On the radial oscillations of incompressible, isotropic, elastic and limited elastic thick-walled tubes

The finite amplitude, free radial oscillations of a thick-walled circular cylindrical tube are studied for an arbitrary incompressible, isotropic and homogeneous rubber-like material having limiting molecular chain extensibility. First, based on classical results for hyperelastic tubes, some results for thick-walled Mooney-Rivlin tubes are described graphically in the phase plane. Then the periodicity of the finite amplitude, free oscillations of a general limited elastic, thick-walled tube is studied; and some analytical results for the Gent model are illustrated in several numerical examples. Results for thick-walled Gent tubes are compared with those for corresponding Mooney-Rivlin tubes; and the motion of thin-walled Gent tubes is illustrated in the phase plane. Physical conclusions are presented. The period of small amplitude oscillations of an arbitrary elastic or limited elastic tube is derived from relations obtained by a linearization of a general class of equations of which the tube problem is a special case. Classical results of the linear theory are thereby recovered and compared with results for Mooney-Rivlin and Gent tubes.     

Nonaxisymmetric Vibrations of Discretely Reinforced Inhomogeneous Multilayer Cylindrical Shells under Nonstationary Loads

The equations of nonaxisymmetric vibrations of discretely reinforced multilayer cylindrical shells are analyzed. A refined Timoshenko model of shells and beams is used to analyze elements of an elastic structure. The vibration equations for an inhomogeneous elastic system are derived using the Reissner variational principle. The numerical solver of the dynamic equations is based on the integro-interpolation method used to construct finite-difference schemes for equations with discontinuous coefficients. The dynamic behavior of a five-layer cylindrical shell under distributed nonstationary loading is analyzed     

Asymptotics for the eigenelements of vibrating membranes with very heavy thin inclusionsComportement asymptotique des éléments propres pour des membranes vibrantes avec des couches très minces et très lourdes

We consider the vibrations of a membrane that contains a very thin and heavy inclusion around a curve γ. We assume that the membrane occupies a domain $\text{Ω}$ of $\text{R}{}^2$. The inclusion occupies a layer-like domain $\text{ω}{}_{\mathrm{\epsilon }}\text{?Ω}$ of width 2ε and it has a density of order O(ε^?3). The density is of order O(1) outside this inclusion, the concentrated mass around the curve γ. ε is a positive parameter, ε∈(0,1). By means of asymptotic expansions, we describe the behaviour, as ε→0, of the eigenelements (λ^ε,u^ε) of the associated spectral problem. We provide complete asymptotic series for the low frequencies λ^ε=O(ε²), the medium frequencies λ^ε=O(ε) and the corresponding eigenfunctions u^ε. To cite this article: Y. Golovaty et al., C. R. Mecanique 330 (2002) 777–782.     

Effects of charge-density-wave depinning on the low frequency shear compliance of NbSe3

We report on measurements of the voltage dependence of the complex shear compliance of two crystals of the charge-density-wave (CDW) conductor NbSe₃, for torsional frequencies between 1 Hz and 71 Hz. For both samples, there is a frequency independent, ∼1% increase of the magnitude of the compliance when the voltage exceeds the threshold for CDW depinning, but the internal friction has a striking sample dependence which we do not understand. For one sample, there is a frequency independent decrease in internal friction with CDW depinning, suggesting that the elastic changes are not relaxational and might reflect changes in the screening of the crystal strain by the CDW. For the second sample, the sign and magnitude of the change in internal friction is strongly frequency dependent, which we associate with a change in screening due to the finite electron diffusion time. The second sample also exhibits a frequency dependent peak in internal friction near threshold that may reflect relaxation of the CDW phase. Received 14 August 2001 and Received in final form 3 October 2001     

Investigation of the Raman spectra of CuxAgl−xGaS2 solid solutions

Raman spectra in (┴, ┴) and (║, ║) polarizations are investigated on crystals of CuGaS₂, AgGaS₂ compounds and Cu_xAg_l−xGaS₂ solid solutions. The frequencies of longitudinal and transverse optical phonons are determined, their concentration dependences are constructed, and the behavior of the vibrational modes in Cu_xAg_l−xGaS₂ solid solutions is established. Belarusian State University of Information Science and Radioelectronics, 6P, Brovka St., 220069, Minsk, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 3, pp. 447–449, May–June. 1998.     

