Natural Vibrations of Complex Bodies

The paper sets forth a modified preconditioned conjugate-gradient method with shifted aggregated multilevel preconditioning (MPCG_AMIS). The method is intended to solve large-scale natural-vibration problems. Such problems are typical for the finite-element analysis of buildings and other complex structures and bodies. Using a proper shift in preconditioning improves considerably the spectral properties of the preconditioner and, hence, improves convergence. Using the MPCG_AMIS allows us to avoid lock of convergence, which is the case in the conventional PCG method. The performance of the method is illustrated by examples     

Modeling the thermomechanical behavior of physically nonlinear materials under monoharmonic loading

We analyze approximate approaches to the modeling of the thermomechanical behavior of physically nonlinear materials under harmonic loading. The approaches are based on various harmonic-linearization schemes and the concept of complex moduli. Mechanical and mathematical features of various schemes are considered. Some modifications of the model are proposed to account for various aspects of material behavior under harmonic loading. The problems of vibration and dissipative heating of physically nonlinear bodies are formulated. The main thermomechanical characteristics are analyzed for some classes of problems.The study was partially sponsored by the State Fund for Basic Research of the Ministry of Education and Science of Ukraine (Grant No. 01.07/00050).Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 3–34, September 2004.     

An invariant manifold approach to nonlinear normal modes of oscillation

Summary A method for determining the amplitude-dependent mode shapes and the corresponding modal dynamics of weakly nonlinear vibratory systems is described. The method is a combination of a Galerkin projection and invariant manifold techniques and is applied to a class of distributed parameter vibratory systems. In this paper the general theory for a class of conservative systems is outlined and applied to determine the nonlinear mode shapes and modal dynamics of a linear Euler-Bernoulli team attached to a nonlinear elastic foundation.     

Die inneren Schwingungen der Tetrahetero-Tetrahedran-Anionen Ge44, Sn44- und Pb44

The Internal Vibration of the Tetrahetero-Tetrahedrane Anions Ge₄^4?, Sn₄⁴-, and Pb₄⁴ The Frequencies of the internal vibrations ν₁ (A₁), ν₂(E), ν₃(T₂) of the tetrahetero-tetrahedrane an ions Ge₄⁴- and Sn₄⁴- are determined from the infrared and Raman spectra of K₇LiGe₈ and KSn, respectively. A comparison of the characteristic vibration of tetrahedrane anions X₄⁴- (X = Si, Ge, Sn)and the isoelectronic neutral tetrahedranes Y₄ of the neighbouring elements (Y = P, As, Sb) shows a rather constant ratio of the corresponding frequencies k = v^?(X₄⁴-) = 0,77. This allows for an estimate of v^?(Pb₄⁴-) from the known Bi₄data. In the inflated spectrum of KPb bands are observed in the predicted frequency range.     

Force field calculation for inplane vibrations of ethylene usingcndo/Force method

cndo/Force method is used to evaluate redundancy-free internal valence force field (rfivff) for inplane vibrations of ethylene. The bending force constants, the stretch-band and bend-bend interaction force constants are predicted reasonably well in magnitude and sign by this method; whereas stretching force constants and stretch-stretch interactions are overestimated. Initial force field is set up by transferring stretching force constants from structurally-related molecules and including the rest of the force constants fromcndo force field. The field so constructed is subjected to refinement by the least square method. A total of 64 vibrational frequencies of C₂H₄, C₂D₄, C₂H₂D₂ and their¹³C isotopic modifications are used to determine force field containing 15 parameters. The final force field is found to be reasonable on the basis of frequency fits, potential energy distribution and band assignments.     

Far-infrared spectra of lanthanide complexes with 8-hydroxyquinoline

Summary Vibrational spectra of lanthanide oxines have been measured in the far-infrared region. In addition, the similar yttrium complex was investigated for further experimental evidence for the proposed band assignments. The most important metal-oxygen and metal-nitrogen bond vibrations have been attributed to absorptions between 390–350 cm^–1 and 210–170 cm^–1, respectively.

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Ferne IR-Spektren von Lanthanidenkomplexen mit 8-Hydroxychinolin

Zusammenfassung Es wurden die Vibrationsspektren von Lanthanid-Oxinen im fernen IR-Bereich gemessen. Zusätzlich wurde der analoge Yttrium-Komplex untersucht, um die Bandenzuordnungen experimentell zu stützen. Die wichtigsten Metall-Sauerstoff- und Metall-Stickstoff-Bindungsschwingungen wurden den Absorptionen zwischen 390–350 cm^–1 und 210–170 cm^–1 zugeordnet.

     

Cartesian Dynamics of Simple Molecules III Non-Linear Triatomics (C2v Symmetry)

A simple spring model for the molecular vibrations of non-linear triatomic molecules with C_2v symmetry is described in terms of Cartesian co-ordinates. Analytical expressions for the stretching and bending mode frequencies are obtained and compared with previous derivations. Optimized values of force constants are calculated for models involving two or three adjustable parameters. The validity of the model is demonstrated by the satisfactory agreement between calculated and observed frequencies of isotopic species. The model provides a simple explanation of the near degeneracy of the symmetric and asymmetric stretching frequencies of H₂S and H₂Se.     

IR spectral fingerprints of carbonyl groups in graphite oxide: a theoretical study

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Relationship Between 1H-1H and 19F-19F Inter-Ring Coupling Constants in Fused Aza-Aromatic Systems

A complete analysis of the proton magnetic resonance spectra of quinoline¹ and isoquinoline^2,3 allowed to obtain signs and accurate magnitudes of the ¹H-¹H inter-ring coupling constants (HIRC). Since corresponding ¹⁹F-¹⁹F inter-ring coupling constants (FIRC) in perfluoro-quinoline⁴ and -isoquinoline⁵ are available it was worthwhile to consider whether a correlation could be established between HIRC and FIRC. A correlation of this kind would be of obvious interest to a better understanding of the transmission mechanism of long-range ¹⁹F-¹⁹F couplings.