High Frequency Vibrational Modes Research Articles

DYNAMIC STRESS ANALYSIS OF GAS TURBINE ROTOR AIRFOILS USING THERMOELASTIC TECHNIQUES

Summary The SPATE system provided a means for experimental ther-moelastic analysis of high frequency modes of vibration of a complicated turbine impeller which did not facilitate analysis with conventional methods due to low stress response and high modal density. Testing also demonstrated a unique experimental stress analysis technique which was applied to a blade and vane airfoil and exhibited excellent stress distribution correlation with an established experimental technique (brittle lacquer) and with analytical stress distributions predicted by NASTRAN. Full field dynamic stress analysis of gas turbine compressor airfoils accomplished using thermoelastic techniques provided an efficient method of determining optimum strain gage locations for monitoring rig and engine vibratory stress. Significant cost savings could be realized using this technique from: (1) reduction in the amount of instrumentation required to characterize airfoil dynamic behavior and (2) increased vibratory response mode coverage thereby preventing the re-running of engine test programs to measure vibratory stress response levels of unexpected resonances encountered during initial engine testing. Care is required when using SPATE results for vibratory modes resulting in high bi-axial stress distributions since the system output indicated stress magnitudes based on the sum of the principal stresses which could be significantly higher than either of the individual principal stresses.

Low temperature optical absorption spectroscopy: an approach to the study of stereodynamic properties of hemeproteins.

In this short review we show how suitable analysis of the temperature dependence of the optical absorption spectra of metalloproteins can give insight into their stereodynamic properties in the region of the chromophore. To this end, the theory of coupling between an intense allowed electronic transition of a chromophore and Franck-Condon active vibrations of the nearby atoms is applied to the Soret band of hemeproteins to obtain an analytical expression suitable for fitting the spectral profile at various temperatures. The reported approach enables one to separate the various contributions to the overall bandwidth together with the parameters that characterize the vibrational coupling. The thermal behavior of these quantities gives information on the dynamic properties of the active site and on their dependence upon protein structure and ligation state. The Soret band of hemeproteins appears to be coupled to high frequency vibrational modes of the heme group (as already shown by resonance Raman spectroscopy) and to a "bath" of low frequency modes most likely deriving from the bulk of the protein. For the deoxy derivatives inhomogeneous broadening arising from conformational heterogeneity appears to contribute substantially to the linewidth. The data indicate the onset, at temperatures near 180 K, of large scale anharmonic motions that can be attributed to jumping among different conformational substates of the protein.

Structure-dynamics-function relationships in Asian elephant (Elephas maximus) myoglobin. An optical spectroscopy and flash photolysis study on functionally important motions

In this work we report the thermal behavior (10-300 K) of the Soret band lineshape of deoxy and carbonmonoxy derivatives of Asian elephant (Elephas maximus) and horse myoglobins together with their carbon monoxide recombination kinetics after flash photolysis; the results are compared to analogous data relative to sperm whale myoglobin. The Soret band profile is modeled as a Voigt function that accounts for the coupling with high and low frequency vibrational modes, while inhomogeneous broadening is taken into account with suitable distributions of purely electronic transition frequencies. This analysis makes it possible to isolate the various contributions to the overall lineshape that; in turn, give information on structural and dynamic properties of the systems studied. The optical spectroscopy data point out sizable differences between elephant myoglobin on one hand and horse and sperm whale myoglobins on the other. These differences, more pronounced in deoxy derivatives, involve both the structure and dynamics of the heme pocket; in particular, elephant myoglobin appears to be characterized by larger anharmonic contributions to soft modes than the other two proteins. Flash photolysis data are analyzed as sums of kinetic processes with temperature-dependent fractional amplitudes, characterized by discrete pre-exponentials and either discrete or distributed activation enthalpies. In the whole temperature range investigated the behavior of elephant myoglobin appears to be more complex than that of horse and sperm whale myoglobins, which is in agreement with the increased anharmonic contributions to soft modes found in the former protein. Thus, to satisfactorily fit the time courses for CO recombination to elephant myoglobin five distinct processes are needed, only one of which is populated over the whole temperature range investigated. The remarkable convergence and complementarity between optical spectroscopy and flash photolysis data confirms the utility of combining these two experimental techniques in order to gain new and deeper insights into the functional relevance of protein fluctuations.

