Fundamental Normal Modes Research Articles

Resonance Raman effect in bis- N-sulfinylimine disulphide (OSNSSNSO): Theoretical and experimental studies

The vibrational spectra of bis- N-sulfinylimine disulphide (OSNSSNSO) were analysed according to the usual method, including a normal coordinate analysis complemented by results originating from ab initio calculations (HF/3-21G∗, with an additional set of d orbitals at the nitrogen atoms ( α d = 0.8) HF 6-31 + G∗ and MP2 6-31 + G∗ ) and density functional theory ( B3 PW91 6-31 + G∗ and B3 LYP 6-31 + G∗ ) calculations. Excited state geometries of S 2(NSO) 2 were determined from experimental data using the time-dependent theory of spectroscopy. The excitation profiles were calculated for five fundamental normal modes and additionally for one overtone. The transferability of the configuration of the RNSO compounds and the capability for estimating the extension of the chromophore through the resonance Raman effect were tested again.

Resonant vibrational excitation of furan by low energy electron impact

Our purpose was to investigate the resonant vibrational excitation of furan (C4H4O) in its electronic ground state by electron collisions. The electron energy loss measurements have been carried out at intermediate and low impact energies for a scattering angle of 30°. The spectra show peaks or groups of peaks corresponding to the excitation of the fundamental normal modes as also of the first harmonics and combinations. The energy dependence curve for the excitation of the C–H stretching vibrational modes is also reported for the impact energy range of 3–10 eV. It exhibits a broad structureless band with a maximum centered around 6 eV, which reveals an excitation mechanism through the intermediate of a shape resonance built on the electronic ground state of the neutral molecule. A comparison with benzene is made in order to help the analysis and to assign the nature as well as the symmetry of the resonance.

Viscoelastic relaxation of a Burgers half-space: implications for the interpretation of the Fennoscandian uplift

We investigate the load-induced response of a Burgers earth model. In particular, using the incremental field equations and interface conditions of viscoelastodynamics, we give closed-form solutions for a two-layer half-space subjected to surface loading. In the special case of homogeneity, the solution shows that the Burgers half-space is characterized by two fundamental normal modes: Mo and M∞. They correspond to the short-and long-time viscosities, ηo and η∞, which describe the creep behaviour of the transient Burgers rheology at short and long times after the onset of loading. In the more general case of a Burgers substratum overlain by an elastic layer, the number of normal modes increases to four: Mo, Lo, M∞, L∞. Values of the parameters specifying the Burgers substratum are estimated by predicting the observed post-glacial uplift in Fennoscandia with a simple model of the Pleistocene glaciation history. The calculations return the following results: (1) an upper bound on η∞ cannot be determined; (2) a comparison with uplift curves for a steady-state Maxwell substratum shows that the marginal and peripheral regions of the Fennoscandian ice sheet are most sensitive to transient creep in the Earth's mantle; and (3) an estimate of η∞ cannot be obtained without a priori knowledge of the other parameters of Burgers rheology.

Sound insulation of a rectangular thin membrane with additional weights

As a result of experiments on sound insulation under conditions of normal incidence, it has been confirmed that attaching small weights to a membrane improves the sound insulation efficiency in a frequency range from natural frequency of the whole membrane to that of the partial area divided by the additional weights. This effect is due to the interfering mode mixing of the fundamental normal mode of the membrane and the divided mode with the same phases formed by attaching the additional weights to the membrane, and not due to mass law. In the present paper this mechanism is studied and revealed through both experiments and numerical analyses. This method is simple, lightweight, possible to tune and effective in a lower frequency range, and hence it is thought that this method has the possibility of being developed into a useful one in the field of noise control.

Causation of Large-Amplitude Coastal Seiches on the Caribbean Coast of Puerto Rico

Abstract Sea-level oscillations at supertidal frequency with amplitudes of the order of the mean tidal range have been reported from the Caribbean coast of Puerto Rico. Analysis of a 10-year time series of digital tide data from Magueyes Island, Puerto Rico, demonstrates that sea-level variance at the fundamental normal mode (sciche) frequency of the shelf has a pronounced fortnightly distribution with a maximum occurring 6–7 days after new and full moon. The sieche variance also shows a bimodal seasonal distribution with an inverse relationship to easterly wind stress. It is argued that the sciches are excited by internal waves generated by strong tides in the southeastern Caribbean. Support is provided by airborne radar imagery showing sea-surface patterns suggesting the presence of internal waves near the southern Aves Ridge, and by the results of two field experiments, carried out during times when large-amplitude sciches were expected, to search for evidence of internal wave forcing near the shelf br...

Black-hole normal modes: A WKB approach. II. Schwarzschild black holes.

