Showing papers on "Normal mode published in 1998"

Comparative study of damage identification algorithms applied to a bridge: I. Experiment

Abstract: Over the past 30 years detecting damage in a structure from changes in global dynamic parameters has received considerable attention from the civil, aerospace and mechanical engineering communities. The basis for this approach to damage detection is that changes in the structure's physical properties (i.e., boundary conditions, stiffness, mass and/or damping) will, in turn, alter the dynamic characteristics (i.e., resonant frequencies, modal damping and mode shapes) of the structure. Changes in properties such as the flexibility or stiffness matrices derived from measured modal properties and changes in mode shape curvature have shown promise for locating structural damage. However, to date there has not been a study reported in the technical literature that directly compares these various methods. The experimental results reported in this paper and the results of a numerical study reported in an accompanying paper attempt to fill this void in the study of damage detection methods. Five methods for damage assessment that have been reported in the technical literature are summarized and compared using experimental modal data from an undamaged and damaged bridge. For the most severe damage case investigated, all methods can accurately locate the damage. The methods show varying levels of success when applied to less severe damage cases. This paper concludes by summarizing some areas of the damage identification process that require further study.

Identification and treatment of internal rotation in normal mode vibrational analysis

Abstract: A procedure that automatically identifies internal rotation modes and rotating groups during the normal mode vibrational analysis is outlined, and an improved approximation to the corrections for the thermodynamic functions is proposed. The identification and the characterization of the internal rotation modes require no user intervention and make extensive use of the information imbedded in the redundant internal coordinates. Rigid-rotor internal rotation modes are obtained by fixing stretching, bending, and out-of-plane bending motions and solving the vibrational problem for the constrained system. Normal vibrational modes corresponding to internal rotations are identified by comparing them with the constrained modes. The atomic composition of the rotating groups is determined automatically and the kinetic energy matrix for internal rotation is given by either the constrained Wilson-G matrix or the Kilpatrick and Pitzer protocol. The potential periodicity, the rotating tops’ symmetry numbers, and the well-multiplicity are obtained using simple rules. These parameters can be altered by user input. An improved analytical approximation to the partition function for a one-dimensional hindered internal rotation has been developed that reproduces the accurate values tabulated by Pitzer and Gwinn to ±0.4% with a maximum error of 2.1%. This approximation is shown to behave better than previously available approximations over a wider range of regimes. The one-dimensional rotor treatment is generalized to give useful approximations to the multidimensional rotor thermodynamic functions that can be a good start for more thorough studies.

Structure and Vibrational Spectra of the Zwitterion l-Alanine in the Presence of Explicit Water Molecules: A Density Functional Analysis

Abstract: Ab initio B3LYP/6-31G* optimized geometries, vibrational frequencies, and absorption intensities have been calculated for the l-alanine zwitterion (ALAZW) structures stabilized by four neighboring water molecules. The ALAZW structures were stabilized by the addition of four neighboring water molecules because at the B3LYP/6-31G* level of theory the ALAZW is not stable in the absence of the water molecules and will be converted to the nonionized species. The ALAZW was not stable at this level of theory within the Onsager continuum model using the recommended cavity radius obtained from the solute volume calculations. Geometry optimization of the ALAZW in the presence of the explicit water molecules resulted in different optimized structures for the amino acid itself. The distributed origin gauge atomic axial tensors and the electric dipole−electric dipole polarizability derivatives calculated at the RHF level of theory were combined with the B3LYP normal modes, frequencies, and atomic polar tensors to calc...

Generalized theory of helicon waves. II. Excitation and absorption

Abstract: Helicon waves in a plasma confined by a cylinder are treated. The undamped normal modes of the helicon (H) and Trivelpiece–Gould (TG) waves have distinctly different wave patterns at high magnetic fields but at low fields have similar patterns and therefore interact strongly. Damping of these modes, their excitation by antennas, and the rf plasma absorption efficiency are considered. Nonuniform plasmas are treated by solving a fourth-order ordinary differential equation numerically. A significant difference between this and earlier codes which divide the plasma into uniform shells is made clear. Excitation of the weakly damped H wave, followed by conversion to the strongly damped TG wave which leads to high helicon discharge efficiency, is examined for realistic density profiles. A reason for the greater heating efficiency of the m=+1 vs the m=−1 mode for axially peaked profiles is provided.

