Bridge decks are commonly subjected to harsh environmental conditions that often lead to serious corrosion problems triggered by blisters under the hot mix asphalt bridge deck surfacing and secretly evolving during weather exposure until damage is often detected too late. Blisters may form under both the waterproofing dense mastic asphalt layer or under the waterproofing membrane which is often applied as additional water protection under the mastic asphalt (MA). One of the main technical issues is the formation of blisters under the membrane and asphalt-covered concrete structures caused by a complex mechanism governed by bottom-up pressure and loss of adhesion. A linear viscoelastic finite-element model was developed to simulate time-dependent blister growth in a dense mastic asphalt layer under uniformly applied pressure with and without temperature and pressure fluctuation. A finite element model was developed using ABAQUS with linear viscoelastic properties and validated with a closed form solution from first-order shear-deformation theory for thick plates. In addition, the blister test was conducted on different samples of MA in the laboratory and digital image correlation measurement technique was used to capture the three-dimensional vertical deflection of the MA over time. It was found that the blister may grow continuously under repeated loading conditions over subsequent days. With respect to blistering under waterproofing membranes, mechanical elastic modeling and experimental investigations were performed for three different types of membranes under in-plane stress state. The orthotropic mechanical behavior of a polymer modified bitumen membrane (PBM) was determined from biaxial test data. Finally, blister tests by applying controlled pressure between orthotropic PBMs and concrete plates were performed for studying the elliptical adhesive blister propagation using digital 3D image correlation. The energy calculated from elliptical blister propagation was found comparable to the adhesive fracture energy from standard peeling tests for similar types of PBMs. This indicates that the peeling test assists to evaluate and rank the adhesive properties of different types of membranes with respect to blister formation at room temperature without conducting time consuming and complicated pressurized blister propagation tests using digital 3D image correlation. / <p>QC 20130625</p>

The topic of the master’s thesis is a design of steel structure of footbridge. Footbridge goes across the roadways and railway. It is a design of a new structure in Nová Karolina in Ostrava. Span of footbridge is 200m. The footbridge’s superstructure is two steel arches angled toward each other and fixed to the foundation blocks. The supporting beam of the bridge deck is connected to the arch by tie-rods. The deck beam is a welded box section. The tie-rods are arranged to the V-shaped system. Deck of footpath is semi through type and orthotropic. The arches are connected at the top by lateral bracing. Lateral bracing is Saint Andrew's Cross type system.

No description available.

Orthotropic steel deck has been widely used over the decades especially on long-span bridges due to its light weight and fast construction. However fatigue cracking problems on the welds have been observed in many countries. Rib-to-deck welds need special care since they are directly under wheel loads, which cause large local stress variations and stress reversals. Currently the only requirement by AASHTO bridge code is that the rib-to-deck welds need to be fabricated as one-sided partial penetration welds with minimum penetration of 80% into the rib wall thickness. However considering the thin rib plate thickness, it is very difficult to achieve this penetration without a "melt-through" or "blow-through" defect. Large cost has been caused for the repair. However recent research has found that the fatigue performance of the rib-to-deck weld is not directly related to its penetration. Other factors contribute to the fatigue performance as well. Therefore, alternative requirements which are more cost-effective and rational are desired. The objective of this research is to provide recommendations to the design and fabrication of rib-to-deck welds by investigating their fatigue performance with different weld dimensions, penetrations, and welding processes. Fatigue tests were performed to 95 full-scale single-rib deck segments in 8 specimen series fabricated with different welding processes and root gap openness. Specimens were tested under cyclic loads till failure. Three failure modes were observed on both weld toes and the weld root. Test results showed that the fatigue performance was more affected by other factors such as failure mode, R-ratio and root gap openness, rather than the weld penetration. The failure cycles were recorded for the following S-N curve analysis. Finite element analysis was performed to determine the stress state on the fatigue cracking locations. Special considerations were made for the application of hot-spot stress methodology, which post-processes the FEA results to calculate the stress values at cracking locations with the structural configuration taken into account. The hot-spot stress range values were derived and adjusted accounting for the fabrication and test error. Hot-spot S-N curves were established for each specimen series. Statistical analyses were performed to study in depth the effect of weld dimensions and test scenarios. Multiple linear regression (MLR) was performed to investigate the effects of different weld dimensions; and multi-way analysis of covariance (Multi-way ANCOVA) for the effects of specimen series, failure mode, R-ratio and weld root gap. It was found that the weld toe size was more relevant to the fatigue performance, other than the weld penetration. The failure mode and R-ratio were very influential on the fatigue performance. Recommendations to the weld geometry were proposed based on the MLR model fitting. S-N data were re-categorized based on ANCOVA results and the lower-bound S-N curve was established. AASHTO C curve was recommended for the deck design. / Master of Science