We employ a semianalytic technique, based on a modified WKB approach, to determine the complex normal-mode frequencies of Schwarzschild black holes. It yields a simple analytic formula that gives the real and imaginary parts of the frequency in terms of the parameters of the black hole and of the field whose perturbation is under study, and in terms of the quantity (n+(1/2)), where n=0,\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2,..., and labels the fundamental mode, first overtone mode, and so on. In the case of the fundamental gravitational normal modes of the Schwarzschild black hole, the WKB estimates agree with numerical results to better than 0.13% in the real part of the frequency and 0.22% in the imaginary part. The agreement for both the real and imaginary parts of the low overtones is better than 0.5%. The relative agreement improves with increasing angular harmonic.

Black hole normal modes - A semianalytic approach

A new semianalytic technique for determining the complex normal mode frequencies of black holes is presented. The method is based on the WKB approximation. It yields a simple analytic formula that gives the real and imaginary parts of the frequency in terms of the parameters of the black hole and of the field whose perturbation is under study, and in terms of the quantity (n + 1/2), where n = 0, 1, 2,... and labels the fundamental mode, first overtone mode, and so on. In the case of the fundamental gravitational normal modes of the Schwarzschild black hole, the WKB estimates agree with numerical results to better than 7 percent in the real part of the frequency and 0.7 percent in the imaginary part, with the relative agreement improving with increasing angular harmonic. Carried to higher order the method may provide an accurate and systematic means to study black hole normal modes.

Bulk thermoelastic attenuation of composite materials

A theoretical derivation is made for the effective, frequency‐dependent thermoelastic bulk modulus of an isotropic composite subjected to hydrostatic stress producing volumetric strain . No heat transfer is permitted to occur at the outer boundary of the composite, but as a consequence of differential heating, heat transfer among the constituents, and hence dissipation, occurs in the interior. Thus between the limits ω = 0 and ω = ∞K*(ω) is complex and the thermoelastic damping may be measured by QK−1 = Im (K*)/Re(K*). Parametric studies show the influence of various elastic and thermal properties on thermoelastic damping. Numerical calculations are made for a hypothetical lower mantle assemblage of stishovite and magnesiowüstite. The results show that thermoelastic dissipation in the lower mantle can account for the observed attenuation of the fundamental radial normal mode and can also provide interesting constraints on grain sizes.

Effects of normal mode loss in dielectric waveguide directional couplers and interferometers

Theoretical arguments and experimental evidence are presented to show that the two fundamental normal modes of a coupled waveguide structure have different attenuations in traversing such a structure. The effects of this phenomenon on evanescent wave directional couplers and interferometers are derived. Parasitic effects in Mach-Zehnder and Sagnac interferometers utilizing directional couplers are described. An asymmetric output for the recently demonstrated all-single-mode fiber resonator is predicted and compared to experimental results. Some qualitative results are presented for integrated optic directional coupler switches.

Infrared investigation of the phase transition in K2SO4

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The vibrational spectra and rotational isomerism of methane disulfonyl chloride

The infrared and Raman spectra of methane disulfonyl chloride and its deuteroderivatives have been studied in the liquid and solid phases. Experimental evidence was obtained for hindered internal rotation about the SC bond and the preferred configuration is probably that involving the closest approach of CH and SCl groups, which is consistent with the facile formation of sulfene intermediates by such compounds. A tentative assignment of vibrational frequencies to the fundamental normal modes is proposed and force constants calculated. Relatively strong CH ⋯ Cl internal hydrogen bonding is suggested in solid crystals.

On the Dynamical Evolution of Clusters of Galaxies

The theory of the dynamics of star clusters (cf. Spitzer 1975 for a review) is by now so well developed that we have, or think we have, a moderately accurate picture of the physical processes acting in and the overall evolution of spherical systems. in contrast, flattened and/or rotating systems are apparently subject to a variety of ill-understood instabilities which ultimately are a manifestation of the second law of thermodynamics; at given total energy, a system will tend to increase the fraction of its kinetic energy in disordered rather than ordered form. But spherical systems (globular clusters, elliptical galaxies, Morgan cD clusters of galaxies) are relatively smooth and featureless; they show little substructure indicating, presumably, that they are quite stable to perturbations of their fundamental normal modes, and they are normally modeled as rather “hot”, pressure supported systems.