Computation of seismograms and atmospheric oscillations by normal-mode summation for a spherical earth model with realistic atmosphere

Abstract: We describe a theory to compute seismograms and atmospheric disturbances such as ionospheric oscillations or pressure variations in a realistic spherical earth model with atmosphere. This theory is valid for a source located either in the solid earth or in the atmosphere. Solid earth and atmospheric normal modes are computed for a radiation boundary condition that models the dissipation of acoustic signals in the high atmosphere of the Earth. We show that the coupling between ground and atmosphere occurs at a set of frequencies related to fundamentals and harmonics of atmospheric modes. Spheroidal modes near these frequencies have up to 0.04 per cent of their energy in the atmosphere, and thus may be strongly excited by atmospheric sources. This theory can be used for more accurate modelling of the seismic data from meteoritic events or volcanic eruptions as well as for the analysis of barograms or ionograms recorded after large earthquakes.

Dynamics of Bose-Einstein condensed gases in highly deformed traps

Abstract: We provide a unified investigation of normal modes and sound propagation at zero temperature in Bose-Einstein condensed gases confined in highly asymmetric harmonic traps and interacting with repulsive forces. By using hydrodynamic theory for superfluids we obtain explicit analytic results for the dispersion law of the low-energy discretized modes for both cigar- and disk-shaped geometries, including the regime of large quantum numbers where discrete modes can be identified with phonons. The correspondence with sound propagation in cylindrical traps and the one-dimensional nature of cigar-type configurations are explicitly discussed.

Off-resonant fifth-order nonlinear response of water and CS2: Analysis based on normal modes

Abstract: Off-resonant fifth-order nonlinear response functions of liquid water and liquid CS2 are analyzed based on two normal-mode schemes, quenched and instantaneous normal modes. It was found that the fifth-order response function is very sensitive to the mode mixing in polarization, arising from the quadratic term of polarization with respect to the different modes. The echo signal is drastically reduced by this off-diagonal mode mixing in polarization even without any rapid frequency modulation mechanism. The near absence of echo signal thus obtained for liquids is consistent with the recent experimental results for liquid CS2. The present calculation yields the different fifth-order signals for different polarization geometries, as experimentally shown by Tokmakoff and Fleming [J. Chem. Phys. 106, 2569 (1997)]. The mode mixing dynamics is investigated in terms of the bispectra of total potential energy and polarizability.

Cellular detonation stability. Part 1. A normal-mode linear analysis

Abstract: A detailed investigation of the hydrodynamic stability to transverse linear disturbances of a steady, one-dimensional detonation in an ideal gas undergoing an irreversible, unimolecular reaction with an Arrhenius rate constant is conducted via a normal-mode analysis The method of solution is an iterative shooting technique which integrates between the detonation shock and the reaction equilibrium point Variations in the disturbance growth rates and frequencies with transverse wavenumber, together with two-dimensional neutral stability curves and boundaries for all unstable low- and higher frequency modes, are obtained for varying detonation bifurcation parameters These include the detonation overdrive, chemical heat release and reaction activation energy Spatial perturbation eigenfunction behaviour and phase and group velocities are also obtained for selected sets of unstable modes Results are presented for both Chapman–Jouguet and overdriven detonation velocities Comparisons between the earlier pointwise determination of stability and interpolated neutral stability boundaries obtained by Erpenbeck are made Possible physical mechanisms which govern the wavenumber selection underlying the initial onset of either regular or irregular cell patterns are also discussed

Vibrational Assignment of Torsional Normal Modes of Rhodopsin: Probing Excited-State Isomerization Dynamics along the Reactive C11C12 Torsion Coordinate

Abstract: The resonance Raman spectrum of the 11-cis retinal protonated Schiff base chromophore in rhodopsin exhibits low-frequency normal modes at 93, 131, 246, 260, 320, 446, and 568 cm-1. Their relatively strong Raman activities reveal that the photoexcited chromophore undergoes rapid nuclear motion along torsional coordinates that may be involved in the 200-fs isomerization about the C11C12 bond. Resonance Raman spectra of rhodopsins regenerated with isotopically labeled retinal derivatives and demethyl retinal analogues were obtained in order to determine the vibrational character of these low-frequency modes and to assign the C11C12 torsional mode. 13C substitutions of atoms in the C12−C13 or C13C14 bond cause the 568-cm-1 mode to shift by ∼8 cm-1, and deuteration of the C11C12 bond downshifts the 568- and 260-cm-1 modes by ∼35 and 5 cm-1, respectively. The magnitudes of these shifts are consistent with those calculated for modes containing significant C11C12 torsional character. Thus, we assign the 568-cm-1 ...

