Numerical investigation of geometrically nonlinear clamped uniform rods and rods with sections varying exponentially free vibration

Purpose: The present paper is intended to investigate the problem of linear and non-linear longitudinal free vibration of uniform rods and rods whose cross-sections vary exponentially at large vibration amplitudes. Design/methodology/approach: The method adopted consists in discretizing the energy term on linear kij and non-linear rigidity tensor bijkl, as well as the mass tensor mij. Therefore, the formulation of this structure is based on Lagrange equations and the harmonic balance method so as to obtain the nonlinear algebraic equations. These latter are solved numerically and analytically through the explicit and linearized method. Findings: The response of Clamped-Clamped uniform and non-uniform rods on our structure are highlighted in the amplitude frequency and associated first three mode shapes. Moreover, this research leads to study the influence of the exponential slope on the maximum displacement, thus emphasizing the non-uniform bars usefulness. The obtained results are then compared with the available literature with a view to validating this theory. Research limitations/implications: As a perspective, the method used in this paper would be pushed to study the FDM material, taking into account other parameters related to additive manufacturing, and later to be validated experimentally. Practical implications: Longitudinal vibrations are important in mechanical structures; therefore, the determination of their dynamic behaviour needs to be understood. In the present study, the effect of the displacement amplitude on the exponential slope of the structure was analysed, which led to the determination of the reduction range of the vibration amplitude under resonance. However, this should be taken into account in the design process. Besides, the usefulness of the non-linearity geometric effects was demonstrated to examine these structures by considering all the parameters involved. Originality/value: A linearized procedure is used to solve a nonlinear algebra equation. The use of this method leads to reduce calculation time contrary to iterative methods

A study of the phase transitions, electronic structures and thermodynamic properties of Mg2X (X = Ge, Si and Sn) under high pressure

In this work, we theoretically investigate phase transitions, electronic structures and thermodynamic properties of Mg2X (X = Ge, Si and Sn) under high pressures. To reach this goal, the total energy has been calculated by using the full-potential linearized augmented plane wave (FP-LAPW) method with generalized gradient approximation (GGA), local density approximation (LDA) and Engel–Vosko approximation (EV-GGA), which are based on the exchange-correlation energy optimization. The fully relaxed structure parameters of Mg2X compounds are in good agreement with the available experimental data. Our results demonstrate that the Mg2X compounds undergo two pressure-induced phase transitions. The first one is from the cubic antifluorite (Fm3¯m) structure to the orthorhombic anticotunnite (Pnma) structure in the pressure range of 3.77–8.78 GPa (GGA) and 4.88–8.16 GPa (LDA). The second transition is from the orthorhombic anticotunnite structure to the hexagonal Ni2In-type (P63m¯mc) structure in the pressure range of 10.41–29.77 GPa (GGA) and 8.89–63.45 GPa (LDA). All the structural parameters of the high pressure phases are analyzed in detail. Only a small difference in the structural parameters is observed at high pressures between the calculated and experimental results. The electronic and thermodynamic properties are also analyzed and discussed. The establishment of the metallic state of the Mg2X (X = Ge, Si and Sn) compounds at high pressure is confirmed

Combined model of human skin - Heat transfer in the vein and tissue: experimental and numerical study

International audienceThe aim of this study is to propose a combined model of heat transfer in the vein and tissue of human skin. It allows to better understand the thermomechanical behavior of the skin and its direct environment when exposed to strong thermal variations. The work is based on experimental and numerical investigations. The first experimental step consists in placing a cooled cylindrical steel bar on the skin of a human forearm and measuring the temperature change using an infrared camera. Blood circulation in the veins was seen to clearly influence heat diffusion. The second experimental step consists in measuring geometrical properties of the veins and blood velocity using an echo-Doppler probe. These experimental measurements provide a numerical model of the skin and its direct vicinity. The three-dimensional multilayer model uses Pennes equation to model biological tissue and the convective heat transport equation, to model blood. The properties of the biological materials obtained from the literature are validated by our experimentation. The numerical model is able to simulate the experimental observations, but also to estimate blood temperature and velocity in the veins