Superconductivity of M3C60 Within Eliashberg Theory11The project supported by National Natural Science Foundation of China and Zhejiang Science Foundation.

The important feature of the alkali-metal-doped C60 is that the intramolecular high-frequency vibration modes arising from the covalent interaction and the intermolecular low-frequency vibration modes arising from the weak Van der Waals interaction both play important roles in the properties of superconductivity. We propose a two-peak form for the phonon density of states. By solving the Eliashberg equations we get the formula for the reduced gap 2Δ0/kBTc and the transition temperature Tc which are all in accordance with the experimental values.

Protein dynamics. Vibrational coupling, spectral broadening mechanisms, and anharmonicity effects in carbonmonoxy heme proteins studied by the temperature dependence of the Soret band lineshape

In this work we study the temperature dependence of the Soret band lineshape of the carbonmonoxy derivatives of sperm whale myoglobin, human hemoglobin, and its isolated alpha and beta subunits. To fit the observed spectral profile we use an analytic expression derived for a system whereby a single electronic transition is coupled to Franck-Condon active vibrational modes, within the adiabatic and harmonic approximation. The vibronic structure of the spectra arises from the coupling with high frequency modes; these modes contribute to the total line shape through a series of Lorentzians with peak positions at vibrational overtones and half width related to the time constant of the population decay of the excited electronic state (homogeneous broadening); moreover, the coupling with low frequency modes broadens each Lorentzian to a Voigtian. Inhomogeneous broadening is modeled as a gaussian distribution of the 0-0 transition frequencies and is therefore added as a constant term to the previous gaussian width. This spectral deconvolution enables us to investigate the different contributions to line broadening and the parameters that characterize the vibrational coupling, as well as their dependence upon protein and solvent composition. The investigation is carried out as a function of temperature in the range 20-300 K; relevant information is obtained by comparing experimental results with theoretical predictions. This work supports a description of the investigated proteins as heterogeneous systems, whose heterogeneity depends on the particular protein and on the composition of the external matrix. The delocalized pi electron cloud of the porphyrin ring is coupled not only to the high frequency vibrational modes of the active site but also to a "bath" of lower frequency modes that involve the entire protein; moreover at suitable temperatures (approximately 200 K), anharmonic motions, which are an obvious prerequisite for the jumping among different conformational substates, become evident.

Failure Detection and Identification of Structural Control Systems

This paper presents a method for the detection, identification, and recovery of component failures of active structural control systems. In this approach, the time and direction of a failure are identified by using innovation process of the Kalman filter and generalized likelihood ratio method. Then, the method sequentially estimates the level of failure by which the fault-free state estimates are corrected for recovery. The detection algorithm is simplified from the view point of computational efficiency and designed for a limited-size memory. This approach is useful for the fault detection of structural control systems in the presence of high-frequency vibration modes which are truncated from the con-troller design. Utility of the proposed method is illustrated with a numerical example of a vibration damping control for beam.

On the Localization of the Vibration Mode of a Sub-Structural Chain-Type Structure

The localization phenomenon for high-frequency vibration modes of imperfectly repetitive structures is considered by using an analogy between computational structural mechanics theory and optimal control theory. In particular, the simplectic matrix method of control theory is applied to the dynamic external stiffness matrix of a typical repeating sub-structure. The eigensolution of the simplectic matrix for the case where the sub-structures are connected by a single line of springs is solved analytically. This gives the passband for the frequency of the travelling waves along the sub-structural chain and the corresponding eigenmode. Hence it is shown how the influence of local disturbances of the sub-structural chain on the behaviour of the whole chain can be considered analytically, thus explaining the mechanism of the localization of high-frequency vibration modes. Numerical examples are therefore not needed, although a few are introduced solely to confirm the correctness of conclusions already drawn from the analytical method.

Vibrational properties of Ba 1- xK xBiO 3: A molecular dynamics study

We present a rigid-ion model of Ba 1- x K x BiO 3 for compositions x=0.25 and x=0.40. Partial vibrational density of states of ions in the compounds Ba 0.75K 0.25BiO 3 and Ba 0.6K 0.4BiO 3 are reported at room temperature and 100 K. The oxygen modes dominate the vibrational spectrum from 150 up to 820 cm -1. The low frequency modes are associated with the cations. The number of substituted K around an oxygen favors high frequency vibrational modes. Qualitative agreement between the calculated phonon density of states of Ba 0.6K 0.4BiO 3 and available experimental data is achieved.

