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.     

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.     

Nonlinear vibrations in beams and frames: The effect of the deformed equilibrium state

In the study of nonlinear vibrations of planar frames and beams with infinitesimal displacements and strains, the influence of the static displacements resulting from gravity effect and other conservative loads is usually disregarded. This paper discusses the effect of the deformed equilibrium configuration on the nonlinear vibrations through the analysis of two planar structures. Both structures present a two-to-one internal resonance and a primary response of the second mode. The equations of motion are reduced to two degrees of freedom and contain all geometrical and inertial nonlinear terms. These equations are derived by modal superposition with additional subsidiary conditions. In the two cases analyzed, the deformed equilibrium configuration virtually coincides with the undeformed configuration. Also, 2% is the maximum difference presented by the first two lower frequencies. The modes are practically coincident for the deformed and undeformed configurations. Nevertheless, the analysis of the frequency response curves clearly shows that the effect of the deformed equilibrium configuration produces a significant translation along the detuning factor axis. Such effect is even more important in the amplitude response curves. The phenomena represented by these curves may be distinct for the same excitation amplitude.     

Convective Instability of the Flow of a Binary Mixture under Conditions of Vibration and Thermal Diffusion

Stability of a plane-parallel flow of a nonuniformly heated binary mixture filling a vertical layer located in a field of gravity and in a high-frequency vibrational field is studied. The axis of vibrations is directed along the layer. The case of rigid and isothermal boundaries of the layer impermeable for the mixture is considered. The influence of thermal diffusion on the evolution of the admixture and the thresholds of flow stability is taken into account. The study is performed on the basis of equations for averaged fields. An asymptotic method with the use of the perturbation wavenumber as a small parameter is applied in the long-wave limit. For arbitrary values of the wavenumber, the limit of stability was determined by numerical integration. Charts of stability of gaseous and liquid binary mixtures are plotted. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 77–84, March–April, 2006.     

Natural Vibrations of a Cylindrical Shell with Circular Ribs Attached by Means of Discrete Elastic Elements

The vibrations of a cylindrical shell reinforced with circular ribs attached to it by means of discrete elastic elements are studied. The problem is solved by the finite-element method. The shell and ribs are modeled by a plane four-node finite element, which is a combination of a four-node plane stress element and a four-node flexural element. The effect of the stiffness of the elastic elements on the natural frequencies and modes is examined __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 108–113, October 2005.     

On Free Nonlinear Vibrations of Fluid-Filled Cylindrical Shells with Multiple Natural Frequencies

Nonlinear free vibrations of a cylindrical shell fully filled with a perfect incompressible fluid are studied. The case is examined where two natural frequencies of the shell are close __________ Published in Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 127–138, October 2005     

Action of a Periodic Load on an Elastic Floating Plate

The problem of the behavior of an elastic floating plate in the form of a strip under the action of a periodic surface load is solved using the Wiener-Hopf technique. The shortwave approximation is found in explicit form. The effect of the frequency and nature of the acting load on the vibration amplitudes of the fluid and the plate is investigated numerically. It is found that for certain loads no waves propagate in the fluid and the vibrations of the plate are localized in the neighborhood of the acting load. Conditions under which local vibration can be realized are found.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 132–146.Original Russian Text Copyright © 2005 by Tkacheva.     

Forced Nonstationary Vibrations of a Sandwich Cylindrical Shell with Cross-Ribbed Core

The equations of nonaxisymmetric vibrations of sandwich cylindrical shells with discrete core under nonstationary loading are presented. The components of the elastic structure are analyzed using a refined Timoshenko theory of shells and rods. The numerical method used to solve the dynamic equations is based on the integro-interpolation method of constructing finite-difference schemes for equations with discontinuous coefficients. The dynamic problem for a sandwich cylindrical shell under distributed nonstationary loading is solved with regard for the discreteness of the core__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 60–67, February 2005.     

Features of the Motion of a Gas-Liquid Medium in a Compound Shell (Sphere and Truncated Cone) Subject to Vibration

The results from an experimental study into the dynamic behavior of a gas-liquid medium and solid particles in a compound shell (sphere-truncated cone) are reported on. The following processes are studied: formation of gas bubbles and their clusters, strong macroflows, and intensive chaotic motion of the medium in the truncated cone as a nonlinear vibrating liquid-gas system__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 112–118, January 2005.     

Non-linear vibrations of suspension bridges with external excitation

Non-linear coupled vertical and torsional vibrations of suspension bridges are investigated. Method of Multiple Scales, a perturbation technique, is applied to the equations to find approximate analytical solutions. The equations are not discretized as usually done, rather the perturbation method is applied directly to the partial differential equations. Free and forced vibrations with damping are investigated in detail. Amplitude and phase modulation equations are obtained. The dependence of non-linear frequency on amplitude is described. Steady-state solutions are analyzed. Frequency-response equation is derived and the jump phenomenon in the frequency-response curves resulting from non-linearity is considered. Effects of initial amplitude and phase values, amplitude of excitation, and damping coefficient on modal amplitudes, are determined.