Coupling Of Vibrational Modes Research Articles

Multilevel Redfield description of the dissipative dynamics at conical intersections

Redfield theory is applied to investigate the photoinduced dynamics at a conical intersection (the so-called system) which is weakly coupled to a thermal environment (the so-called bath). The dynamics of the system is described by a two-state three-mode model Hamiltonian, chosen to represent the S1(nπ*)–S2(ππ*) conical intersection in pyrazine. Dissipative effects are introduced through a bilinear coupling of the system vibrational modes with a harmonic bath, which represents the remaining vibrational degrees of freedom of the molecule and/or interactions with a condensed-phase environment. The Redfield equations for the reduced density matrix are solved numerically without further approximations. From the reduced density matrix the time evolutions of electronic-state populations and vibrational coherences are obtained, as well as time-dependent probability densities of individual vibrational modes. The results provide a visualization of the essential features of the ultrafast (time scale of 10 fs) internal-conversion process at the conical intersection and the ensuing vibrational cooling process on the lower adiabatic potential-energy surface. The effect of vibrational damping on the linear optical absorption spectrum is also investigated.

A practical method for the use of curvilinear coordinates in calculations of normal-mode-projected displacements and Duschinsky rotation matrices for large molecules

While use of curvilinear coordinates such as bond lengths and bond angles is common in accurate spectroscopic and/or scattering calculations for triatomic and other small molecules, their use for large molecules is uncommon and restricted. For large molecules, normal-mode analysis is feasible but gives sensible results only if the dynamical or spectroscopic process being considered involves changes in angular coordinates, including ring deformations, which are so small that the motion can be approximated by its tangential component. We describe an approximate method by which curvilinear normal-mode-projected displacements and hence Franck–Condon factors, reorganization energies, and vibronic coupling constants, as well as Duschinsky (Dushinsky, Duschinskii) rotation matrices, can be evaluated for large systems. Three illustrative examples are provided: (i) to understand the nature of the first excited state of water, illustrating properties of large-amplitude bending motions; (ii) to understand the nature of the “boat” relaxation of the first excited state of pyridine, illustrating properties of large-amplitude torsional motions; and (iii) to understand the coupling of vibrational modes to the oxidation of bacteriochlorophyll-a, a paradigm with many applications to both chemical and biological electron transfer, illustrating properties of macrocyclic deformations. The method is interfaced to a wide variety of computational chemistry computer programs.

A frequency response function-based structural damage identification method

This paper introduces an frequency response function (FRF)-based structural damage identification method (SDIM) for beam structures. The damages within a beam structure are characterized by introducing a damage distribution function. It is shown that damages may induce the coupling between vibration modes. The effects of the damage-induced coupling of vibration modes and the higher vibration modes omitted in the analysis on the accuracy of the predicted vibration characteristics of damaged beams are numerically investigated. In the present SDIM, two feasible strategies are introduced to setup a well-posed damage identification problem. The first strategy is to obtain as many equations as possible from measured FRFs by varying excitation frequency as well as response measurement point. The second strategy is to reduce the domain of problem, which can be realized by the use of reduced-domain method introduced in this study. The feasibility of the present SDIM is verified through some numerically simulated damage identification tests.

Femtosecond vibrational-electronic four-wave-mixing spectroscopy

Two novel two-dimensional vibrational-electronic spectroscopies are theoretically proposed. The first method uses electronically off-resonant fields to create a vibrational coherence state in the ground electronic state and then thus created transient grating is probed by using a time-delayed electronically resonant field. The second method is to use an infrared pulse to create a vibrational coherence state and an electronically two-photon resonant field is used to probe the IR-induced vibrational grating in time. These two methods are found to be useful in selectively studying vibronic coupling of the solvent intermolecular vibrational modes to the electronic transition of a chromophore dissolved in an isotropic medium.

Squeal of a Disk Brake of Floating Type for Cars. 1st Report. Relationship between Occurrence of Squeal and Contact Region between Rotor and Pads in Experiment.

This paper describes the experimental results of squeal of disk brake of floating type. The squeal of new type has a low frequency and a coupled vibration mode between rotor and caliper through pads. From the experiments, it was made clear that the occurrence of the squeal changes according to the contact distribution in the circumferential and the radial directions between rotor and pads. In the case of cutting a part of pad surfaces in the circumferential direction, it is effective for squeal reduction to cut the pointed end pad surfaces of leading side on the inner side, and in the case of cutting a part of pad surfaces in the radial direction, it is effective for squeal reduction to cut outer pad surfaces of inside in the radial direction. Moreover, frictional vibration of a block subjected to distributed friction at contact surface was treated analytically and experimentally and a common mechanism of vibration of block and disk brake was found.

