Vibration of cracked shafts in bending

Cracked rotating shafts exhibit a certain particular dynamic response due to the local flexibility of the cracked section. In this response, most of the features of the response of a shaft with dissimilar moments of inertia can be identified. Moreover, the non-linear behavior of the closing crack introduces the characteristics of non-linear systems. For many practical applications, the system can be considered bi-linear and analytical methods can be applied. A de Laval rotor with an open crack is investigated by way of application of the theory of shafts with dissimilar moments of inertia. Furthermore, analytical solutions are obtained for the closing crack under the assumption of large static deflections, a situation common in turbomachinery. Finally, a solution is developed for the case in which the local flexibility function is found experimentally.     

核物质对称能斜率对快转中子星性质的约束（英文）

在过去的十余年中,对非对称核物质的对称能的研究无论从实验还是理论上都取得了较大的突破,这对中子结构及其物态方程的理解具有十分重要的意义。本研究将采用一个相对保守的对称能斜率范围(25 Me VL105Me V)来研究其对快速转动中子星性质的约束,这些性质包括:质量-半径关系、转动惯量、引力红移以及转动形变等。通过该对称能斜率的约束,发现典型中子星(M=1.4M⊙)的半径约束在10.28～13.43 km范围内,这与最近的相关观测相一致。如果观察发现了质量较小的毫秒脉冲星,则将为核物质的对称能较软提供有效的证据。另外还发现,对角动量的一致性可为快转中子星转动惯量的上限提供约束。最后,根据具有低质量伴星的双星EXO0748-676的红移观测,给出了该脉冲星的质量下限(1.5M⊙)。     

Effects of variable inertia on the damped torsional vibrations of diesel engine systems

In the past the effects of ignoring the variable inertia characteristics of reciprocating engines on the accuracy of torsional-vibration calculations were considered to be negligible. The associated secondary resonances and regions of instability tended to be dismissed by most engineers as interesting but of no importance. The situation changed in recent years since there was evidence of the existence of the secondary resonance effects which could have contributed to a number of otherwise inexplicable crankshaft failures in large slow speed marine engines.The cyclic variation of the polar moment of inertia of the reciprocating parts during each revolution causes a periodic variation of frequency and corresponding amplitude of vibration of reciprocating engine systems. It also causes an increase in the speed range over which resonance effects are experienced. In the present paper a study of the effects of damping on the motion of the variable inertia system has been carried out. When the variable inertia effect is allowed for, the equation of motion including the effects of damping is non-linear. For small displacements, the equation can be linearized to predict important characteristics of the motion.Computer methods making use of a numerical analysis process, namely the modified Euler's equations, have been applied in the investigations. The waveform responses are studied at different speeds of engine rotation. The effects of damping and of variations in the ratio of the average reciprocating inertia to average total inertia on the regions of instability have been investigated.     

Double-Blocking Effects in Odd-odd Superdeformed Nucleus 194Tl

Six superdeformed bands of odd-odd nucleus ¹⁹⁴Tl in A～190 mass region are studied using the particle-number conserving method for treating the cranked shell model with pairing interactions. Calculated results agree with experiments very well. Based on our calculation the configurations of the six superdeformed bands are assigned and the influence of blocking effects of proton and neutron on moments of inertia is investigated in detail. The variation of moments of inertia with rotational frequency is mainly attributed to the intruder shells (neutron N=7 and proton N=6), whereas the contributions to moment of inertia from other shells remain almost unchanged with rotational frequency.     

A comparison of the known SD bands in the mass A≈80 region

The mass A≈80 region is now firmly established as the newest region of superdeformation, with up to 11 nuclei exhibiting as many as 21 superdeformed bands. The dynamic moments of inertia of these bands reveal a variety of interesting features, such as superdeformed band crossings and the first pair of identical superdeformed bands in the mass A≈80 region. Cranked shell model calculations have been performed and the bands are interpreted in terms of the number of high-N intruder orbitals occupied. The differences in dynamic moments of inertia and the proposed single particle configurations are discussed.     

Rotational Spectroscopy and Ring-Puckering Conformation of 3-Hydroxytetrahydrofuran

The microwave spectrum of 3-hydroxytetrahydrofuran was recorded using a Fourier transform microwave spectrometer; the rotational constants (MHz) are: A = 5581.8230(7), B = 3638.8316(7), and C = 2924.7410(7). Microwave spectra for four (13)C isotopic species were recorded in natural abundance. Stark effect measurements were used to determine the projections of the dipole moment on the principal inertial axes: μ(a) = 0.956(1) D, μ(b) = 0.875(2) D, μ(c) = 1.050(2) D, and μ(tot) = 1.667(2) D. The internal coordinates of the carbon and oxygen atoms were least-squares fit to the 15 moments of inertia, and the best-fit structure is a C(4')-endo envelope ring conformation, in good agreement with ab initio calculations (MP2/6-31Gdaggerdagger). Copyright 2000 Academic Press.     

