L’étude de la propagation des ondes élastiques dans des plaques présentant des défauts en surface ou en volumetrouve sa place dans divers domaines industriels (aéronautique, automobile, aérospatial,…) pour le contrôle de l’état de santé des matériaux. L’étude menée ici en ondes transversales horizontales (SH) porte plus particulièrement sur les effets de rugosité aux interfaces d’une structure tri-couche, deux plaques isotropes collées par une couche mince de colle (les interfaces entre la couche de colle et les deux plaques sont rendues rugueuses pour améliorer l’adhésion), les plaques n'étant pas obligatoirement de même nature. L’objectif à terme est de caractériser cette rugosité et par-delà d'analyserson influence sur la qualité de collage. Les rugosités peuvent être quelconques ; celles considérées ici sont soit périodiques, soit pseudo-aléatoires. Les approches retenues sont analytiques, numériques et expérimentales. L’approche analytique basée sur une formulation intégrale adaptée à la propagation en ondes SH est utilisée pour déterminer les champs de déplacements et de contraintes dans les deux plaques. L’étude numérique par éléments finis qui utilise le logiciel COMSOL donne les coefficients de transmission. L’étude expérimentale met en oeuvre des transducteurs piézoélectriques à ondes transversales pour l’émission, et un vibromètre laser en réception, l’objectif étant de générer et d’identifier les modes propagatifs dans les structures étudiées, et d’évaluer leur comportement selon le type de rugosité.Les résultats et comparaisons portent sur les champs (déplacement-contrainte) et les coefficients de transmission enprésence de rugosité, avec ou non accords de phase lorsque des périodicités apparaissent sur les profils de rugosité. / Analysing the elastic wave propagation in rough plates opens the way to several applications such as the health monitoringof materials in industrial sectors (aeronautics, automotive, aerospace,..). The study here in using shear horizontal waves(SH), focuses on the effects of roughness at the interfaces of a bi-layered structure which consists of two isotropic platesadhesively bonded using a thin layer of glue (the interfaces between the adhesive layer and the two plates are roughenedto improve adhesion), the plates being not necessarily of the same nature. The aim of this study is to characterize thisroughness and beyond to analyze its influence on the quality of bonding. The roughness may have any profile; thoseconsidered here are either periodic or pseudo-random. The approaches used are analytical, numerical and experimental. The analytical approach, based on the integral formulation developed for SH-wave propagation, is used to determine the fields of displacements and stresses in both plates. The numerical finite element analysis using the COMSOL software gives the transmission coefficients. In the experimental study, shear waves piezoelectric transducers are used for the emission and a laser vibrometer for the reception; the final aim being to generate and to identify the modes propagating in the studied structures, and to evaluate their behavior depending on the roughness. The displacement and stress perturbation maps, and transmission coefficients are presented in the presence of roughness, with or without phase-matching.

In this Thesis, the problem of the Free Vibrations Analysis of Doubly Stiffened Composite, Orthotropic and/or Isotropic, Base Plates or Panels (with Orthotropic Stiffening Plate Strips) is investigated. The composite plate or panel system is made of an Orthotropic and/or Isotropic Base Plate stiffened or reinforced by adhesively bonded Upper and Lower Orthotropic Stiffening Plate Strips. The plates are assumed to be the Mindlin Plates connected by relatively very thin adhesive layers. The general problem under study is considered in terms of three problems, namely Main PROBLEM I Main PROBLEM II and Main PROBLEM III. The theoretical formulation of the Main PROBLEMS is based on a First Order Shear Deformation Plate Theory (FSDPT) that is, in this case, the Mindlin Plate Theory. The entire composite system is assumed to have simple supports along the two opposite edges so that the Classical Levy&#039 / s Solutions can be applied in that direction. Thus, the transverse shear deformations and the rotary moments of inertia of plates are included in the formulation. The very thin, yet elastic deformable adhesive layers are considered as continua with transverse normal and shear stresses. The damping effects in the plates and the adhesive layers are neglected. The sets of the systems of equations of the Mindlin Plate Theory are reduced to a set of the Governing System of First Order Ordinary Differential Equations in the state vector form. The sets of the Governing System for each Main PROBLEM constitute a Two-Point Boundary Value Problem in the y-direction which is taken along the length of the plates. Then, the system is solved by the Modified Transfer Matrix Method (with Interpolation Polynomials and/or Chebyshev Polynomials)which is a relatively semi-analytical and numerical technique. The numerical results and important parametric studies of the natural modes and the corresponding frequencies of the composite system are presented.

