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Vibrational analysis forced vibration

The homonuclear rare gas pairs are of special interest as models for intennolecular forces, but they are quite difficult to study spectroscopically. They have no microwave or infrared spectmm. However, their vibration-rotation energy levels can be detennined from their electronic absorjDtion spectra, which he in the vacuum ultraviolet (VUV) region of the spectmm. In the most recent work, Hennan et al [24] have measured vibrational and rotational frequencies to great precision. In the case of Ar-Ar, the results have been incoriDorated into a multiproperty analysis by Aziz [25] to develop a highly accurate pair potential. [Pg.2447]

The model consists of a two dimensional harmonic oscillator with mass 1 and force constants of 1 and 25. In Fig. 1 we show trajectories of the two oscillators computed with two time steps. When the time step is sufficiently small compared to the period of the fast oscillator an essentially exact result is obtained. If the time step is large then only the slow vibration persists, and is quite accurate. The filtering effect is consistent (of course) with our analytical analysis. Similar effects were demonstrated for more complex systems [7]. [Pg.278]

Notice that although the energies and forces are evaluated quantum mechanically in HyperChem, the vibrational analysis has been purely classical. [Pg.336]

Similar information can be obtained from analysis by dynamic mechanical thermal analysis (dmta). Dmta measures the deformation of a material in response to vibrational forces. The dynamic modulus, the loss modulus, and a mechanical damping are deterrnined from such measurements. Detailed information on the theory of dmta is given (128). [Pg.258]

Once the 3D strucmre of a molecule and all the parameters required for the atomic and molecular connectivities are known, the energy of the system can be calculated via Eqs. (l)-(3). First derivatives of the energy with respect to position allow for determination of the forces acting on the atoms, information that is used in the energy minimization (see Chapter 4) or MD simulations (see Chapter 3). Second derivatives of the energy with respect to position can be used to calculate force constants acting on atoms, allowing the determination of vibrational spectra via nonnal mode analysis (see Chapter 8). [Pg.11]

For complex offshore structures or where foundations may be critical, finite-element analysis computer programs with dynamic simulation capability erm be used to evaluate foundation natural frequency and the forced vibration response. [Pg.320]

Analysis of a vibrational spectnim gives rUe and hence the force constant ks. [Pg.33]

A clear understanding of the mechanical movement of machines and their components is an essential part of vibration analysis. This understanding, coupled with the forces applied by the process, are the foundation for diagnostic accuracy. [Pg.670]

The boundary conditions established by the machine design determine the freedom of movement permitted within the machine-train. A basic understanding of this concept is essential for vibration analysis. Free vibration refers to the vibration of a damped (as well as undamped) system of masses with motion entirely influenced by their potential energy. Forced vibration occurs when motion is sustained or driven by an applied periodic force in either damped or undamped systems. The following sections discuss free and forced vibration for both damped and undamped systems. [Pg.677]

Stiffness Stiffness is a spring-like property that describes the level of resisting force that results when a body undergoes a change in length. Units of stiffness are often given as pounds per inch (Ibf/in). Machine-trains have more than one stiffness property that must be considered in vibration analysis shaft stiffness, vertical stiffness, and horizontal stiffness. [Pg.677]

While steady-state data provide a snapshot of the machine, dynamic or real-time data provide a motion picture. This approach provides a better picture of the dynamics of both the machine-train and its vibration profile. Data acquired using steady-state methods would suggest that vibration profiles and amplitudes are constant. However, this is not tme. All dynamic forces, including mnning speed, vary constantly in all machine-trains. When real-time data acquisition methods are used, these variations are captured and displayed for analysis. [Pg.687]

V-belts are common intermediate drives for fans, blowers, and other types of machinery. Unlike some other power-transmission mechanisms, V-belts generate unique forcing functions that must be understood and evaluated as part of a vibration analysis. The key monitoring parameters for V-belt-driven machinery are fault frequency and mn-ning speed. [Pg.705]

The 13C-NMR spectra of 4-7, 9-11 show a close similarity to the spectral data of analogous carbene complexes. The shift differences between the metal carbonyls of the silylene complexes and the related carbon compounds are only small. These results underline the close analogy between the silicon compounds 4-7, 9-11 and Fischer carbene complexes. This view is also supported by the IR spectral data. On the basis of an analysis of the force constants of the vco stretching vibration,... [Pg.18]

Vibrational spectroscopy has played a very important role in the development of potential functions for molecular mechanics studies of proteins. Force constants which appear in the energy expressions are heavily parameterized from infrared and Raman studies of small model compounds. One approach to the interpretation of vibrational spectra for biopolymers has been a harmonic analysis whereby spectra are fit by geometry and/or force constant changes. There are a number of reasons for developing other approaches. The consistent force field (CFF) type potentials used in computer simulations are meant to model the motions of the atoms over a large ranee of conformations and, implicitly temperatures, without reparameterization. It is also desirable to develop a formalism for interpreting vibrational spectra which takes into account the variation in the conformations of the chromophore and surroundings which occur due to thermal motions. [Pg.92]

For larger systems, where MP4 calculations are no longer tractable, it is necessary to use scaling procedures. The present results make it possible to derive adapted scaling factors to be applied to the force constant matrix for each level of wave function. They can be determined by comparison of the raw calculated values with the few experimental data, each type of vibration considered as an independent vibrator after a normal mode analysis. [Pg.404]

Regardless of the force field chosen, the calculation of vibrational frequencies by the method outlined above is based on the harmonic approximation. Tabulated values of force constants can be used to calculate vibrational frequencies, for example, of molecules whose vibrational spectra have not been observed. However, as anharmonicities have been neglected in the above analysis, the resulting frequency values are often no better than 5% with respect to those observed. [Pg.123]

For polyatomic molecules, the stretching force constant for a particular bond cannot in general be obtained in an unambiguous manner because any given vibrational mode generally involves movements of more than two of the atoms, which prevent the expression of the observed frequency in terms of the force constant for just one bond. The vibrational modes of a polyatomic molecule can be analyzed by a method known a normal coordinate analysis to... [Pg.42]

In a similar way the potential constant method as described here allows the simultaneous vibrational analysis of systems which differ in other strain factors. Furthermore, conformations and enthalpies (and other properties see Section 6.5. for examples) may be calculated with the same force field. For instance, vibrational, conformational, and energetic properties of cyclopentane, cyclohexane and cyclodecane can be analysed simultaneously with a single common force field, despite the fact that these cycloalkanes involve different distributions of angle and torsional strain, and of nonbonded interactions 8, 17). This is not possible by means of conventional vibrational spectroscopic calculations. [Pg.173]


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See also in sourсe #XX -- [ Pg.264 , Pg.301 , Pg.313 ]




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