Die Corioliskopplung im quantenmechanischen N-Körperproblem

In describing a system ofN particles (e.g. nucleons) in the body-fixed coordinate system of instantaneous principal axes of inertia, in the rotation-vibration part of the Hamiltonian there occur the hydrodynamical moments of inertia. It is, however, not possible to use them as effective moments of inertia as long as the Coriolis term in the Hamiltonian does not vanish. In order to obtain a quantitative picture of the Coriolis coupling influence upon the moments of inertia, we show by means of a unitary transformation how the Coriolis coupling can be eliminated in the limiting case of a rigid body and how by such a procedure the hydrodynamical moments of inertia are transformed into the rather different moments of the rigid body.     

超形变核全同带的研究

简述了超形变原子核全同带的研究进展情况,并以Bohr-Mottelson的I(I+1)展开转动谱公式对部分典型的超形变带进行了分析.发现所谓全同带的确只是两个带的J⁽²⁾比较接近,它们的J⁽¹⁾和J₀并不相等,而且signature对偶带更接近全同.     

Effect of positional substitution of amino group on excited state dipole moments of quinoline

The effect of positional substitution of amino group on the ground and excited state dipole moments of quinoline ring has been investigated using solvatochromic shift methods. The excited state dipole moments of 5aminoquinoline (5AQ) and 3aminoquinoline (3AQ) have been estimated from the spectral data in different non-polar, polar aprotic and polar protic solvents using Bakhshiev and Kawski-Chamma-Viallet equations. It has been observed that both grounds as well as excited state dipole moments for 5AQ are higher than those for 3AQ by approximately a factor of two. Higher values of the excited state dipole moments for both 3AQ and 5AQ as compared to corresponding ground state values have been attributed to intramolecular charge transfer processes. The role of specific solute-solvent interaction on excited state dipole moment in addition to the general solvent effects has been discussed.     

Dynamic instability of supercritical driveshafts mounted on dissipative supports—Effects of viscous and hysteretic internal damping

The case of a rotating shaft with internal damping mounted either on elastic dissipative bearings or on infinitely rigid bearings with viscoelastic suspensions is investigated in order to obtain the stability region. A Euler-Bernoulli shaft model is adopted, in which the transverse shear effects are neglected and the effects of translational and rotatory inertia, gyroscopic moments, and internal viscous or hysteretic damping are taken into account. The hysteretic damping is incorporated with an equivalent viscous damping coefficient. Free motion analysis yields critical speeds and threshold speeds for each damping model in analytical form. In the case of elastic dissipative bearings, the present results are compared with the results of previous studies on finite element models. In the case of infinitely rigid bearings with viscoelastic suspensions, it is established that viscoelastic supports increase the stability of long shafts, thus compensating for the loss of efficiency which occurs with classical bearings. The instability criteria also show that the effect of the coupling which occured between rigid modes introducing external damping and shaft modes are almost more important than damping factor. Lastly, comparisons between viscous and hysteretic damping conditions lead to the conclusion that an appropriate material damping model is essential to be able to assess these instabilities.     

Bounds to frequencies of shafts in torsional vibration with restraints and attached masses

In this paper upper and lower bounds are given to eigenvalues of torsional vibration of the following uniform structures: free shaft elastically restrained at a point; fixed shaft elastically restrained at a point; free shaft with masses elastically attached at points; fixed shaft with a mass elastically attached over an interval. Upper bounds were obtained by using the well-known Rayleigh-Ritz procedure. The more difficult problem of obtaining lower bounds was resolved by using recently developed methods of Bazley and Fox. The various problems discussed in this paper illustrate the use of these lower bound methods and their effectiveness in producing excellent bounds.     

Clustering aspects of nuclei in highly deformed states

The potential energies, the moments of inertia, and the quadrupole and octupole moments of dinuclear systems are compared with corresponding values for the highly deformed nuclear states. The idea is advocated that hyperdeformed states of nuclei are close to near-symmetric dinuclear systems. The superdeformed states are considered as asymmetric dinuclear systems. The cluster superdeformed and hyperdeformed states have quite a large octupole deformation. Measurement of octupole deformations of highly deformed nuclei can answer the question of whether these nuclei exist in cluster configurations.     

Line-widths in the vibration rotation spectra of diatomic molecules perturbed by tetrahedral molecules

The line-broadening phenomena for a diatomic polar molecule perturbed by a tetrahedral molecule are analysed. Two points are particularly studied and exemplified in the case of the vibration bands of HCl perturbed by CF₄ and by SiF₄.