Wake interaction experiments with two flexible circular cylinders in flowing water

An examination is made of wake interaction effects between two identical flexible circular cylinders in flowing water. The two vertical cylinders are separated by a variable distance G along a common centre-line in the direction of flow for the range 0·25 < G/ d < 6. Oscillations in the fundamental and second normal modes in the flow direction and in the fundamental mode cross-flow are induced by coherent vortex shedding. Reynolds numbers of the individual cylinders are in the range 10 3 < Re < 2 × 10 4, and the two one-inch diameter cylinders were tested in depths of water varying from 22 diameters to 30 diameters. Results are presented from tests on the uncoupled cylinders and also from tests with the cylinders coupled by elastic or rigid members. The stability of the two cylinders is explained by reference to oscillatory mode shapes and from considerations of the two possible types of vortex shedding (symmetric and alternate). Where possible, comparisons are made with results from wind tunnel investigations.

A new approximate method of finding the loss factors of a sandwich cantilever

Extensively used methods for finding the loss factors of sandwich designs are predominantly based on the assumption, for the sake of simplicity, that only symmetrical boundary conditions occur. In this paper a new approximate method for the calculation of loss factors and other dynamical characteristics of the damped normal modes for sandwich beams with arbitrary boundary conditions is developed. Based on the linearization of a hysteretically damped sandwich beam in the neighborhood of the corresponding undamped beam, the theory has a number of advantages from the analytical and computational points of view. The method is applied to a damped sandwich cantilever. Numerical results for the fundamental damped normal mode as well as a comparison with the exact method are presented graphically.

Vibrational spectra of eight isotopic species and force constants of 2-bromopropene

Infra-red spectra of eight isotopic species of 2-bromopropene have been measured and analysed. Most fundamental frequencies and normal modes involving mainly motion of the propenyl part were found to be rather close to those of 2-chloropropene. 133 observed fundamentals have been used to calculate the force constants of a harmonic 25 parameter force field analogous to the force field evaluated for the chloro-compound. All force constants except the C—halogen stretching constant turned out to be fairly transferable from one compound to the other.

An experimental study and computation of the infrared absorption spectrum of 3,5-dimethyl-4-phenylpyridine

The infrared absorption spectrum of 3,5-dimethyl-4-phenylpyridine in the 400–2000 cm−1 range was obtained. A valence-force model was used to compute the fundamental frequencies and normal vibrational modes. The experimental and computed data were found to be in good agreement. The addition of two methyl groups in the 3,5-positions of theγ-phenylpyridine molecule reduces conjugation between the benzene and pyridine rings, rendering the molecule noncoplanar. The free rotation of the methyl groups about the C-C bond is retarded by the free electron pair in the nitrogen atom of the pyridine ring.

Vibration of Shear Buildings by Flexibility Method

Modified matrix iteration method using inverse of stiffness matrix is described for determination of dynamic response of tall buildings caused by earthquake or blast loadings; as first result method obtains fundamental frequency and normal mode; calculations are based on usual shear building assumption; exact inverse of stiffness matrix of any shear building is given by formula; example.

Magneto-hydrodynamic Oscillations of a Perfectly Conducting Fluid Sphere Placed in a Uniform Magnetic Field

An attempt to improve theories of magneto-hydrodynamic oscillations of a conducting fluid sphere in a uniform magnetic field is made. Unlike the previous theories which have been developed by M. Schwarzschild and T. Rikitake, analytical expressions for zonal oscillations are obtained rigorously in this paper. It turns out that no eigen-periods are determined accurately. However, they are approximately obtained with drastic simplifications. Two fundamental normal modes of oscillation are also approximately obtained and illustrated.

The Piezo-Electric Resonator and Its Equivalent Network

The theory of the piezo-electric and the mechanical behavior of a quartz resonator is stated following Voight and Cady. The functions of the quartz as dielectric and as vibrator are shown to be separable and replaceable by a condenser in parallel with an electrical resonator, i.e., a series chain of inductance, resistance, and capacity. For a Curie-cut quartz rod excited lengthwise through the transverse piezo-electric effect into compressional vibration at the frequency the series elements become L=M/4ϵ2b2; R= N/4ϵ2b2; C=4b2ϵ2/g. This of vibration may be termed the fundamental normal mode since the vibration direction is normal to the electric field. For a Curie-cut quartz plate excited through the longitudinal piezo-electric effect into compressional vibration at the thickness frequency, the series elements become L =e2M/4ϵ2l2b2; R=e2N/4ϵ2l2b2; C=4ϵ2l2b2/e2g. This of vibration may be termed the fundamental parallel mode since the vibration direction is parallel to the electric field. M, N, and g are respectively the half-mass, mechanical resistance factor, and equivalent stiffness of the rod or plate whose thickness along the field is e, and dimensions normal to the field are l and b, the latter being along the optic axis. The parallel capacity is shown to be less than that for a quartz dielectric which is free to assume piezo-electric strain and to be equal to that for unstrained quartz. Phase and amplitude variations of current to the resonator are shown as obtained with the cathode ray oscillograph.