3304 ディスクブレーキの鳴きに関する一考察(OS4 高速化とサービス向上)

This paper describes the numerical results about squeal of disk brake. The squeal considered in this paper is low frequency squeal (1.8-2.5kHz), and has coupled vibration modes between rotor and caliper through pads. To investigate the mechanism of low frequency squeal, disk brake is modeled as a two-degree-of-freedom model. The brake system become unstable and occur the squeal when the coefficient of friction is relatively high. And to make the stiffness of caliper bigger, the squeal is restrained. From the analysis, it was made clear that the coefficient of friction between rotor and pads, and stiffness of caliper (especially the stiffness of trailing side) had grent influence to the low frequency squeal. So in design of the real brake system, these values are very important to restrain the low frequency squeal.

Vibration Analysis of Multi Degree of Freedom System by Simplified Rotor Dynamics Model.

This paper describes the evaluation of analytical Simplified Rotor dynamics Model (SRM) under the multi-freedom condition. Rotor-dynamic of gas-turbine rotor supported by the flexible casing with Legs is selected as the evaluation Model. SRM which consists of the lumped-mass and beam-element is applied for the casing and rotor dynamic system. Proving procedure of SRM is based on 3 Steps. The first step is the fundamental modeling based on test data of casing with support-leg and rotor. Second is the evaluation compared with analytical and test results in revolution under the multi-freedom condition. Third is final step for the applied case. Through these proving procedures, casing and rotor coupled vibration modes of complex vibration structure were made clear by SRM. Further the Influence of support-structure elements were investigated in simple manner by SRM. SRM is conformed to be useful analytical tool for the rotor dynamic characteristics of multi-freedom vibration system.

Electron–vibrational mode coupling in (Ph4P)2·C60·I from Raman scattering

Raman scattering excited with 1064nm laser beam was used to study the temperature properties of the radical anion salt C60 with tetraphenylphosphoniumiodide (Ph4P)2·C60·I. The enhanced intensity, broadening and red-shift of the low-frequency C60 modes were all explained as a result of electron–molecular vibration (e–mv) interactions. The e–mv coupling constants were evaluated for low-frequency Hg and Ag modes of the fullerene monoanion. The determined coupling constants for (Ph4P)2·C60·I are in good agreement with earlier results for the fullerene and its compounds.

Nonlinear Two-Dimensional Vibrational Spectroscopy

There is currently great interest in developing the vibrational analog to two-dimensional NMR spectroscopy. One approach to implementing two-dimensional vibrational spectroscopy is to use doubly vibrationally enhanced (DOVE) four-wave mixing (FWM). Nonlinear signals occur because of correlations and mode coupling that are induced by interactions involving the driven modes. Since cross peaks do not occur between modes if interactions are absent, spectral congestion is removed and only the coupled modes remain. We describe the development of a two-dimensional doubly vibrationally enhanced four wave mixing method that extends the doubly resonant nonlinear spectroscopies to vibrational nonlinearities. We demonstrate the selective enhancements of coupled modes that are possible with the double resonances where the intensity of the enhancements reflects the strength of the interactions that are responsible for the vibrational mode coupling. We also demonstrate the capabilities for selectively enhancing specific sample components in an isotopic mixture. Since biological applications of DOVE require aqueous environments, we have examined the ability of DOVE methods to discriminate against the strong water absorption and have found that water has a small vibrational nonlinearity that allows DOVE of the solutes. Our results demonstrate the feasibility and features required to make DOVE methods practical for a wide range of scientific applications where identification of intra- and intermolecular interactions is important.

NHY coupling and localized vibration modes in MX compounds

Abstract The effects of NHY coupling on localized vibration modes around the excitations in MX compounds are investigated. It is shown that the localized modes in an isolated chain will be separated into two chains due to an NHY coupling. Some new modes of lattice vibration are found, which are achieved by the NHY coupling. These results can qualitatively account for the frequency shifts of some modes observed in the Raman and infrared absorption spectra.