L’étude des structures raidies est un sujet de recherche récurrent. En effet, celles-ci sont présentes dans de nombreuses applications industrielles. Leur utilisation offre de nombreux avantages notamment du point de vue de l’allègement, critère qui est particulièrement important dans l’industrie automobile par exemple. Dans un tout autre domaine, la table d’harmonie de piano constitue un exemple typique de ces structures raidies et les problèmes relevés par les professionnels du domaine sont nombreux. Aujourd’hui, les ressources numériques permettent de prendre en compte de nombreux phénomènes dans les modèles développés avec pour conséquence, une difficulté d’interprétation entre les données d’entrée et de sortie. En considérant moins de paramètres à la fois, les modèles simplifiés présentent alors l’avantage de pouvoir en séparer la participation dans le rendu global. En prenant comme point de départ une plaque simplement supportée rectangulaire orthotrope dite « spéciale » dans laquelle la table est inscrite, la forme de la table d’harmonie est recréée par ajout d’une densité de ressorts ponctuels dans le domaine complémentaire. Par couplage avec des superstructures collées sur chaque face, il est possible de déterminer le comportement vibratoire de l’instrument ainsi que le rayonnement acoustique à partir des impédances de rayonnement d’une plaque simplement supportée bafflée. Ce modèle analytique est par la suite couplé à une corde et résolu dans le domaine temporel et présente alors l’avantage de pouvoir évaluer perceptivement l’impact de modifications structurelles. L’originalité d’un tel calcul tient dans le fait que des forces d’interactions assurent la continuité entre les soussystèmes et deviennent des inconnues du problème, comme dans les problèmes de contacts ou de frottements. Enfin, la prise en compte des petites non-linéarités géométriques de la corde sera faite en les considérant comme des seconds membres des équations du mouvement, ce qui permet de conserver la notion de modeslinéaires / Ribbed structures are a current subject of study and they are often used in many industrial domain. Indeed, there use offers some advantages as for example in automotive domain to reduce the weight of vehicule that is an important actual constrain. In the musical domain ribbed structures are also often used and musical instruments mixed structural, perceptive and subjective considerations. In that domain, one of the main difficulties is to translate the language between the science and the music and to make equivalence between phenomena describe by the musicians and scientific indicators. The piano soundboard is a typical example of these ribbed structures and difficulties reported by piano makers are many. Nowadays, numerical computing resources allow to take into account some phenomena in modeling but as a consequence, it appears a “black box effect” between input and output data. Taking into account less parameters, reduced models offer the advantage to separate the influence of each parameter in the final result. Taking into account as starting point a simply supported rectangular plate with special orthotropy, the edges of the soundboard are described by an addition of punctual springs in the fictive domain. Coupling to it some stiffeners on the both faces, it is possible to calculate the vibratory behavior of the instrument such as the acoustic radiation through the acoustical radiation impedances of the baffled simply supported plate. This simplified analytical modeling is representative of phenomena found in the literature and is also well adapted to parametrical studies. So, it highlights the space localizations of vibration, due to the conception of the instrument, and allows studying the influence of structural parameters on the mobility along the bridge, the acoustical radiated power for example. In order to qualify, with a reduced computing cost, the influence of structural parameters on the perceived sound, this analytical model for ribbed structure is coupled to a string and solved in time domain.

