The aim is to derive an expression to calculate the natural frequencies and plot the mode shapes of a simply-supported beam with an overhang with an end overhang point mass by using the Euler-Bernoulli theory in the case of free transverse vibrations. The results are validated by finite element analysis. The importance of the system presented is that it can represent machine tool spindles or even machining tools like boring bars. The results are in good agreement with the results from the finite element analyses. The derived expression can be used in optimizing the value of the point mass and optimizing the support location for better performance of the system without the need to perform complex analysis to obtain the values of the natural frequencies and to plot the mode shapes.

The aim of the paper is to supply updated air convective coefficients by means of three empirical correlations set forth by Zukauskas, Churchill and Hilpert for cylindrical bodies in cross-flow. In this study, low Reynolds numbers and air velocities within the range of were considered, hence, sundry values of convective coefficients were obtained and applied in a lumped heat capacity model. Finite element analysis simulations were implemented, exhibiting good conformity based on these correlations. The findings show that among the three methodologies, Zukauskas's correlation presents minimum standard deviation and the maximum standard deviation is presented by Hilpert's correlation , Churchill correlation presents a standard deviation of . The results are reliable and can therefore be used for analyzing heat convection.

The analysis of heat transfer in solid bodies with orthogonal geometries and knowledge thereof, is of vast importance in different fields of engineering and research. An important field of study is the thermal analysis in machine-parts that in most cases are designed and shaped with orthogonal geometries. Nevertheless, due to the high complexity and the cost that thermal experiments represent, FEM analysis and numerical solutions are used to foresee thermal fields on these components. These methodologies are certainly reliable, although may vary from real experiments. On that account, this paper presents a thermal experimental test in a solid cylinder of length  and  , made of ISO C45 steel that emulates a machine-part (cylindrical parts as shafts, fasteners and the like). The temperature fields along the longitudinal direction  were analyzed in steady and transient state under homogeneous boundary conditions of the first kind (prescribed temperatures at the boundaries). The three solutions, experimental, numerical and FEM simulations were compared with the purpose of validating the results obtained by each method of solution respectively.