Mean amplitudes of vibration: Molecules of the linear and planar AXYZ type

Applying Cyvin’s secular equation method the mean-square amplitude quantities are calculated for molecules of the linear and planar AXYZ type belonging to the symmetry C_s. The mean amplitude values for HN₃, DN₃, HNCS, HNCO, HCOF and DCOF molecules are evaluated at 300° K.     

Force constants and mean amplitudes for some anions of MX6 type (X=F,Cl, Br)

Force constants of the Urey Bradley type for twelve MX₆ ^n? ions ofOh symmetry have been reported. Generalized mean square amplitudes and mean amplitudes of vibration for bonded and non-bonded distances have also been calculated. Thermodynamic quantities for these molecules have been calculated at various temperatures from 50° K to 1600° K using a rigid rotator, harmonic oscillator approximation.     

Potential constants,mean amplitudes of vibration,and thermodynamic properties of ethylene oxide,ethylene oxide-d4 and ethylene sulphide

A normal co-ordinate analysis of ethylene oxide, ethylene oxide-d₄ and ethylene sulphide is carried out and the potential energy constants are determined using both the most general quadratic potential function and Urey-Bradley force field. Using the potential energy constants obtained by the former method the mean amplitudes of vibration of these molecules are calculated by the secular equation method. The thermodynamic properties of these molecules are reported for the ideal gaseous state at one atmosphere pressure for eleven temperatures from 100° K. to 1000° K.     

Anharmonicity factors and potential energy constants of B2H6 and B2D6

The anharmonicity factors of B₂H₆ and B₂D₆ have been calculated using Dennison’s method. Using the calculated harmonic wave numbers, the valence force constants have been obtained by the Wilson’s F-G matrix method.     

Magneto-Structural analysis of rotating electrical machines

The vibrations of the stator core of a rotating electrical machine induce acoustic noise. These oscillations of the stator yoke are excited of the force density due to the magnetic field in the air gap. This requires a transient magnetic field analysis coupled with a dynamic mechanical analysis. Coupling these two different physical fields results in a high numerical effort and usually one direction of the interaction is disregarded. This paper presents a method to calculate the vibrations of a stator core under design operating conditions. For this purpose, harmonic electromagnetic excitation forces have been calculated in a linear magnetic field analyses using the finite element method. The resulting forces have been applied to a linear structural dynamic FE model in the frequency domain. The results of the calculations are harmonic velocities specified by amplitude and phase from the structural surface of the stator core. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electron paramagnetic resonance studies of VO2+ in single crystals of NaCl,KCl and RbCl

Electron paramagnetic resonance (EPR) of VO²⁺ radicals incorporated in face-centred single crystals of NaCl, KC1 and RbCl has been studied in the temperature range of 77° K to 330° K. At liquid nitrogen temperature, anisotropic spectra have been recorded in each case while spectra recorded at room and higher temperatures are isotropic suggesting the existence of a fast readjustment of VO²⁺ molecular ions in the crystals at higher temperature while this motion gets hindered at liquid nitrogen temperatures. Spin-Hamiltonian constants are calculated from the recorded isotropic and anisotropic spectra. The line widths in each case are found to obey a parabolic law originally proposed by Kivelson. The constants which give a close fit have been evaluated. The random orientation and readjustment of V-0 bond in these alkali chloride crystals is explained on the assumption that the medium exhibits a “liquid-like” nature for VO²⁺ molecular ion as far as the electron paramagnetic resonance absorption is concerned.     

Ideal gas thermodynamic properties of xenon compounds

The ideal gas thermodynamic functions from 100° to 1500° K have been computed for three fluorides, three oxyfluorides, and three oxides of xenon using the published spectroscopic data. The thermodynamic properties for XeF₄ and XeF₆ were compared with those reported by Weinstocket al. S^o _298·15 calculated in this work for XeF₄ is higher by 1·5 cal than the third law entropy and that obtained by Weinstocket al. This difference is attributed to the large uncertainty in the third law entropy and the set of vibrational frequencies used by Weinstocket al. For XeF₆ a more reliable and consistent set of frequenices is suggested.     

Optical absorption of Co2+ doped NH4Cl: Phase transformation studies

The absorption spectrum of Co²⁺ doped NH₄Cl has been studied from the room temperature to the liquid nitrogen temperature. A sudden change in the spectrum is observed between 243° K and 233° K which is attributed to the phase transition in the crystal. From the observed spectrum it is suggested that Co²⁺ goes in interstitially as well as substitutionally. Both the types of centers exist at room temperature, but with decrease in temperature substitutional ions migrate to interstitial sites, the process being stimulated at the phase transformation point so that the 77° K spectrum seems to be mostly due to the interstitial centers. The 77° K spectrum is analyzed in the approximation of octahedral symmetry for interstitial ions and the band positions are fitted fairly well with B = 870 cm.^?1 Dq = 850 cm.^?1 and C = 4·4 B. A blue shift of about 100 cm.^?1 is observed for⁴T₁ (P) band at the phase transition which is attributed to the increase in Dq value with the anomalous lattice contraction at the phase transition. The decrease in the lattice parameter calculated from this blue shift is around 0·4% which is in good agreement with the results of X-ray measurements. Two possible models for the interstitial complex are examined and the one with fourfold chlorine coordination associated with two neutral water molecules at the first neighbour (NH₄)⁺ site lying along < 100> direction is suggested to be more probable.     