Frequency and wave-vector dependent dielectric function of water: Collective modes and relaxation spectra

Abstract: The longitudinal frequency and wave-vector dependent complex dielectric response function χ(k,ω)=1−1/e(k,ω) is calculated in a broad range of k values by means of molecular dynamics computer simulation for a central force model of water. Its imaginary part, i.e., Im{e(k,ω)}/|e(k,ω)|2, shows two main contributions in the region of small k values: Debye-like orientational relaxation in the lower frequency part of the spectrum and a damped librational resonance at the high frequency wing. The Debye relaxation time does not follow a de Gennes-like pattern: τ(k) goes through a maximum at k≈k*≈1.7 A−1, while the static polar structure factor S(k) peaks at k≈3 A−1. The resonance frequency ω(k) and the decay decrement γ(k) show a dispersion law, indicative of a decaying optical-like mode, the libron. With an approximate normal mode approach, we analyze the origin of this mode on a molecular level which shows that it is due to a damped propagation of molecular orientational vibrations through the network of hydrogen bonds. At high k the decay, due to dissipation of collective into single particle motions, dominates. The static dielectric function is calculated on the basis of the response function spectra via the Kramers–Kronig relation. In the small k region e(k) decreases from the macroscopic value e≈80 to a value ≈15, i.e. it exhibits a Lorentzian-type behavior. This behavior is shown to be determined by higher order multipole correlation functions. In the intermediate and high k range, our results on e(k) and χ(k) are in excellent agreement with data extracted from experimental partial pair correlation functions: e(k) exhibits two divergence points on the k axis with a range of negative values in between where a maximum in χ(k) is found with χmax(k)≫1, indicative of overscreening. Consequences of quantum corrections to χ(k) with respect to a purely classical calculation are discussed and consequences are shown for the interaction energy between hydrated ions.

Biorthonormal-basis method for the vector description of optical-fiber modes

Abstract: This paper gives the theoretical basis for the development of real vector modal methods to describe optical-fiber modes. To this end, the vector wave equations, which determine the electromagnetic fields, are written in terms of a pair of linear, nonself-adjoint operators, whose eigenvectors satisfy biorthogonality relations. The key of our method is to obtain a matrix representation of the vector wave equations in a basis that is defined by the modes of an auxiliary system. Our proposed technique can be applied to fibers with any profile, even those with a complex refractive index. An example is discussed to illustrate our approach.

A new way of analyzing vibrational spectra : II. Comparison of internal mode frequencies

Abstract: Adiabatic internal frequencies are compared with c-vector frequencies and intrinsic frequencies. It is shown that c-vector modes are not suitable to characterize molecular fragments f since they are not localized in f and their definition leads to nn unreasonable frequency values. Intrinsic frequencies suffer from a strong dependence on the set of internal parameters chosen to describe the geometry of the molecule. Apart from this, they represent averaged frequencies, for which mass effects and electronic effects are not properly separated. Adiabatic frequencies are based on a dynamic principle, separate properly mass effects and electronic effects and do not depend in any

A density functional, infrared linear dichroism, and normal coordinate study of phenol and its deuterated derivatives: Revised interpretation of the vibrational spectra

Abstract: The assignment of the vibrational spectra of phenol has been reexamined on the basis of Raman and new IR measurements and theoretical analysis of the normal modes of vibrations in the electronic ground state. The infrared spectra of C6H5OH, C6D5OD, and C6D5OH have been studied in solution and vapor phases, as well as has the Raman spectra in solutions. New experimental data were obtained from infrared linear dichroism (IR-LD) studies of phenol aligned in uniaxially oriented nematic liquid crystal solution. The measured dichroic ratios and orientation factors indicate an effective Cs symmetry of the molecule with coplanar orientation of OH bond with the benzene ring and supply unique information on the extent of symmetry lowering of benzene normal modes. The fundamental vibrational frequencies, force constants, and dipole derivatives have been calculated by ab initio quantum chemical methods applying the B3P86 density functional approximation with 6-311G** basis set. The force field optimized by means of a...

