Perturbed structures generated using coordinates derived from compliance constants in internal vibrations for QTAIM dual functional analysis: Intrinsic dynamic nature of interactions

Perturbed structures for QTAIM dual functional analysis (QTAIM‐DFA) are proposed to generate using the coordinates corresponding to the compliance force constants in internal vibrations (CIV). In QTAIM‐DFA, total electron energy densities H_b( r _c) are plotted versus H_b( r _c) – V_b( r _c)/2 at bond critical points (BCPs) of interactions in question, where V_b( r _c) are potential energy densities at BCPs. Each plot of an interaction based on the data from both perturbed structures and fully optimized one takes the form (θ_p, κ_p), where θ_p corresponds to the tangent line of the plot and κ_p is the curvature. The θ_p values evaluated with CIV are equal to those obtained by partial optimizations with the interaction distance in question being fixed suitably, within the calculation errors. Very high applicability of CIV is demonstrated to generate the perturbed structures for QTAIM‐DFA. Dynamic nature of interactions based on (θ_p, κ_p) with CIV is called “intrinsic dynamic nature of interactions.”     

Periodic solutions to nonlinear one dimensional wave equation with -dependent coefficients

This paper deals with -periodicity and regularity of solutions to the one dimensional nonlinear wave equation with -dependent coefficients

     

Subharmonic Response of a Quasi-Isochronous Vibroimpact System to a Randomly Disordered Periodic Excitation

A quasi-isochronous vibroimpact system is considered, i.e. a linear system with a rigid one-sided barrier, which is slightly offset from the system's static equilibrium position. The system is excited by a sinusoidal force with disorder, or random phase modulation. The mean excitation frequency corresponds to a simple or subharmonic resonance, i.e. the value of its ratio to the natural frequency of the system without a barrier is close to some even integer. Influence of white-noise fluctuations of the instantaneous excitation frequency around its mean on the response is studied in this paper. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, or velocity jumps, thereby permitting the application of asymptotic averaging over the period for slowly varying inphase and quadrature responses. The averaged stochastic equations are solved exactly by the method of moments for the mean square response amplitude for the case of zero offset. A perturbation-based moment closure scheme is proposed for the case of nonzero offset and small random variations of amplitude. Therefore, the analytical results may be expected to be adequate for small values of excitation/system bandwidth ratio or for small intensities of the excitation frequency variations. However, at very large values of the parameter the results are approaching those predicted by a stochastic averaging method. Moreover, Monte-Carlo simulation has shown the moment closure results to be sufficiently accurate in general for any arbitrary bandwidth ratio. The basic conclusion, both of analytical and numerical simulation studies, is a sort of smearing of the amplitude frequency response curves owing to disorder, or random phase modulation: peak amplitudes may be strongly reduced, whereas somewhat increased response may be expected at large detunings, where response amplitudes to perfectly periodic excitation are relatively small.     

Thermodynamic calculations for molecules with asymmetric internal rotors. II. Application to the 1,2-dihaloethanes

The thermodynamic properties of three halocarbon molecules relevant in atmospheric and public health applications are presented from ab initio calculations. Our technique makes use of a reaction path-like Hamiltonian to couple all the vibrational modes to a large-amplitude torsion for 1,2-difluoroethane, 1,2-dichloroethane, and 1,2-dibromoethane, each of which possesses a heavy asymmetric rotor. Optimized ab initio energies and Hessians were calculated at the CCSD(T) and MP2 levels of theory, respectively. In addition, to investigate the contribution of electronically excited states to thermodynamic properties, several excited singlet and triplet states for each of the halocarbons were computed at the CASSCF/MRCI level. Using the resulting potentials and projected frequencies, the couplings of all the vibrational modes to the large-amplitude torsion are calculated using the new STAR-P 2.4.0 software platform that automatically parallelizes our codes with distributed memory via a familiar MATLAB interface. Utilizing the efficient parallelization scheme of STAR-P, we obtain thermodynamic properties for each of the halocarbons, with temperatures ranging from 298.15 to 1000 K. We propose that the free energies, entropies, and heat capacities obtained from our methods be used to supplement theoretical and experimental values found in current thermodynamic tables.     