Calculation of Normal Vibrations and Interpretation of the Quasiline Spectra of Tetraazachlorin

Quasiline fluorescence and fluorescence-excitation spectra of tetraazachlorin and its N-deuterated derivative in n-octane at 77 K have been investigated and the frequencies of the normal vibrations for the electronic states S ₀ and S ₁ have been determined. Calculation of the normal vibrations of these molecules has been done and used to interpret the experimental data. Based on the results of analysis of the intensities in the spectra, the change in the structure of the molecule in the electronic state S ₁ is discussed.     

Mutual Interdependence of Partitions Functions in Vicinity T g of Transition

The solid—liquid transition is described by use of the model incorporating the non-linear interactive oscillators. The individual non-linear oscillators are formed from the mechanical units of about the monomer size and produce the vibrations on the lower amplitude level, for the solid phase, either in amorphous or in crystal-like form. As the temperature starts to overpass the Vogel's temperature, the vibrations of individual units are big enough to cause the permanent displacements of the individual vibrating particles; the material starts to flow and the process of diffusion begins as well. As the temperature is passing through T _g vicinity, the large mechanical heterogeneity's start to appear as the small percentage of oscillators enlarge their amplitude of vibrations enormously and act as the local stress perturbations centers. These centers are responsible for the destruction of original matrixes and the sharp onset of fluidity and diffusion takes place. The upper amplitude of vibration motion is the basic property of a liquid state. The whole system of vibrations in matrix is described by use of techniques of deterministic chaos theories. It is shown as well, how the mutual interplay of the partition functions (vibration and cohesive), plays the important role in transition from liquid to solid states.This revised version was published online in November 2005 with corrections to the Cover Date.     

Lattice dynamics,thermodynamic and elastic properties of CdGeAs2

Summary An extended Keating’s model with two-bond-stretching and one-angle-bending force constants within the rigid-ion approximation is applied to the investigation of the lattice dynamics of CdGeAs₂. Five model parameters of the theory are determined by a least-square fitting to the infrared reflectivity measurements. The phonon spectrum along two high-symmetry directions and the one-phonon density of states are calculated. The theoretical values of the elastic constants, the constant-volume specific heat and the Debye temperature show a reasonable agreement with the experimental data reported by other authors.     

Number of longitudinal normals and degenerate directions for triclinic and monoclinic media

We solved the problem of finding longitudinal acoustic directions of monoclinic media using the eliminant method. By extending Khatkevich's approach and using the Bezout theorem, we proved that the number of longitudinal normals for mechanically stable monoclinic media can not be larger than 13. Both longitudinal normals (n ₁, n ₂, n ₃) lying in and out of plane perpendicular to the two-fold axis (n ₃ ≠ 0) of monoclinic media are considered. Closed-form equations for ratios x = n ₁/n ₃ y = n ₂/n ₃ are derived and exactly solved by the eliminant method. With the help of this method, we show that in the case of the CDP (CsH₂PO₄) crystal, the number of longitudinal normals equals three. Their components are given. For media of higher symmetries (rhombic, trigonal, tetragonal, hexagonal and cubic), our approach yields well-known results obtained mainly by Borgnis and Khatkevich. For triclinic elastic media, we proved that the number of degenerate directions can not be greater than 132. Received 24 August 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: ardud@ift.uni.wroc.pl     

Extended nature of coupled optical interface modes in Thue-Morse dielectric superlattices

We investigate coupled optical interface modes in Thue-Morse (TM) dielectric superlattices composed of two kinds of materials with frequency-dependent dielectric functions. Four basic transfer matrices are derived in the dielectric continuum approximation. By a standard matrix operation method, the trace map of the global transfer matrix in this configuration is obtained. Under Born-von Kármán boundary conditions, the frequency spectra are calculated and their branching rules together with the quartet property are elucidated. It is further proved rigorously that nearly all eigenmodes in this framework have extended nature. The quartet of the eigenmodes is illuminated analytically. The common features and pronounced differences compared with coupled optical interface modes in periodic and Fibonacci dielectric superlattices as well as with other collective elementary excitations in TM structures are also revealed. Received 24 September 2002 / Received in final form 11 January 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: gjin@nju.edu.cn