O Brasil, um país de dimensões continentais e inúmeros rios em seu território, tem uma enorme carência de pontes para pequenos e médios vãos. Atualmente, a elevada produção de madeira de reflorestamento traz à engenharia uma opção de material renovável e ecologicamente correto para se utilizar em prol do ser humano nas obras de infraestrutura, mais especificamente na construção de pontes, uma vez que a madeira possui ótimo desempenho quando sujeita a cargas de curta duração. A utilização de Madeira Laminada Colada (MLC) permite a fabricação de peças de grandes dimensões, com excelente estabilidade, e com elevado controle de qualidade, proporcionando segurança e confiabilidade à estrutura. Este trabalho tem como objetivo o estudo teórico de pontes em vigas de MLC e tabuleiros em painéis de MLC utilizando procedimentos desenvolvidos por pesquisadores internacionalmente renomados e adequando estes procedimentos para as normas e condições brasileiras. Apresentam-se neste trabalho tabelas para pré-dimensionamento deste tipo de ponte para vãos de 8m a 20m para TB-30 e TB-45. Além disso, analisam-se numérica e experimentalmente os ganhos de rigidez e redução de deslocamentos relativos proporcionados pela utilização de vigas de enrijecimento, bem como a influência da seção destas vigas e a quantidade de parafusos utilizados para interligar ao tabuleiro. Por fim, apresentam-se algumas disposições construtivas não estruturais fundamentais para o bom funcionamento deste tipo de estrutura. / Brazil, a continental size country and with many rivers in its territory, has a huge necessity for short and medium spans bridges. Nowadays, the high production of reforestation wood allows to engineering an option of renewable material and ecologically correct to be used in favor to humans in infrastructure works, most specifically in bridges construction, once timber has a great performance in quick loads. The use of Glued-Laminated Timber (Glulam) enable the manufacture of large sizes members, with excellent stability, and a high control of quality in its production, providing a safety and reliability structure. This work aim the theoretical study of glulam stringers bridge and glulam panels deck using procedures developed by international researchers and adapting those procedures for Brazilian conditions and normalizations. Pre-design tables are presented in this work for 8m to 20m spans for TB-30 and TB-45. In addition to, analyses numerical and experimentally the gain of stiffness and the reduction of relative displacements between panels provided by the use of stiffener beams, besides the influence of those beams section size and number of bolts used for deck interconnection. Finally, it is presented some not structural constructive arrangements essential for good performance of this kind of structure.

O tabuleiro laminado protendido é uma composição de peças interligadas por uma tensão de compressão aplicada perpendicularmente às lâminas de madeira. Para aplicar tal tensão, são usados elementos de aço tensionados e a cordoalha engraxada aparece no cenário atual como um material econômico para tabuleiros laminados protendidos, em substituição às barras dywidag, que são comumente utilizadas neste tipo de estrutura em outros países. O funcionamento mecânico do tabuleiro é caracterizado como uma placa ortotrópica, e este trabalho visou determinar as relações entre as constantes elásticas do tabuleiro com a utilização da cordoalha engraxada. Foram analisadas também as perdas de protensão ocorridas ao longo do tempo, causadas pela fluência e relaxação dos materiais e, a partir dos resultados, foi proposta uma equação para determinação teórica da perda de protensão nos tabuleiros. O estudo experimental foi realizado em um modelo em escala reduzida construído no LaMEM (Laboratório de Madeiras e Estruturas de Madeira) para determinar as constantes elásticas e as perdas de protensão. Ao fim do trabalho são apresentados os resultados e comparações com estudos anteriores; também foi confeccionado um Manual de Boa Execução para Tabuleiros Laminados Protendidos de Madeira com Cordoalha engraxada. / The stress-laminated bridge deck is a composition of parts, interconnected by compression stress, perpendicularly applied to the wood laminate. In order to apply such stress, stressed steel elements are used, as well as the greased wire rope, which comes along in the current scenario as an economic material for stress-laminated bridge decks, replacing the dywidag bars, commonly used in this sort of structure in other countries. This bridge deck mechanic function is characterized as an orthotropic plate, and this paper aimed at determining the relation among the decks elastic constants with the greased wire rope. Another analyzed point is the stress loss occurred through time, caused by material creep and relaxation, and, through the results, an equation for the decks stress loss theoretical determination was proposed. The experimental study was developed in a reduced scale built in LaMEM (Laboratório de Madeiras e Estruturas de Madeira) to determine the elastic constants and the stress loss. The results and comparisons with previous studies are presented by the end of this paper; In addition, a handbook of Proper Execution for Stress-laminated Wood Bridge Decks with Greased Wire Rope was developed.