Human reaction to vibrations from blasting activity – Norwegian exposure–effect relationships

Rock blasting may cause disturbances, fear, and annoyance in residential and community areas affected by such activities. These community reactions can be quite strong, even when the blasting activities and the resulting vibrations are unlikely to cause physical damage to building foundations or buildings. A socio-vibrational survey was undertaken to assess residential reactions to blasting activities. Vibration velocities were obtained for 520 respondent dwellings located in seven study areas, and compared to the residents’ assessments of environment quality. Even at low vibration values, many people report annoyance. Exposure–effect relationships with acceptable statistical error bands were obtained. The level of annoyance from long-term blasting activities (quarry blasting) was not higher than from finite periods of more intense blasting activities (road and rail tunnels). Providing information in advance of the blasting activities, can reduce community reactions. Self-reported sensitivity to vibrations was associated with significantly increased annoyance. Sensitivity to vibrations was uncorrelated with exposure to vibrations. Sensitivity to noise and sensitivity to vibration were moderately correlated.     

Gear transmission dynamics: Effects of index and run out errors

This work describes a non-linear dynamic model for the study of the vibration signals generated by gear transmissions. The developed model considers both the parametric excitations due to the variable compliance of bearings and gears, can handle changes in the transmitted torque and allows the integration of the dynamic equations quickly and accurately. This model has been developed previously by the authors to assess the profile deviations on the dynamic behavior of gear transmissions and its influence on the transmitted torque. It also includes the presence of gear defects as cracks and pitting during the calculation of meshing forces. In this paper, the model has been enhanced in order to include two common defects such as index errors and run out or eccentricity errors. Index errors occur as a result of a non-uniform angular distribution of the tooth profiles along the pitch circle. Run out appears due to the displacement of the geometric center of the gear with respect to the center of rotation of the shaft on which it is mounted. Although both errors are caused by different reasons, sometimes they have been confused because of their similitudes. The procedure for including both kinds of errors in the model is described and simulations under several transmitted torques are presented. The results are assessed and compared focusing the attention on certain transmission parameters and magnitudes as transmission error, load forces in the tooth flanks and demodulation techniques on the resulting vibratory signals.     

Nonlinear Response of Cylindrical Shells to Random Excitation

An analytical study of nonlinear flexural vibrations of cylindrical shells to random excitation is presented. Donnell's thin-shell theory is used to develop the governing equations of motion. Thermal effects for a uniform temperature rise through the shell thickness are included in the formulation. A Monte Carlo simulation technique of stationary random processes, multi-mode Galerkin-like approach and numerical integration procedures are used to develop nonlinear response solutions of simply-supported cylindrical shells. Numerical results include time domain response histories, root-mean-square values and histograms of probability density. Comparison of Monte Carlo results is made to those obtained by statistical linearization and the Fokker–Planck equation.     

An Approximate Analysis of Dry-Friction-Induced Stick-Slip Vibrations by a Smoothing Procedure

This paper deals with a systematic procedure to find both stable and unstable periodic stick-slip vibrations of autonomous dynamic systems with dry friction. In this procedure, the discontinuous friction forces are approximated by smooth functions. Using the simple shooting method with a stiff-ODE solver, in combination with a path following algorithm, branches of periodic solutions are computed for a changing design variable. For testing purposes, both 1 and 2-DOF autonomous block-on-belt models and a 1-DOF autonomous drill string model from literature are investigated. Comparison of the results shows that the smoothing procedure accurately describes the behavior of the discontinuous systems. The proposed procedure can also easily be applied to more complex MDOF models, as well as to nonautonomous dynamic systems.     

IR spectroscopic investigation of structural hydroxyl groups in W−Si heteropolycompound supported on Al2O3

Structural hydroxyl and deuteroxyl groups within the K₄[SiW₁₂O₄₀]/Al₂O₃ and K₆[SiW₁₁PdO₃₉]/Al₂O₃ systems were studied by diffuse-reflectance FTIR spectroscopy in a spectral range of fundamental stretching vibrations, first overtones, and combination bands of stretching and bending vibrations. For hydroxyl groups, the region of combination vibrations is the most informative. The calculated frequencies of bending vibrations of hydroxyl groups (865 and 730 cm⁻¹) are characteristic of acidic OH groups. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2017–2020, October, 1999.     

Molecular anharmonicity: A computer-aided treatment

We present a new software package for the theoretical treatment of anharmonic vibrational spectra of nonlinear polyatomic molecules. The package, called “B&D,” computes vibrational energies starting from sets of force constants defined as potential energy derivatives. The method employed allows us to combine experimental rotation-vibration data with any information made available from ab initio calculations. The package follows the natural procedure in which a molecular problem is solved, both in the symbolic construction of Hamiltonian operator and basis functions and in the numerical computation of the Hamiltonian matrix elements. The novelty consists in making the entire procedure fully automatic, so that the occurrence of errors is greatly reduced and the laborious process involved in deriving and implementing the Hamiltonian is dramatically simplified. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1716–1730, 1999