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.     

High resolution FTS studies of glow discharge spectra line profiles and line widths

High resolution studies using Fourier transform spectrometry of the spectra emitted in the visible and ultraviolet regions by a microwave boosted glow discharge source have shown that when the source is operated in the dc (unboosted) mode, two anomalous forms of line profile occur for some analyte elements. (1) Some Fe I lines appear to have a triangular base of half-width about five times greater than that of the line proper. (2) Some Fe II and Ti II lines exhibit satellites about 8 cm(-1) wide and an intensity of up to 2% of the peak value on either side of the main line. Both effects depend on the carrier gas and its pressure and are much less pronounced or even absent in the boosted mode. They could both affect the accuracy of analytical results, particularly for depth-profiling. Further studies are in progress.