Real-time vibrational mode-coupling associated with ultrafast geometrical relaxation in polydiacetylene induced by sub-5-fs pulses

The relaxation time of the free-exciton→geometrically relaxed 2 1 A g state in polydiacetylene is determined as 65–80 fs, depending on the probe energy. The vibrational non-equilibrium in the relaxed 2 1 A g state is characterized by the modulations of instantaneous frequencies and amplitudes of CC and C–C stretching modes with a 145-fs oscillation period. The frequency modulation is anti-phase between the two modes, and the amplitude and frequency are also anti-phase for both modes. These are explained by the coupling of the stretching modes through an in-plane bending mode with 230 cm −1. This is the first real-time observation of dynamic vibrational mode coupling.

Theoretical description of the nonlinear response functions associated with eight distinctive three-dimensional vibrational spectroscopies

The three-dimensional (3D) vibrational spectroscopies are theoretically considered in terms of the associated nonlinear response functions. Since the 3D vibrational spectroscopy involves three vibrational coherence evolutions in the ground electronic state, it is found that there are eight distinctive possibilities when a vibrational coherence state can be created via an infrared field–matter interaction or two off-resonant optical field–matter interactions via Raman. The nonlinear response functions associated with eight distinctive 3D vibrational spectroscopies, where seven of them are novel methods, are presented and expressed in terms of the linear response functions by taking the lowest-order contributions. The analytic expressions of the 3D Fourier spectra are obtained. By using the results, how to utilize the 3D vibrational spectroscopic methods to measure the higher-order vibrational mode coupling arising from the anharmonicity of the multidimensional potential energy surface as well as from the nonlinearity of the dipole moment or polarizability with respect to the vibrational degrees of freedom is discussed. Numerical calculations of the results for a three-oscillator model system are presented, and a few characteristic peaks uniquely appearing in the 3D vibrational spectra are discussed in detail. Finally, the third-order nonlinear terms of dipole moment and polarizability are found to be of critical use in the structure determination, assuming that the collective dipole moment and polarizability is mainly determined by the dipole-induced–dipole interaction effect.

Fundamental Vibration Modes of Stiffened Tank Plate in Contac with Fluid

Vibration design of stiffened plates of tank wall is usually carried out in such way that the natural frequencies of both panel vibration and stiffened plate vibration should exceed the exciting frequencies to avoid the resonance. However, panel and stiffener coupling mode of vibration would appear in tank wall adjoining fluid as fundamental vibration mode due to the configuration of tank. If such vibration mode occure, it may cause vibration problem because the natural frequency of this coupling mode vibration is lower than the above two frequencies.In this paper, vibration mode of tank wall filled with fluid is investigated by analytical approach in terms of added mass effect of fluid and the followings are clarified : 1) The natural frequency of panel and stiffener coupling vibration mode “sp” is always lower than that of stiffened plate vibration mode “s”, although it never happens without fluid interaction. The reduction of this natural frequency is caused by the coupling with stiffened plate and small panels due to added mass effect.2) The natural frequency of panel and stiffener coupling vibration mode “sp” becomes lower than that of panel vibration mode “p” in case that the configuration of the tank satisfies, roughly saying, B/L≤0.3 or H/L≥0.5Therefore, in designing the tank structure, it is important to consider the natural frequency of panel and stiffener coupling mode to prevent vibration problem according to the tank dimension.

Reduced-Order Controller of Transverse-Torsional Coupled Vibration Based on Linear Matrix Inequalities

This paper is concerned with the application of reduced-order controller to a flexible structure hav ing the transverse-torsional coupled vibration modes. The dynamical model of the structure is first presented and then the robust controller for the structure is designed by using the H ∞-control theory. Furthermore, the order of the controller is reduced by using the combination of the alternating-projection method and the weighted-balanced realization. The performance of the reduced-order controller is examined through simu lation and experiment. To verify its robustness and validation in the transverse-torsional coupled vibration condition, the lumped mass is added on the right side at the 3rd story. From these results, it is made clear that the reduced-order controller obtained by the proposed method is effective in reducing the vibration of the structure, where the order of the controller can be reduced to 8th order from 30th order.

Intensity-dependent decarbonylation dynamics in Cr(CO) 6·(CH 3OH) n heteroclusters at 280 nm

Femtosecond pump/probe studies of ultrafast decarbonylation and solvent dynamics of Cr(CO) 6·(CH 3OH) n heteroclusters with respect to pump intensity at 280 nm are presented. The dynamics changes significantly when increasing pump intensity. In contrast to sequential decarbonylation at low pump intensity, Cr(CO) 5, which is formed from Cr(CO) 6 ( 1 T 1u) after ejection of CO on the timescale of our femtosecond pulses, absorbs an additional pump photon at higher intensities. This species yields further fragments from a highly excited state on an ultrafast timescale. The picosecond dynamics of the solvated fragments formed involves solvent cluster loss and evaporation by coupling of vibrational molecular modes to cluster modes.