A new way of analyzing vibrational spectra : IV. Application and testing of adiabatic modes within the concept of the characterization of normal modes

Abstract: The CNM characterization of normal modes method for extracting chemical information out of vibrational spectra is tested for vibrational spectra of molecules with relatively strong or relatively weak coupling between internal vibrational modes. Symmetry, parameter set stability, and frequency uncertainty tests are applied to check whether internal vibrational modes, internal mode frequencies, and amplitudes A comply with symmetry, are independent of the set of internal parameters O used to nU n describe molecular geometry or fulfill a Lorentzian correlation between amplitudes AnU and frequency differences a a â a a a . In all cases considered, amplitudes A nU n U n U based on adiabatic internal modes and mass or force constant matrices as metric O are superior to any other definition of amplitude. They represent the basic elements of the new CNM method that leads to chemically reasonable results and presents a new way of extracting chemical information out of vibrational spectra. A number of deficiencies of e. the potential energy distribution PED analysis is discussed. a 1998 John Wiley & Sons, Inc. Int J Quant Chem 67 :4 1 a55, 1998

Dynamic structure factor of vitreous silica from first principles: Comparison to neutron-inelastic-scattering experiments

Abstract: Using a first-principles approach, we study the vibrational properties of vitreous SiO2 which are measured in neutron-scattering experiments. We adopt a model structure consisting of corner-sharing tetrahedra, which was previously generated using first-principles molecular dynamics. We calculate the dynamic, structure function S(q,E) as a function of wave vector q and energy E by taking explicitly into account the correlations between different atoms as given by the normal modes. The effects of temperature and finite displacements are also considered. Overall, the agreement with experiment is very good, as illustrated by the comparison for the density of states. However, the calculated and measured S(q,E) differ in some cases up to a factor of 2 in absolute intensity. Nevertheless, the oscillations in S(q,E) describing the correlations between the motions of the atoms are accurately reproduced. The neutron effective density of states obtained directly from S(q,E) yields a good representation of the actual density of states. By introducing a comprehensive scheme, we clarify the relation between neutron and infrared spectre. In particular, we show that the neutron density of states does not distinguish between longitudinal and transverse excitations. Other properties such as the mean-square displacements and the elastic structure factor are also evaluated and found to be in good agreement with experiment.

On the density distribution within the Earth

Abstract: SUMMARY The distribution of density as a function of position within the Earth is much less well constrained than the seismic velocities. The primary information comes from the mass and moment of inertia of the Earth and this information alone requires that there be a concentration of mass towards the centre of the globe. Additional information is to be found in the frequencies of the graver normal modes of the Earth which are sensitive to density through self-gravitation eVects induced in deformation. The present generation of density models has been constructed using linearized inversion techniques from earlier models, which ultimately relate back to models developed by Bullen and based in large part on physical arguments. A number of experiments in non-linear inversion have been conducted using the PREM reference model, with fixed velocity and attenuation, but with the density model constrained to lie within fixed bounds on both density and density gradient. A set of models is constructed from a uniform probability density within the bound and slope constraints. Each of the resultant density models is tested against the mass and moment of inertia of the Earth, and for successful models a comparison is made with observed normal mode frequencies. From the misfit properties of the ensemble of models the robustness of the density profile in diVerent portions of the Earth can be assessed, which can help with the design of parametrization for future reference models. In both the lower mantle and the outer core it would be desirable to allow a more flexible representation than the single cubic polynomial employed in PREM.

Ballooning instability of a thin current sheet in the high-Lundquist-number magnetotail

Abstract: Two-dimensional simulations of the magnetotail in the high-Lundquist-number regime indicate the slow growth of thin current sheets and an impulsive intensification of the cross-tail current density at near-Earth distances during a short interval just before the onset of the expansion phase, consistent with multi-satellite observations. Such a two-dimensional magnetotail, symmetric along y and containing a thin current sheet, is found to be unstable to a symmetry-breaking, ideal compressible ballooning instability with high wave number along y. The linear instability is demonstrated by numerical solutions of the ideal ballooning eigenmode equation for a sequence of two-dimensional thin current sheet configurations in the impulsive growth phase. Line-tied boundary conditions at the ionosphere are imposed, and shown to play a crucial role in the stability analysis. It is suggested that the ideal ballooning instability, which has strong spatial variation along y, provides a possible mechanism for disrupting the cross-tail current at onset.

