THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Magneto-volume effects in Fe–Cu solid solutions

The magnetic properties of Fe–Cu metastable solid solutions have been investigated by means of neutron diffraction and magnetisation measurements. These compounds exhibit ferromagnetic order with Curie temperatures above room temperature for concentrations beyond 40 at% in Fe. The magnetic moment at 5 K can reach values over 2 μ_B, while the high field susceptibility is similar to that found in FCC–FeNi Invar alloys. These features together with the low values for the linear coefficient for thermal expansion in the ferromagnetic region suggest that magneto-volume anomalies, including Invar behaviour, play a major role in the magnetic properties of this system when the crystal structure is face centred cubic. Such behaviour could be explained using theoretical total-band energy calculations.     

Crystal chemistry of AB2X4 (X = S,Se, Te) compounds

An attempt is made to correlate the crystal structures of ternary chalcogenides of composition AB₂X₄ with the cationic radius ratio and a pseudo force-constant involving their electronegativities. The resultant diagram adequately resolves structures based on the types K₂SO₄, monoclinic, olivine, MnY₂S₄, Th₃P₄, and CaFe₂O₄ but structure types based on spinel, Cr₃Se₄, and Ag₂HgI₄ are not resolved. Crystal chemical arguments are used to explain these observations and to advance reasons for the successes and failures of this method for predicting structure types.     

Synthesis and kinetics of polymerization of unsaturated monomers with OH groups in their structure: I.3-hydroxyneopentyl acrylate

The synthesis of new unsaturated monomers containing functional groups has been theoretically analyzed by considering a simple kinetic scheme. In the reactions between acetyl and acryloyl chloride with neopentylglycol, it was shown that the comparison between theoretical and experimental results, does not allow us to conclude that the two rate constants controlling the reactions are equivalent. Kinetic experiments of the polymerization of 3-hydroxyneopentyl acrylate were carried out in benzene and 1,4-dioxane solution at different temperatures. Dilatometric techniques and nonlinear least-squares methods were used to obtain kinetic data and to determine the kinetic constants, respectively. The values of $k_p /k_t^{1/2}$ for this monomer were found higher in dioxane than in benzene due, probably, to the fact that in the last solvent the polymerization is heterogeneous. The activation energy, determined by using different values of $k_p /k_t^{1/2}$ was found 7.6 kcal/mol. The stereostructure of the polymers derived from 3-hydroxyneopentyl acrylate and 3-acetoxyneopentyl acrylate was determined by ¹³C-NMR spectroscopy from the analysis of the resonance signals belonging to the carbonyl groups, obtaining values for the fraction of isotactic dyads in the range 0.36 ± 0.03 for both polymers. Finally, the glass transition temperatures of both polymers, determined calorimetrically, were found 281 and 255 K, respectively. © 1994 John Wiley & Sons, Inc.