A simple analytical method is developed to estimate frequencies of longitudinal modes in closed hard-walled ducts with discontinuities in a cross-sectional area. The approach adopted is based on a general expression for the acoustic impedance for a plane wave motion in a duct and conditions of impedance continuity at duct discontinuities. Formulae for mode frequencies in a form of transcendental equations were found for one, two and three discontinuities in a duct cross-section. An accuracy of the method was checked by a comparison of analytic predictions with calculation data obtained by use of numerical implementation based on the forced oscillator method with a finite difference algorithm.
Fe - 4,25% C alloy was directionally solidified with a constant temperature gradient of G = 33,5 K/mm and growth rate of v = 83,3 μm/s (300 mm/h) using a vacuum Bridgman-type crystal growing facility with liquid metal cooling technique. To reveal more detailed microstructure, the deep etching was made. This was obtained in the process of electrolytic dissolution. The microstructure of the sample was examined on the longitudinal and transverse sections using an Optical Microscope and Scanning Electron Microscope. Using the Electron Backscattered Diffraction technique, phase map and analysis of phase were made. In this paper the analysis of Fe-C alloy eutectic microstructure is presented. Regular eutectic structure was obtained. The fracture surfaces show lamellar structure. Microscopic observation after electrolytic extraction indicates that the grains of longitudinal shape of eutectic cementite have been obtained. These grains are characterized by layered construction with many rounded discontinuities.