In this paper, a new application of the Numerical Assembly Technique is presented for the balancing of linear elastic rotor-bearing systems with a stepped shaft and arbitrarily distributed mass unbalance. The method improves existing balancing techniques by combining the advantages of modal balancing with the fast calculation of an efficient numerical method. The rotating stepped circular shaft is modelled according to the Rayleigh beam theory. The Numerical Assembly Technique is used to calculate the steady-state harmonic response, eigenvalues and the associated mode shapes of the rotor. The displacements of a simulation are compared to measured displacements of the rotor-bearing system to calculate the generalized unbalance for each eigenvalue. The generalized unbalances are modified according to modal theory to calculate orthogonal correction masses. In this manner, a rotor-bearing system is balanced using a single measurement of the displacement at one position on the rotor for every critical speed. Three numerical examples are used to show the accuracy and the balancing success of the proposed method.

The main aim of the study was to search for the relationship between the anisotropy of the structure of polyfurfuryl alcohol (PFA) – polymer/compressed expanded graphite (CEG)-matrix composites at subsequent stages of the technological process and characteristics of the acoustic emission (AE) descriptors. These composites, obtained after successive technological procedures of impregnation, polymerization, and carbonization, possess different structure, densities, porosity, and other physicochemical properties. In the structures of composites prepared on the basis of CEG, two basic directions can be distinguished: parallel to the bedding plane of graphite sheets and perpendicular to it. The measurements were carried out for the stress acting in these two main directions. The investigation has shown that the AE method enables the detection of anisotropy in the structure of materials. The results of the research show that all four of the acoustic emission descriptors studied in this work are sensitive to the technological stages of these materials on the one hand and their structure anisotropy on the other. Fourier analysis of the recorded spectra provides interesting conclusions about the structural properties of composites as well as a lot of information about the bonding forces between the carbon atoms of which the CEG matrix is composed and the PFA polymer or turbostratic carbon.

In the paper, the numerical method of solving the one-dimensional subdiffusion equation with the source term is presented. In the approach used, the key role is played by transforming of the partial differential equation into an equivalent integro-differential equation. As a result of the discretization of the integro-differential equation obtained an implicit numerical scheme which is the generalized Crank-Nicolson method. The implicit numerical schemes based on the finite difference method, such as the Carnk-Nicolson method or the Laasonen method, as a rule are unconditionally stable, which is their undoubted advantage. The discretization of the integro-differential equation is performed in two stages. First, the left-sided Riemann-Liouville integrals are approximated in such a way that the integrands are linear functions between successive grid nodes with respect to the time variable. This allows us to find the discrete values of the integral kernel of the left-sided Riemann-Liouville integral and assign them to the appropriate nodes. In the second step, second order derivative with respect to the spatial variable is approximated by the difference quotient. The obtained numerical scheme is verified on three examples for which closed analytical solutions are known.

This paper investigates the preparation of silicon nitride composites with multi-walled carbon nanotubes (MWCNTs). Samples containing 1–10 wt% MWCNTs were ultrasonically processed in non-aqueous suspensions, dried, pressed, and then subjected to non-pressure sintering at 1600 °C for 2 h. The preliminary results showed that the mixture of activated silicon nitride and covered MWCNTs could be sintered. The porosity of the obtained samples ranged from 0.27 to 36.94 vol.%. The microstructure was observed by scanning electron microscopy (SEM), and the mechanical properties (hardness and fracture toughness) were also determined. Good hardness values were obtained for samples prepared by sintering the mechanically activated precursor under a flowing nitrogen atmosphere using the lowest fraction of CNTs. Residual activator reduced the densification of the composites.