The aim of this work is to investigate the nonlinear dynamics of a forced cardiac pacemaker model represented by a forced modified van der Pol oscillator by using the method of harmonic balance and the method of multiple time scales. The amplitudes of the forced harmonic, primary resonant state, super-harmonic and sub-harmonic resonant state oscillations are obtained and the effects of some system parameters on these amplitudes are investigated; hysteresis and jump phenomena are found. Three similar oscillators are then coupled together via time-delay coupling to model the heart rhythm and the effect of the coupling factor and time delay is also investigated. The overall model is then discretized using the fourth-order Runge–Kutta algorithm. A corresponding very high-speed integrated circuit hardware description language code is then written, synthesised and implemented using the Vivado-2017.4 software for the Artix7-xc7a35tftg256-1 field programmable gate array chip. The chip statistics, time series electrocardiograms and phase portraits of the model are derived; a good correlation between theoretical results (obtained with MATLAB program and Vivado software) and practical results is observed.

The dynamic of a cantilever beam with tip mass is studied under an aerodynamic loading. The effects of coupling is investigated by tacking into account the fluid flow. Using the multiple time scale method, the approximative solutions are found and the study of their stability is made by the Routh-Hurwitz stability criterion. The influence of parameters on the system is studied at the harmonic and subharmonic resonances. The results show that, the effects of tip mass can be neglected in harmonic resonance case ,while they are more important in subharmonic resonance cases. The results equally demonstrate that an increase of the stable state fluid velocity reduces the amplitude of vibrations. In addition, the hysteresis phenomenon studies show that it is principally induced by nonlinearity coefficients. Finally, time-delay feedback control is applied and the effects of controlling are observed on amplitude response curve at the harmonic resonance, from where we note that optimized choice of control parameters can be useful in controlling vibrations.

The objective of this work is to prevent damage of the arterial wall, using a theoretical model of hyperelastic, anisotropic, and dynamic behavior of the human arterial. This work is mainly focused on the properties of the hydrostatic stress and the evolution of stenosis. This work is mainly focused on the properties of the hydrostatic stress and the evolution of stenosis in order to understand the effect of the size of the plaque deposit, the loss of elasticity of the wall, and the increase in the density of the blood on the mechanical behavior of the human arterial wall. The great contribution of this work shows us that increasing the size of the plaque also increases arterial stress, and the radial growth of the plaque is very dangerous compared to the longitudinal growth. Furthermore, atherosclerosis promotes the loss of elasticity of the arterial wall and increases the density of blood mass. Indeed, all these subsequent phenomena increase arterial stress. All the results are in good agreement with the expected result of the literature and could play an important role in the diagnosis of the patient with an arterial injury. It will also help the doctor and the surgeon to make a good clinical decision and good treatment planning.

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The aim of our work is to characterize a mortar with a cement/"Ndoor" composite binder. We determine experimentally the mechanical properties of a mortar modified by partial substitution of cement by an addition called "Ndoor". In experimental campaign, we realize different formulations of mortar diversified by the dosage of cement and "Ndoor", which were made in the form of prismatic specimens 4*4*16 cm3. Compression tests were carried out, which allowed us to obtain the values of compressive strength and tensile strength. The results show that the "Ndoor" improves the development of the mechanical resistances at the young age especially for values of substitution of the order of 2.5%, 5% and 7.5%. As a complement to the tests, a modeling having a predictive character of the elastic behavior of a mortar elastic behavior of a composite cement/"Ndoor" binder mortar is done. For this purpose, we have mortar has two phases : the hydrated cement paste and the inclusions (sand and "Ndoor"). The elastic properties of the cement paste are determined by the self-coherent homogenization model. Knowing the elastic properties of the cement paste and the inclusions, those of the mortar are deduced by the diluted scheme model of ESHELBY. The results show that, in the presence of the "Ndoor", as the mass ratio e/c increases, the Young’s modulus of the modified mortar decreases