Mean amplitudes of vibration: Pyramidal XYZ2 molecules

The theory of mean square amplitude of vibration using the symmetry co-ordinates has been applied to the pyramidal XYZ₂ molecular model. The elements of the mean square amplitude matrices and the mean amplitude quantities at 300° K. for thionyl halides have been reported.     

Mean amplitudes of vibration: Bent symmetrical XY2 molecules and groups

Applying the secular equation method of Cyvin, the mean-square amplitudes and the mean amplitudes for ten bent symmetrical XY₂ molecules and groups at 300° K. have been evaluated.     

Raman and infrared spectra of ammonium selenate and lithium ammonium selenate

The Raman and infrared absorption spectra of (NH₄)₂ SeO₄, (ND₄)₂ SeO₄ and Li (NH₄) SeO₄ have been recorded at 300° K; while the spectra of the non-deuterated compounds have been recorded at 110° K also. (NH₄)₂ Se0₄ crystal exhibits 33 Raman lines, while LiNH₄SaO₄ shows 30 Raman lines at 300° K. Proper assignments have been given to the observed vibration frequencies. The SeO₄ ^?? ions and the (NH₄)⁺ ions are found to be highly distorted in these selenates. There is lowering of the N-H vibration frequencies due to hydrogen bonding. The present spectroscopic investigations do not reveal the existence of any phase transition in these selenates in the temperature region investigated.     

Esr of CaS:Mn2+: A case with zero cubic field splitting

Electron spin resonance studies on powdered samples of CaS:Mn²⁺ and SrS:Mn²⁺ at 300° and 77° K reveal the usual six-line hyperfine structure due to Mn⁵⁵. CaS:Mn²⁺ exhibits additional fine structure satellites which have been analysed on the basis of a near zero cubic field splitting.     

Mechanical properties of polymers at 4.2°K and their dependence on chemical structure and the conditions of physical structure formation

Values of the modulus of elasticity, proportionality limit, and fracture strains and stresses have been measured at 4.2°K for polymers with different chemical structure and for a series of physically modified polymers. Relations have been established between the cryogenic values of the mechanical properties, the chemical structure of the macromolecules, and the conditions of formation of the physical structure of the polymer.     

Temperature dependence of the knight shift of207Pb resonance in Na15Pb4 intermetallic compound

Knight shift of²⁰⁷Pb resonance in Na₁₅Pb₄ intermetallic compound has been determined in the range of temperatures between 120° K. and 480° K. The shift has been found to be negative with reference to²⁰⁷Pb resonance in solid lead nitrate and decreases in magnitude with increasing temperature. The results are discussed in the light of the electronic structure of the alloy.     

Mechanical behavior of a number of polymers at helium temperatures

An experimental investigation of the mechanical behavior of a number of polymers in the range 4.2–240°K has been made. It has been shown that at helium temperature the Poisson ratio is governed by the free volume. It has been established that the dynamic Young's modulus and shear modulus of these polymers at 4.2°K depend on the chemical structure: their values are determined by the mean distance between neighboring macromolecule chains.     

复合形在欧氏空间中的实现问题Ⅲ

<正> 设 K 是一个有限单形复合形,我们恒可视 K 为一充分高维数 N 的欧氏空间中的欧氏复合形,此时其所定空间将记为(?).在研究 K 是否可实现于某一确定维数 m 的欧氏盘间R~m 中的时候,我们曾引进下面的一些定义(见[1],记号略有不同):     

Analysis of the Forced Vibration of Two Bolted Half-Pipes with Extended Friction Contacts

The present paper deals with the forced vibration analysis of a test structure. The test structure consists of two parts, an upper and a lower half pipe, joint in two bolted flanges which represent the extended friction contacts. Depending on the clamping loads different normal pressure distributions can be established in the contact interfaces. Since the test structure is loaded with a harmonic external force relative displacements occur in the contact interface. This leads to microslip effects affecting the dynamic behaviour. The experimental validation of the calculation method accounting for these effects is shown by comparing measured and calculated frequency response functions (FRF). (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mean amplitudes of vibration: Some pyramidal XY3 and tetrahedral XY4 molecules

The theory of the determination of the mean amplitudes of vibration in molecules using the symmetry co-ordinates has been applied to the cases of arsenic halides belonging to the pyramidal XY₃ type and a few silicon and stannic halides of the tetrahedral XY₄ type. The mean square amplitudes and mean amplitudes of vibration have been evaluated at 298° K.     

Mean amplitudes of vibration: SeO3 and ClF3

The method of the determination of the mean amplitudes of vibration in molecules using the symmetry co-ordinates has been applied to the cases of SeO₃ ion belonging to the pyramidal XY₃ type, and ClF₃ of the planar XYZ₂ type. The mean square amplitude and mean amplitudes of vibration have been evaluated at 300° K.     

On the parametric excitation of rotors with rolling element bearings

In this approach a 1-DOF-model for a rotor in rolling element bearings is derived. The nonlinear equation of motion with a cubic restitution force and harmonic time dependent variation is solved by Multiple Time Scales Approach. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)