Analysis of a Hydrodynamic Bearing Under Transverse Vibration of an Axially Moving Band

This paper presents a mathematical model of the flow and pressure developed in a hydrodynamic guide bearing film under transverse vibration of a translating band. The guide bearing is commonly used in band and circular sawing systems. The perturbed pressure is derived in the frequency domain based on a linearized, incompressible fluid film model. Unsteady fluid inertia, caused by the high frequency vibration modes of the flexible band, is included in the model. The perturbed pressure is generated by two mechanisms, one caused by the band convection, and the other by the band transverse vibration. Moreover, the pressure generations are governed by fluid impedance functions, which characterize the viscous diffusion across the film. Results for both the transient and steady state responses of the film are presented and discussed. It is shown that the pressure component caused by the band convection, which has not been considered in the literature, is important at low frequency. The pressure component caused by the band transverse vibration is dominant at high frequency.

Vibrational contributions to rougheting; a study for the (111) and (100) FCC Lennard-Jones systems

It is well known that simple lattice-gas models of surfaces predict roughening temperatures ( T R) for close packed faces, as determined by the temperature at which step free energies vanish, to be above the melting point. Further, these models predict T R to scale as the ratio of the number of inplane bonds for different faces. Vibrational contributions, in the form of line tensions and step entropies calculated in the harmonic limit, to the roughening temperature are calculated for the (111) and (100) faces of a face center cubic Lennard-Jones system. Inclusion of these effects reduces T R significantly to temperatures below the melting point and brings T R for the (111) and (100) closer together in agreement with experiment. However, the ordering of T R switches from that expected, that is the (111) transition now occurs below that of the (100). Local density of state spectra show the 〈011〉 step on the (100) face to exhibit localized high frequency vibration modes above the bulk continuum.

Effect of friction on electron transfer: The two reaction coordinate case

Electron transfer is a very important reaction in many biological processes such as photosynthesis and oxidative phosphorylation. In many of these reactions, most of the interesting dynamics can be included by using two reaction coordinates: one fast (local high frequency vibration modes) and one slow (outersphere modes such as solvent polarization). We report a model to describe this problem, which uses path integral techniques to calculate electron transfer rates, and also to obtain the Fokker–Planck equations associated with this model. Different limiting cases lead to qualitatively different results such as exponential or nonexponential time decay for the donor survival probability. Conditions for the validity of the adiabatic or the nonadiabatic limits will be discussed. Application of this model to real systems is proposed, in particular for a porphyrin rigidly linked to a quinone, which is a very interesting model compound for primary events of photosynthesis. This model can also be used for other multicoordinate biological reactions such as ligand binding to heme proteins. Also, in the concluding part of Sec. III, we discuss the important limit where the fast vibronic mode is much faster than all the other nuclear modes coupled to the problem. In this limit the fast mode ‘‘renormalizes’’ the electronic matrix element, and this considerably simplifies the treatment of the problem, reducing it to coupling only to the slow modes.

Neutron study of a displacive phase transition in N-nitrodimethylamine (DMN) : High and low frequency vibrational modes; high pressure effect on the transition temperature; principal compressibilities

N-Nitrodimethylamine is known to undergo a displacive structural phase transition at T t ∼107 K, (atmospheric pressure) associated with a soft-mode observed in the low temperature phase Raman spectrum. The soft-model has already been assigned to a lattice vibration although crystallographic observations of the symmetry breaking distortion suggest that a coupling with an internal vibration should not be ruled out. To clarify this point neutron inelastic spectra have been recorded. They lead to a better assignment of both the high and low frequency vibrations and to the conclusion that no softening of an intramolecular mode is visible. High pressure (up to 3.5 Kbars) neutron scattering experiments are also described. They give both the directions and magnitudes ( k 1=0.33× 10 −2, k b =1.17 × 10 −2, k 3 = 0.12× 10 −2Kbar −1) of the isothermal principal compressibilities of DMN and the dependence of T t on pressure ((d T t /d P) P=0 ∼ + 4.3 Kbar −1). Spectroscopic and crystallographic data now available on DMN allow us to discuss the mechanism of the transition. An extension of Samara's rule to molecular crystals is attempted

A search for high frequency vibrational modes at a stepped surface

In this paper we present a theory of the vibrations of atoms in the vicinity of a stepped surface on a Bravais crystal. The static relaxations in the positions of the atoms in the crystal are determined, and the atomic force constants are then calculated in the relaxed atomic configuration. The general theory is applied to a simple stepped surface, and the local phonon density of states is carried out for atoms at several points on the stepped surface by the real space continued fraction recursion method. No evidence is found for high frequency surface phonons.

