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.     

Viscosities of liquid CdTe near melting point from ab initio molecular-dynamics calculations

Recent experimental results for the viscosity of liquid CdTe exhibit disparate behavior as a function of temperature. While some measurements show the expected Arrhenius-type behavior, other measurements show an anomalous temperature dependence indicating an increase in viscosity with increasing temperature. We present ab initio molecular-dynamics simulations of liquid cadmium telluride near its melting point and use the Stokes-Einstein relation to extract values of the viscosity constant. We find no anomalous behavior; the viscosity decreases monotonically with temperature and is consistent with an Arrhenius like behavior. Although calculated values are slightly smaller than those measured, the predicted activation energy agrees well with experiment.