Scientists and engineers measure dielectric constant because it gives them better understanding of materials and helps them to know how to integrate these materials into their design processes;it also helps them to shorten design life cycle,and aside these two functions,it has numerous uses all of which cannot be enumerated in this section.Owing to its usefulness,various measurement methods of dielectric constant of materials have been developed over the years.Each method has its limitations which affect the accuracy of the measurement;these limitations range from frequency,temperature,and  mearsurement environment to material under test.   In this thesis,four most common methods of measuring dielectric constant were discussed and the most accurate one,the resonant method,was chosen and worked on .The project was executed by making a mathematical analysis of the ring resonator which was later simulated in HFSS to get results which would be comparable to ones obtained in  laboratory measurements.   The ring was fabricated and taken to the laboratory for measurement.Two monopole antennas were connected to the two ports of a VNA with one antenna serving as the transmitter and the other serving as the receiver.   The resonant frequencies obtained were combined with the geometric parameters of the ring resonator and that of the MUT in equations written into MATLAB scripts;this equations were used to extract the dielectric constant of the MUT.

L’objet de ce travail de thèse consiste à utiliser un formalisme vibratoire pour la détermination de contraintes dans les dépôts à l’aide de la méthode dynamique résonante. Ceci a nécessité le développement d’un formalisme vibratoire adapté aux massifs revêtus, en reliant le niveau de contrainte à la variation des fréquences de résonance mesurées. L’étude a été effectuée en menant trois approches en parallèle : numérique, analytique et expérimentale. En premier lieu, nous avons réalisé des simulations numériques par éléments finis, afin de déterminer la distribution de contraintes dans l’épaisseur d’une poutre composite contrainte et d’évaluer l’effet de ces profils de contraintes sur la fréquence de résonance. Les résultats numériques ont permis d’optimiser le développement d’un nouveau formalisme vibratoire analytique. Pour valider ce dernier formalisme, il nous a fallu l’appliquer sur des dépôts réels,en confrontation avec les résultats d’autres méthodes de mesures de contraintes (DRX/Stoney). Cette confrontation numérique-analytique/expérimentale a révélé que la méthode dynamique résonante est pertinente pour des systèmes de dépôts ayant des rapports d’épaisseur supérieur à0,01. / The aim of this work is to use a new vibratory formalism in order to determine the level of internal stresses in coated materials using the dynamic resonant method. This requires the improvement of vibratory formalism, which allows to link the stress level to the variation of resonance frequency in free flexural mode. This study was conducted by doing three different approaches: numerical, analytical and experimental measurements in real coating. Numerical simulations were conducted by finite element method in static mode to determine the stress distribution in depth. Furthermore, we made other numerical simulations in dynamic mode to evaluate the effect of these static results on the resonant frequency, in comparison with those of coated material without stress. At this stage, these numerical studies let us to develop the vibratory formalism analytically. To validate this latter formalism, we applied it in a real coating for measuring the stress level and we made comparisons with results from others methods(DRX/Stoney). This confrontation (numerical-analytical/experimental measurements) found that dynamic resonant method is efficient for coated material having a thickness ratio moreimportant than 0,01.