A gauge theory of the integral form: Lattice-like gauge theory invariant under translation and rotation

We construct a gauge theory of the integral form which is invariant under translation and rotation and in which very high frequency vibration modes (which must be described in terms of quarks and gluons) are cut off in the same manner as in the usual lattice gauge theory.

The investigation of high frequency vibration modes of PZT-4 transducers using ESPI techniques with reference beam modulation

In this paper the experimental vibration amplitudes together with the vibration modes of the PZT-4 transducer radiating front face are presented for generation in various media. The studies were carried out using an electronic speckle pattern interferometer (ESPI) with reference beam modulation to give resolution down to 20 Å of surface amplitude. Analogies are drawn between these transducers and the resonant vibration modes of thin plates. The relationship between the surface vibration amplitudes and the radiation beam pattern of the transducers is also presented.

Resonance enhancement of the vibrations of cytochrome a3 and its conformation in oxidized cytochrome oxidase

Summary Resonance enhancement of high and low frequency vibrational modes of oxidized cytochrome a 3 in several cytochrome oxidase species have been observed when flowing samples and excitation frequencies of 413.1 nm and 406.7 nm were used. The data are interpreted by excitation profile arguments which incorporate optical parameters from the spectra of cytochromes a and a 3 deduced by Vanneste ( Biochemistry 5 , 838–848 (1966)). The carbonyl of oxidized cytochrome a 3 is conjugated with the heme a π-electron system independent of both its iron spin state and the redox state of cytochrome a . This contrasts with the behavior of cytochrome a and of reduced cytochrome a 3 . Mechanistic implications of these conformational differences are briefly considered.

Central force model for the high frequency vibrational bands of glasses

We have set up a simple model for the high frequency vibrational modes of A nX m glasses (i.e. those modes which are probed most easily in infrared absorption and Raman scattering experiments). This model involves using only nearest neighbor central forces and is a generalization of previous work by Sen and Thorpe for AX 2 glasses in which the vibrational spectrum is derived from the connectivity matrix of the structure. Simple algebraic expressions are obtained for the band edges and applied to the spectra of glassy GeS 2, GeO 2 and P 2O 5. The dominant features of the spectra are associated with particular band edges in the central force model, taking due account of selection rules governing polarized Raman scattering in network glasses. Errors to be expected from the omission of non-central forces and long-range Coulomb forces are discussed.

High-frequency vibrational modes at stepped Pt(111) surfaces

We show that vibrational modes with frequencies above the maximum in the bulk can occur at the steps of the Pt(332) or $6(111)\ifmmode\times\else\texttimes\fi{}(11\overline{1})$ surface, as observed by Ibach and Bruchmann, if the largest force constants are increased by \ensuremath{\sim} 30---40% at the steps. The calculations are done by applying the recursion method within clusters of thousands of atoms, with a rotationally invariant first- and second-neighbor bond-angle model for the interatomic forces.

Modelling vibrational modes in diacetylene polymers

High-frequency vibrational modes in polydiacetylene polymers have been simulated using a simple point-mass and harmonic- force-constant model. Excellent agreement has been found between the frequencies of these modes and those observed in resonant Raman scattering from crystals of polydiacetylene polymers with four radically different sidegroups. The atomic displacement vectors for each mode have also been calculated and related to backbone-sidegroup interactions on the polymer chain.

Multiphonon absorption in As 2S 3As 2Se 3 glasses

Multiphonon absorption in As 2S 3 and As 2Se 3 glasses is well explained by a molecular model in terms of combination bands of high frequency vibrational modes of pyramidal As Y 3 and bent As YAs groups ( Y = S or Se). Multiphonon absorption coefficients in mixed As 2S 3As 2Se 3 glasses are nearly additive in terms of the pure components, suggesting a high degree of non-random mixing.