Mechanism of resonance and cancellation for train-induced vibrations on bridges with elastic bearings

In this paper, the mechanism involved in the phenomena of resonance and cancellation in the train-induced vibrations of railway bridges with elastic bearings is explained using an analytical approach. The train is modelled as a sequence of moving loads of constant intervals. The vibration shape of the elastically supported beam is approximated by the combination of a flexural sine mode and a rigid body mode. The present results indicate that under certain conditions, resonances of much higher peaks can be excited on elastically supported beams by moving trains at much lower speeds than those on simply supported beams. The cancellation is a phenomenon more decisive than that of resonance, in that it can suppress the latter even when the condition of resonance is met. Moreover, the speed for cancellation to occur is generally independent of the support stiffness. To verify the analytical results presented herein, a field test was conducted on two adjacent elastically supported bridges in existing railway lines. In the design of railway bridges, it is important that the phenomenon of resonance not be overlooked, as it is harmful not only to the riding comfort of passengers, but to the maintenance of railway tracks.     

Piezoelectric lattice vibrations at optical frequencies

A relationship is proposed between the piezoelectric coefficient and the dielectric constant (or refractive index) based on classical dispersion theory. Piezoelectric lattice vibrations are associated with ionic polarizations at optical frequencies. This relation is applied to study the piezoelectric lattice vibrations in α-quartz, and agreement is found between the calculated and the measured value of the piezoelectric coefficient. No direct experimental method for measurement of piezoelectric coefficients at optical frequencies exists; however, in terms of the proposed relation, piezoelectric coefficients at optical frequencies can be evaluated from infrared reflection measurements.     

Approximate calculation of frequencies of localized vibrations

An exact calculation of the frequencies of localized vibrations in a crystal with defects meets with considerable difficulties and therefore only the simplest cases have been calculated [9, 10]. An approximate calculation is confined to computing the frequencies of a system composed of several atoms in the neighbourhood of the defect. The interaction between this system and the other atoms of the lattice, which however are immobile in this approximation, is taken into consideration. Since the analytical estimate of the approximation is very rough, the approximate and exact calculations have been compared for some concrete cases (Fig. 1, 2). It is clear from these calculations that the use of the proposed approximation leads to good results.

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Highly excited vibrations of molecules at combination and difference frequencies

An equation for highly excited vibrations of molecules at combination and difference frequencies is derived by means of modification of the basic equation for the normal vibrations of molecules by applying the direct product operation of matrices and using the properties of this operation with respect to the eigenvalues and eigenvectors of the multiplicand matrices. From the solution of the equation derived, the elements of vibration patterns are determined, which allow one to find expressions for the structural molecular parameters and the coefficients of kinematic interactions and to study their changes.     

Chemical effects on the frequencies of Si-H vibrations in amorphous solids

We show that the frequencies of the bond-stretching vibrations of Si-H groups in amorphous solids, such as a-Si and a-SiO₂, vary systematically with the electronegativities of the next nearest neighbor atoms of the network. This induction effect is well-known in substituted silane molecules, SiHR₁R₂R₃; however, this represents the first discussion of a similar effect in network solids. The empirical relationship developed for the vibrational frequencies in the silane molecules is shown to apply to the solid state network structures as well. The applicability of this analysis to other network amorphous solids is illustrated by comparing the vibrational frequencies of the P = 0 bond in molecules, 0 = PR₁R₂R₃, and network glasses, e.g., a-P₂O₅, and a-P₂O₅-SiO₂.     

Dynamic gratings in KDP induced by piezoelectric vibrations at optical frequencies

Optical interference fringes were observed in the beam spot of the He-Ne laser transmitted through KDP. The interference fringes originate from the dynamic gratings induced by the electromagnetic field of the incident light. Diffraction fringes appear only in certain propagation directions of light through KDP. This observation is different from that monitored in α-quartz.     

Effect of mode interaction on spectroscopic parameters of molecular vibrations with combination frequencies

An equation has been obtained for excited vibrations with combination frequencies by modifying the equation for the normal vibrations of the molecules, using the direct product operation and its properties for the eigenvalues and eigenvectors of the cofactor matrices within matrix perturbation theory. From the solution of the equation, the elements of the vibrational mode tensor are determined, for which formulas are written (in terms of projectors of the matrix of the dynamic coefficients) that take into account their changes for excited vibrations. Using these formulas makes it possible to study the effect of perturbations on the change in the intramolecular and spectroscopic parameters of combination vibrations of the molecules. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 4, pp. 421–425, July–August, 2006.     

Reference frequencies for the validation of numerical solutions of transverse vibrations of non-uniform beams

Tables of natural frequencies, calculated from exact analytical solutions are presented for beams of various geometries including truncated tapered cantilevers and pre-twisted uniform beams. Independent numerical solutions are used in several instances to confirm the accuracy which can be as high as six significant figures.     

Calculation and analysis of the frequencies of normal vibrations of 2,3-Di-O-nitro-methyl-β-D-glucopyranoside

A calculation of the frequencies and forms of the normal vibrations of the 31-atom molecule 2,3-di-O-nitromethyl-β-D-glucopyranoside has been performed. Particular emphasis has been placed on the interpretation of the strongest bands in the spectrum of 2,3-di-O-nitro-methyl-β-D-glucopyranoside, which are due to vibrations of the nitrate groups. The present work has been reported at the IV International Congress of theoretically competent chemists, Jerusalem (Israel), July 7–12, 1996. B. I. Stepanov Institute of Physics, Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 6, pp. 724–728, November–December, 1997.     

Classical harmonic vibrations with micro amplitudes and low frequencies monitored by quantum entanglement

We study the entanglement dynamics of the two two-level atoms coupled with a single-mode polarized cavity field after incorporating the decoupled atomic centers of mass classical harmonic vibrations with micro amplitudes and low frequencies. We discover a new quantum mechanical measurement effect for the entanglement dynamics. We propose a quantitative vibrant factor to modify the concurrence of the two atomic states. When the vibrant frequencies are very low, we obtain that: (1) the factor depends on the relative vibrant displacements and the initial phases rather than the absolute amplitudes, and reduces the concurrence to three orders of magnitude; (2) the concurrence increases with the increase of the initial phases; (3) the frequency of the harmonic vibration can be obtained by measuring the maximal value of the concurrence during a small measurement time. These results indicate that the extremely weak classical harmonic vibrations can be monitored by the entanglement of quantum states. The effect reported in the paper always works well as long as the internal degrees of freedom of the system (regardless of unitary evolution or non-unitary evolution with time) are decoupled with the external classical harmonic vibrations of atomic centers of mass.