New developments in the analysis of vibrational spectra On the use of adiabatic internal vibrational modes

Abstract: Publisher Summary Depending on geometry, conformation, and electronic structure, each molecule has vibrational spectra that are measured with the help of infrared or Raman spectroscopy. Conclusions can be drawn from the measured vibrational spectra with regard to the structure of a compound. Vibrational frequencies and force constants in the harmonic approximation can be calculated and these values are used for the analyses of measured vibrational spectra. This chapter presents a way of analyzing calculated vibrational spectra in terms of internal vibrational modes associated with the internal coordinates used to describe geometry and conformation of a molecule. An internal mode is localized in a molecular fragment by describing the rest of the molecule as a collection of massless points that just define molecular geometry. Alternatively, the new fragment motions can be considered as motions that are obtained after relaxing all parts of the vibrating molecule but the fragment under consideration. The new modes are suited to analyze the vibrational spectra of a molecule in terms of internal coordinate modes, to correlate the vibrational spectra of different molecules, and to extract chemically useful information directly from vibrational spectra. The chapter discusses the concept of localized internal vibrational modes, the basic equations of vibrational spectroscopy, previous attempts of defining internal vibrational modes, definitions of adiabatic internal modes, adiabatic internal force constant, mass, and frequency, characterization of normal modes in terms of internal vibrational modes, definition of internal mode amplitudes, and analysis of vibrational spectra in terms of adiabatic internal modes. There is the explanation of the correlation of vibrational spectra of different molecules, derivation of bond information from vibrational spectra, and adiabatic internal modes from experimental frequencies, and a generalization of Badger's rule. There are details on intensities of adiabatic internal modes and investigation of reaction mechanism with the help of the CNM analysis.

FTIR and Polarised Raman Spectra of Acrylamide and Polyacrylamide

Abstract: The Fourier Transform Infrared (FTIR) and Laser Raman spectra of acrylamide and polyacrylamide are presented. The frequencies were assigned to various fundamental modes on the basis of normal coordinate calculations. The agreement between the observed and calculated frequencies was good, and the assignment of the normal modes was satisfactorily realized.

Two-mode response of simply supported, rectangular laminated plates

Abstract: Two-mode responses of thin rectangular laminated plates subjected to a harmonic excitation are studied by using the method of multiple scales (MMS). The plates are assumed to be simply supported along all edges, and internal resonances between two symmetric modes of vibration are analysed. In order to use MMS properly, we introduce new detuning parameters which indicate the relationship of natural frequencies of each mode. It is found analytically that two-mode responses can occur at each primary resonance. The accuracy of analytical results is confirmed in comparison with results of numerical integration of the equation of motion. Furthermore, it is detected that the two-mode response near the primary resonance of the second mode loses its stability via a Hopf bifurcation, giving rise to quasi-periodic response.

Biophysical aspects of coherence and biological order.

Abstract: Biological Order * Thermodynamic Aspects of Order * Normal Modes * Quantum Mechanical Theory of Rate Equations * Energy Condensation * Coherence in Systems with Random Energy Supply * Spectral Transformation of Energy * Oscillating Electric Field Generated by Living Cells * Information Transfer Between Oscillation Systems * Interaction Between Vibration Systems * Heat Bath Coupling Effects * Coherent States in Cancer Cells.

Ab initio calculations of radiationless transitions between excited and ground singlet electronic states of ethylene

Abstract: General expressions for internal conversion (IC) rate constant calculations have been derived by taking into account displacements, distortions, and rotation (mixing) of normal modes. The electronic part of the rate constant has been computed through the ab initio calculations of vibronic coupling. The corresponding expressions for the simplest two-mode case as well as for the general n-mode case have been derived. We demonstrate the effect of rotated (mixed) normal modes on the IC rate constants based on a model consisting of one promoting and two mixed modes. The dynamics of excited states of C2H4 has been investigated based on the internal conversion mechanism. The calculated rate of internal conversion show that the lifetimes of the excited π–3p and π–π* states of C2H4 are on the picosecond scale. We predict that if the molecule is excited to a Rydberg π–3p state, it relaxes to the ground state via the cascade mechanism, π–3p→π–3s(1B3u)→π–π*(1B1u)→1Ag.