(i) The influence of the electrostatic potential energy (i.e. dipole-octopole and quadrupole-octopole couplings) on reorientation during a collision is introduced, and it appears, to a large extent, to be competitive with the effect of the shorter range angle independent contributions to the potential. Consequently only a weak vibrational effect from the 0–1 to the 0–2 bands is observed when the octopole moment of the tetrahedral molecule is taken into account, in agreement with the experiments.

(ii) For the systems mentioned above the moments of inertia allow us to apply a convenient simplified formalism for the line-broadening calculations. In this formalism the rotational degrees of freedom of the perturber are considered as classical. The results of these theoretical considerations are in good agreement with the presently available experimental data.     

Identification of Bandhead Spin and Identical Bands for Odd-A Nuclei in $A\sim190$ Superdeformed Mass Region

The dynamical moment of inertia is estimated with its even-power expansion of the rotational frequency and in accordance we determine the intermediate spins of the superdeformed (SD) rotational bands. Using Marquardt method of nonlinear least-squares routines, we determine the expansion coefficients by fitting the proposed dynamical moment of inertia with its recent experimental data of the SD nuclei in the A=190 mass region. The comparison between our theoretical and available experimental data for the dynamic moment of inertia and spin shows good agreements. Also, we have calculated the static moment of inertia at three alternative values of spin. The value of spin at which the two moments of inertia are nearly equals is to be regarded as a bandhead spin of the corresponding band. These studies are carried out for eighteen bands of odd-A nuclei of the superdeformed region 190, namely ¹⁸⁹Hg(b1), ¹⁹¹Hg(b1, b2, b3, b4), ¹⁹³Hg(b2, b3, b5), ¹⁹⁵Hg(b1, b2, b3, b4), ¹⁹³Tl(b1, b2, b3, b5), ¹⁸⁹Tl(b1), and ¹⁹⁷Bi(b1). We also notice the occurrence of identical SD bands with near identical transition energies among the considered SD bands.     

Microscopic Mechanism of Large Fluctuation in Odd-Even Differences in Moments of Inertia for Actinide Nuclei

The experimental large fluctuation in odd-even differences in moments of inertia of deformed actinide nuclei is investigated using the particle-number conserving (PNC) method for treating the cranked shell model with monopole and quadrupole pairing interactions. PNC calculations show that the large odd-even difference in moments of inertia mainly comes from the interference contributions j(μν) from particles in high j intruder orbitals μ and ν quite near the Fermi surface, which have no counterpart in the BCS formalism. The effective monopole and quadrupole pairing interaction strengths are determined to fit the experimental odd-even differences in binding energies and bandhead moments of inertia. The experimental results for the variation of moments of inertia with rotational frequency ω are reproduced well by the PNC calculation. The nearly identical experimental moments of inertia between ²³⁶U(gsb) and ²³⁸U(gsb) at low frequencies ħω≤0.20 MeV are also reproduced quite well.     

几种演示影响刚体滚动因素的物理实验仪

改进和研制了几种演示刚体平面平行运动(滚动)的物理实验仪,突出演示了转动惯量、滚动半径、刚体质量等因素对运动的影响．仪器结构简单,构思巧妙,演示效果良好．     

Dynamic rotational characteristics of actinides on empirical approach

In the paper calculation of the moments of inertia for nuclei from the region 87 ≤ Z ≤ 100 and 130 ≤ N ≤ 156 was made in dependence on the angular momentum of their rotational states. The experimental values of the moments of inertia were calculated for rotational energy of the classic rotor in its quantum form, with the use of a simple formula. The moment of inertia term appearing in the formula was treated as a variable. The calculations were carried out on the basis of experimental data for the energies of the rotational levels for 51 bands built on ground states for even-even nuclei and for nuclei with odd mass number A. In addition, 30 rotational bands built on excited states were also analysed in the investigated region in case of even-even nuclei. For many bands and nuclei the considered dependence of the moment of inertia on angular momentum has been found in the analytical form by fitting polynomials to the experimental data. It turned out that obtained results for the moments of inertia made it possible to describe the energies of rotational levels with a relative deviation not greater or only slightly greater than 1%. In general, in the case of 12 bands of ground level the maximum relative deviation of obtained level energies is smaller than 1%.      

An analytical formulation of the forced responses of damped rings

An analysis in which an interaction formulation is used for the forced vibratory responses of a ring having a number of mass segments adhered to it by a viscoelastic material is presented. The mass segments are discretely distributed around the circumference of the ring, and the excitation is a concentrated vibratory radial force located on the surface of the ring. The mass segments may not have to be identical, nor do their distributions have to be uniform. The analysis can readily be extended to more complicated damped shell structural systems. The driving point mechanical impedances at a location midway between two mass segments for a given damped system are given as an example. These solutions compare very well with experimental data and theoretical results available. Also presented is a comparison of driving point mechanical impedances for two damped systems with different thicknesses of the viscoelastic layers.