量耗散也越强. 裂隙的纵横比主要决定模量频散速率最快或能量耗散最强时对应的特征频率. 若孔隙介质中不含有裂隙,即裂隙密度是0时,排水体积模量退化为Biot理论中的排水体积模量.     

A Universal Reduced Rupture Creep Approach for Prediction of Long Term Failure Behavior of Aged Glass Polymers from the Short Term Test of Rupture Creep Compliance by the Unified Master Curved Extrapolation

The prediction of long term failure behaviors and lifetime of aged glass polymers from the short term tests of reduced rupture creep compliance (or strain) is one of difficult problems in polymer science and engineering. A new “universal reduced rupture creep approach” with exact theoretical analysis and computations is proposed in this work. Failure by creep for polymeric material is an important problem to be addressed in the engineering. A universal equation on reduced extensional failure creep compliance for PMMA has been derived. It is successful in relating the reduced extensional failure creep compliance with aging time, temperature, levels of stress, the average growth dimensional number and the parameter in K-W-W function. Based on the universal equation, a method for the prediction of failure behavior, failure strain criterion, failure time of PMMA has been developed which is named as a universal “reduced rupture creep approach”. The results show that the predicted failure strain and failure time of PMMA at di?erent aging times for different levels of stress are all in agreement with those obtained directly from experiments, and the proposed method is reliable and practical. The dependences of reduced extensional failure creep compliance on the conditions of aging time, failure creep stress, the structure of fluidized-domain constituent chains are discussed. The shifting factor, exponent for time-stress superposition at differentlevels of stress and the shifting factor, exponent for time-time aging superposition at different aging time are theoretically defined respectively.     

Effect of Interruptions in Loading on the Durability and Deformability of Structural Plastics

An alternative way of estimating the durability of structural plastics under stresses = const 0.4-0.8_f(_f is the failure stress) based on test data obtained in multiple rectangular loading-rest cycles is proposed. It is also suggested to employ the decrease in the instantaneous elastic modulus as a criterion for evaluating the residual service life of plastic parts and structures and elucidating the reasons for their early failure. For the first time, a possibility of considerably increasing the durability and endurance of structural plastics under short pulsed loadings with relatively long interruptions at the initial stage of stress concentration is considered. The cases of a significantly increased endurance of plastics caused by long interruptions after some fatigue loading by high-frequency tension cycles with a zero maximum stress are explained. First experimental confirmations of an increased durability and endurance of microcomposites subjected to short pulsed loadings alternating with long interruptions are obtained. The evolution of the effect of the loading-rest modes on the durability of massive specimens, microcomposites, and dry fibrous reinforcing fillers is demonstrated with examples of a glass-fabric laminate, a microcomposite, and a nonimpregnated glass strand.     

压缩CO2中聚合物玻璃化转变温度的实验研究

 玻璃化转变温度（T_g）是聚合物重要的特性参数，压缩CO₂环境中聚合物的玻璃化转变温度的测定，更是超临界流体技术在聚合物科学领域中成功应用的前提条件。根据蠕变柔量实验原理，自建一套测定高压环境下玻璃化转变温度的实验装置。利用该装置对聚对苯二甲酸乙二醇酯（PET）、聚苯乙烯（PS）、聚氯乙烯（PVC）以及聚甲基丙烯酸甲酯（PMMA）在大气中及压缩CO₂环境中的T_g进行了测定。设定实验的平衡吸附温度为室温，平衡吸附压力范围分别为：PET，0~3.5 MPa；PS，0~11.0 MPa；PVC，0~9.0 MPa；PMMA，0~4.5 MPa。在大气中测定的结果与文献中的结果相吻合，表明所设计的实验方法及实验装置是可靠并有效的，可用于高压环境下聚合物的玻璃化转变温度的测定。从压缩CO₂中的聚合物T_g测定结果可以看出，CO₂对聚合物具有较明显的溶胀、增塑作用，可显著降低聚合物的T_g。     

关于酸、碱平衡调节中肺作用的数学描述

在正常或疾病情况下,人体内酸碱平衡的调节是一个颇为复杂的过程.迄今尚存很多争议性问题,近年国外多倾向于建立各种数学模型,以期揭示体内酸碱平衡的调节机制.本文将“顺应性”这一概念,引入到人体酸碱平衡调节的研究中,并观察了在代谢性酸中毒和代谢性碱中毒时,肺参与代偿调节的顺应性变化范围和变化幅度,为应用数学模型进一步深入探讨机体内复杂的酸碱平衡调节机制,提供新的研究途径和手段.