Eigenfrequencies of radial vibrations of a spherical sandwich shell

Free across-the-thickness vibrations of a closed spherical shell consisting of three rigidly connected layers with arbitrary physical constants and thicknesses are studied. A closed-form solution in displacements to a one-dimensional (along the radius) vibration problem for a homogeneous spherical shell is derived and then used in posing a boundary-value problem on free vibrations of a heterogeneous sphere. Based on the degeneration of the sixth-order determinant of a system of homogeneous equations satisfying the corresponding boundary conditions, a transcendental equation for eigenfrequencies is found. Transformation variants for the equation of eigenfrequencies in the cases of degeneration of physical and geometric parameters of the compound shell are considered. The main attention in investigating the lowest frequency is given to its dependence on the structure of shell wall, whose parameters greatly affect the calculated values of the high-frequency vibration spectrum of the shell. Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 839–852, November–December, 2008.     

Induced and back scattering in a ruby laser

From the condition of generation (of the reproducibility of opposite waves for a pass around a resonator) it follows that in addition to amplitude-phase changes an active medium must also compensate for backscatter in the resonator. The most probable mechanism involved in this compensation is nonlinear backscatter. In the process of generation, nonlinear scattering compensates for resonator scattering as a result of self-regulation. Amplitude-frequency characteristics are determined by the types of vibrations of a resonator, whereas nonlinear effects specify these characteristics. Higher College of Communication, 8/2 Staroborisovskii Trakt, 220114, Minsk, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 6, pp. 881–887, November–December, 1998.     

Numerical solution to the initial-boundary-value problem of electroelasticity for a radially polarized hollow piezoceramic cylinder

The paper proposes and analyzes different approaches to constructing numerical schemes to solve the nonstationary vibration problem for a radially polarized piezoelectric hollow cylinder with different electric boundary conditions under mechanical loading. It is established that when the cylinder is subjected to internal pressure, the radial displacements are similar and the longitudinal displacements substantially different in cylinders with electroded and nonelectroded surfaces __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 12, pp. 67–75, December, 2006.     

Two-end observability of elastic vibrations in distributed and lumped parameter systems

The boundary observation problems (initial state reconstruction) of vibrations in objects with distributed and lumped parameters are solved. The vibrations in an object with distributed parameters are described by boundary value problems with boundary conditions of various types. An object with lumped parameters is described by a second-order ordinary differential equation.     

Surface lattice dynamics of thep(3×1)−Ag(110) system

Summary We present a detailed study of the lattice dynamics of thep(3×1)O-Ag(110) surface to determine the structural changes of the substrate upon oxygen chemisorption. The lattice dynamical calculations are carried out using central forces with nearest-neighbour interactions and assuming different surface structures. The limits of the models are discussed. A comparison with the dispersion curves measured along two azimuthal directions by means of energy-resolved He-atom scattering unambiguously shows the reconstruction of the silver substrate. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Rayleigh Quotient, Ritz Method and Substructuring to Study Vibrations of Structures Coupled to Heavy Fluids: Potential of the Artificial Spring Method

The linear study of free vibrations of structures coupled to incompressible and inviscid fluids are studied by using the Rayleigh-Ritz method. The system is modelled by using different components. The artificial spring method is used to synthesise these components. The advantage is that admissible functions are defined in each component and the continuity condition of translational and rotational displacements between the rigid joints of the structure is no longer required. The fluid-structure interaction can be accurately described by using this method, including the effect of the free surface waves and the dynamic interaction among structural components via the fluid medium. An application of the method to a vertical circular tank partially filled with water is also presented in order to show the potential of the method. This revised version was published online in July 2006 with corrections to the Cover Date.     

Light absorption due to higher harmonics of molecular vibrations in transparent amorphous polymers for plastic optical fibers

We have studied simple empirical equations to estimate light absorption loss α_v due to harmonics of molecular vibrations of transparent amorphous polymers used in plastic optical fibers (POFs). In the visible region, absorption involves two losses. One is α_v, and the other is the electronic transition absorption loss, α_e. Of the two, α_v is considerably larger than α_e in the wavelength region used for optical communication with POFs. We have clarified relationships between chemical structure of repeat units of polymers and α_v. We find that α_v is proportional to the concentration of specific chemical bonds (C? H, N? H, and Obond;H bonds) in the polymer solid, and we propose empirical equations to estimate α_v from the polymer density and the chemical structure of the repeat unit. These equations are used to estimate α_v of several polymers [i.e., poly(methyl methacrylate), polystyrene, and polycarbonate]. The estimated values are nearly equal to the experimental or reference values. Furthermore, to minimize the attenuation in the POF, we conclude that the POF core polymer should have no N? H, O? H, or aliphatic C? H bonds in its repeat unit.     

Comparison of Theoretical Methods and Basis Sets for ab initio and DFT Calculations of the Structure and Frequencies of Normal Vibrations of Polyatomic Molecules

The dependence of the quality of calculation of the geometric parameters and frequencies of normal vibrations on the choice of the theoretical method and the basis set of Gaussian functions has been investigated within the framework of four approximations (DFT/B3LYP, HF, MP2, MP3), using benzene and s-triazine molecules as an example. It has been shown that the molecular parameters calculated using the basis set without polarization functions within the framework of any of the above theoretical methods agree poorly with the experimental data. It has been concluded that the use of the basis set 6-31G(d) within the framework of these methods with allowance for the electron correlation for calculating the geometric parameters and frequencies of normal vibrations of polyatomic cyclic compounds is most optimum in terms of the relation between the expenditure of time and the quality of the calculation. The coefficients of linear scaling of frequencies have been obtained by the DFT/B3LYP method for 22 basis sets that were tested on porphin, pyrrole, indene, and pyridine molecules. Atypically large errors in determining the frequencies of some benzene and s-triazine vibrations have been obtained in a number of quantum-mechanical calculations with large basis sets. The changes in the force field for these cases have been investigated with the example of the benzene molecule.     

Calculation and analysis of the frequencies of normal vibrations of 2,3-Di-O-nitro-methyl-β-D-glucopyranoside

A calculation of the frequencies and forms of the normal vibrations of the 31-atom molecule 2,3-di-O-nitromethyl-β-D-glucopyranoside has been performed. Particular emphasis has been placed on the interpretation of the strongest bands in the spectrum of 2,3-di-O-nitro-methyl-β-D-glucopyranoside, which are due to vibrations of the nitrate groups. The present work has been reported at the IV International Congress of theoretically competent chemists, Jerusalem (Israel), July 7–12, 1996. B. I. Stepanov Institute of Physics, Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 6, pp. 724–728, November–December, 1997.     

Quantum simulation of vibration states and Franck-Condon overlap in non-separable potentials

Summary Taking into consideration nuclear motion in non-separable potentials, we have probed the solution of the Schrödinger equation by random walk sampling in imaginary time on a two-dimensional example. Evaluation of the many-dimensional Franck-Condon overlap and the chemical species conversion rate is outlined.