In this Thesis, the problems of the Free Flexural (or Bending) Vibrations of Composite, Orthotropic Plates and/or Panels with Various Bonded Joints are formulated and investigated in detail. The composite bonded plate system is composed of Plate Adherends adhesively bonded by relatively very thin adhesive layers. The general problem is considered in terms of the three Main PROBLEMS, namely Main PROBLEM I, Main PROBLEM II and Main PROBLEM III. The theoretical formulation of the Main PROBLEMS is based on Mindlin Plate Theory which is a First Order Shear Deformation Plate Theory (FSDPT). Thus, the transverse shear deformations, the transverse and the rotary moments of inertia of the plates are included in the formulation. Very thin, elastic deformable adhesive layers are considered as continua with transverse normal and shear stresses. The damping effects in the plates and the adhesive layers are neglected. The entire composite bonded joint assembly is assumed to be simple supported along the two opposite edges, so that the Classical Levy&amp / #8217 / s Solutions can be applied in this direction. The dynamic equations of the Bonded Joint System which combines together the Mindlin Plate dynamic equations with the adhesive layer equations are reduced to a system of First Order Ordinary Differential Equations in the state vector form. This special form of the Governing System of the First Order Ordinary Differential Equations are numerically integrated by means of the Modified Transfer Matrix Method which is a combination of the Classical Levy&amp / #8217 / s Method, the Transfer Matrix Method and the Integrating Matrix Method (with Interpolation Polynomials and/or Chebyshev Polynomials). The Main PROBLEMS are investigated and presented in terms of the mode shapes and the corresponding natural frequencies for various sets of boundary conditions. The significant effects of the hard and the soft adhesive layer elastic constants on the mode shapes and on the natural frequencies are demonstrated. Some important parametric studies such as the influences of the Joint Length Ratio, the Joint Position Ratio, the Bending Stiffness Ratio, etc. on the natural frequencies are computed and plotted for the hard and soft adhesive cases for several support conditions.

Noise and vibration suppression is an important aspect in the design process of structures and machines. Undesirable vibrations can cause fatigue in a structure and are, therefore, a risk to the safety of a structure. One of the most effective and widely used methods of mitigating these unwanted vibrations from a system is passive damping, by using a viscoelastic material. This dissertation will primarily focus on constrained layer passive damping treatments in structures and the investigation of associated complex modes. The key idea behind constrained damping treatment is to increase damping as affected by the presence of a highly damped core layer vibrating mainly in shear. Our main goal was to incorporate viscoelastic material in a thick stiffened panel with plate-strip stiffeners, to enhance the damping characteristics of the structure. First, we investigated complex damped modes in beams in the presence of a viscoelastic layer sandwiched between two elastic layers. The problem was solved using two approaches, (1) Rayleigh beam theory and analyzed using the principle of virtual work, and (2) by using 2D plane stress elasticity based finite-element method. The damping in the viscoelastic material was modeled using the complex modulus approach. We used FEM without any kinematic assumptions for the transverse shear in both the core and elastic layers. Moreover, numerical examples were studied, by including complex modulus in the base and constraining layers. The loss factor was calculated by modal strain energy method, and by solving a complex eigenvalue problem. The efficiency of the modal strain energy method was tested for different loss factors in the core layer. Complex mode shapes of the beam were also examined in the study, and a comparison was made between viscoelastically damped and non-proportionally damped structures. Secondly, we studied the free vibration response of an integrally stiffened and/or stepped plate. The stiffeners used here were plate-strip stiffeners, unlike the rib stiffeners often investigated by researchers. Both plate and stiffeners were analyzed using the first-order shear deformation theory. The deflections and rotations were assumed as a product of Timoshenko beam functions, chosen appropriately according to the given boundary conditions. Unlike Navier and Levy solution techniques, the approach used here can also be applied to fully clamped, free and cantilever supported stiffened plates. The governing differential equations were solved using the Rayleigh-Ritz method. The development of the stiffness and the mass matrices in the Ritz analysis was found to consume a huge amount of CPU time due to the recursive integration of Timoshenko beam functions. An approach is suggested to greatly decrease this amount of CPU time, by replacing the recursive integration in a loop structure in the computer program, with the analytical integration of the integrand in the loop. The numerical results were compared with the exact solutions available in the literature and the commercially available finite-element software ABAQUS. Some parametric studies were carried out to show the influence of certain important parameters on the overall natural frequencies of the stiffened plate. Finally, we investigated the damped response of an adhesively bonded plate employing plate-strip stiffeners, using FSDT for both the plate and stiffeners. The problem was analyzed using the principle of virtual work. At first, we did not consider damping in the adhesive in order to validate our code, by comparing our results with those available in the literature as well as with the results obtained using ABAQUS 3D model. The results were found to be highly satisfactory. We also considered the effect of changing the stiffness of the adhesive layer on the vibration of the bonded system. As a second step, we included damping in the stiffened structure using complex modulus approach, a widely used technique to represent the rheology of the viscoelastic material. We observed an overall increase in the natural frequencies of the system, due to the damping provided by the viscoelastic material. Moreover, it was noticed that when the thickness of the adhesive layer is increased, the natural frequencies and loss factor of the stiffened structure decrease. A viscoelastic material with high loss factor and small thickness will be a perfect design variable to obtain overall high damping in the structure. / Ph. D.