Free Vibration and Stability of a Spinning Disk-Spindle System

This work examines the free vibration and stability of a spinning, elastic disk-spindle system. The extended operator formulation is exploited to discretize the system using Galerkin’s method (Parker, 1999). The coupled vibration modes of the system consist of disk modes, in which the disk dominates the system deformation, and spindle modes, in which the spindle dominates the system deformation. Both the natural frequencies and vibration modes are strongly affected by disk flexibility. If the membrane stresses associated with disk rotation are neglected then the system exhibits flutter instabilities, but these instabilities are not present when membrane stresses are modeled. Natural frequency veering between disk and spindle frequencies is prominent at low speeds and substantially affects the spectrum and stability. No veering is observed at high speeds where rotational stress stiffening diminishes disk-spindle coupling and causes the natural frequencies to converge to those of a rotating spindle carrying a rigid disk. Changes to the vibration modes are examined in terms of a strain energy ratio measuring the contribution of the disk strain energy to the total modal strain energy.

Time- and frequency-resolved coherent two-dimensional IR spectroscopy: Its complementary relationship with the coherent two-dimensional Raman scattering spectroscopy

A theoretical description of the coherent two-dimensional IR spectroscopy is presented. Two consecutive IR pulses can be used to create two consecutive vibrational coherence states. The third off-resonant optical pulse is used to probe the two-dimensional transient grating thus created and then the scattered field is measured. The corresponding nonlinear response functions are obtained in the analytic forms by assuming that the vibrational modes are weakly anharmonic Brownian oscillators. Since one can experimentally control the two delay times as well as the two IR field frequencies, it is possible to extract vital information on the vibrational relaxation in time domain as well as the intra- and intermolecular vibrational mode couplings in frequency domain. Numerical calculations are carried out to clarify the quantitative features of the coherent 2D IR spectroscopic phenomenon.

On the resonant coherent two-dimensional Raman scattering

A theoretical description of the resonant coherent two-dimensional Raman scattering (ReCOTRAS) process is presented. In comparison to the third-order coherent Raman scattering, ReCOTRAS measurement in frequency domain is a two-dimensional experiment probing two vibrational coherence states simultaneously. By using three external fields with frequencies and wave vectors as (ω1,ω2,ω3) and (k1,k2,k3), it is found that the ReCOTRAS field is generated with the frequency and the wave vector of 3ω1−ω2−ω3 and 3k1−k2−k3, respectively. It is shown that this experiment can provide two-dimensional vibrational spectrum that contains crucial informations on the vibrational mode-couplings in both the ground and the excited states. Unlike its off-resonant analogue, this method can be used to study the vibrational interactions in the electronic excited state.

Analysis i Required Frequency Band of Electric-Structural-Acoustic Coupled System.

When an acoustic field in an enclosed space is controlled using the structural vibration control by the piezoelectric actuator, electric system, structural system and acoustic system are influenced each other. Thus this system must be considered as electric-structural-acoustic coupled system. In this paper, the analysis in the required frequency band of electric-structural acoustic coupled system has been carried out. In this analysis, the structural vibration is approximated by the superposition of the electric-structural coupled vibration modes which are included in the required frequency band, and the truncated frequency band are compensated by the residual terms. This truncation method is the application of the authers' previous method. As a numerical example, a flexible rectangular prism model is taken up and the vibration of structure, the voltage of piezoelectric actuator and the sound pressure in the model are calculated using the proposed method. It is shown that the analysis of coupled system has reached the accurate results comparing with the one of nucoupled system, the calculated results using the proposed method agree with the exact ones which are obtained by using the full frequency band, and calculation time is saved.

Controller-Order Reduction of Transverse-Torsional Coupled Vibration Control Based on Modal Truncation

This paper is concerned with the problem of reducing a high-order controller to a reduced-order one for flexible structures which have transverse-torsional coupled vibration mode without significant errors. Firstly, the controller is designed for the structure by using H∝ control theory. Due to using the frequency weighting filter for compensating the unstructured uncertainty, the order of that controller leads to the high order, meanwhile, the high-order controller is not practical in implementation. Secondly, the order of the controller is reduced by using the modal truncation. This method is verified by comparing to the model reduction which has been widely used to find a reduced order controller. From the simulation and experiment results, it is confirmed that the reduced order controller obtained by the controller reduction is better than the reduced-order controller obtained by the model reduction.