Métodos convencionais, tais como o método da chapa ortotrópica, têm sido aplicados por muitos anos no estudo de painéis reforçados pela sua simplicidade e facilidade de aplicação na determinação de tensões agentes nas fases iniciais da espiral projeto. Não estão disponíveis na literatura, porém, análises comparativas do método da chapa ortotrópica com procedimentos numéricos utilizando elementos finitos (MEF) que permitam a determinação da acurácia ou da ordem de grandeza dos desvios inerentes à aplicação desta metodologia. O presente trabalho apresenta análises comparativas entre estas duas metodologias na solução de painéis reforçados submetidos a carga lateral uniforme, tipicamente aplicados a estruturas navais (chapa em apenas um dos lados com reforçadores em T). Com este objetivo foram construídos modelos de painéis simplesmente apoiados e engastados (modelagem com elementos de viga e casca) com diferentes espaçamentos e diferentes inércias de reforçadores, configurando uma ampla matriz de análise paramétrica. Os resultados de deflexões e tensões nas vigas e chapas obtidos dos modelos MEF foram parametrizados em função das variáveis da chapa ortotrópica (razão de aspecto virtual), (coeficiente de torção) e K (parâmetro adimensional de tensões e de deflexão). Esta parametrização permite gerar curvas numéricas de tensão e deflexão dos modelos em estudo. As curvas numéricas assim geradas são comparadas com as curvas propostas pelo método da chapa ortotrópica para painéis reforçados simplesmente apoiados, de tal maneira que sua comparação permita, além de determinar a sensibilidade dos resultados numéricos em função das mudanças de inércia e espaçamento entre reforçadores, aferir o nível de desvio oriundo do uso da metodologia da chapa ortotrópica em relação ao método dos elementos finitos. Resultados mostram que as curvas derivadas da metodologia da chapa ortotrópica fornecem bons resultados para as deflexões e tensões transversais nas vigas no centro do painel reforçado. Para as tensões longitudinais nas vigas, uma curva corrigida de tensões longitudinais máximas é fornecida. No caso das curvas de tensões longitudinais e transversais na chapa, as curvas da chapa ortotrópica fornecem valores conservadores de tensão no centro do painel em relação aos valores obtidos dos modelos MEF. Adicionalmente, uma vez que o método da chapa ortotrópica só fornece curvas para chapa sem reforçadores no caso de condição de engaste, curvas numéricas das diferentes variáveis são fornecidas para esta condição. Analogias são feitas com a solução fornecida pelo método da chapa ortotrópica para painéis reforçados com razão de aspecto =, borda longitudinal engastada e borda transversal apoiada. Adicionalmente, resultados analíticos baseados na teoria de grelhas são comparados com os valores fornecidos pelas curvas numéricas para painel engastado obtendo-se resultados consistentes. Com esta análise foi possível determinar a aplicabilidade e limitações do método da chapa ortotrópica no estudo de painéis reforçados simplesmente apoiados. O estudo também fornece novas curvas numéricas para painéis reforçados engastados. / Conventional methods, such as the orthotropic plate, have been applied for many years in the study of stiffened plates to obtain the stresses acting on the structure in the early stages of the structural design, because of its simplicity and easy application. However, comparative analyses of the orthotropic plate method with numerical methods using finite element analyses (FEM) to determine its accuracy or inherent errors are not available in the literature. This study presents comparative analyses between the solutions of the two methodologies for reinforced panels subjected to lateral uniform load, typically applied to marine structures (plate only on one side with T beams). Models of reinforced panels were implemented for a simply supported and clamped boundary conditions with different spacing between stiffeners and different stiffeners`s inertia, setting up a broad array of parametric analysis. The deflections and stresses in beams and plate derived from the MEF analyses were parameterized as function of the orthotropic plate parameters: (virtual aspect ratio), (torsion coefficient) and K (dimensionless parameter of stress and deflection). This enables the generation of parametric numerical curves of stresses and deflections for the models under study. The numerical curves generated in this way were compared with the analytic curves proposed by the orthotropic plate theory for reinforced panels with simply supported boundary conditions. The comparisons allow, in addition to a sensitivity analysis of the numerical curves as a function of inertia and spacing between stiffeners, the assessment of inherent deviation for the orthotropic plate theory when compared with the finite element analyses. From the comparative analyses, it is possible to conclude that the curves proposed for the orthotropic theory for deflection and stresses of the transverse beam at the center of the reinforced panels have a good correlation with the numeric curves and provide accurate results. For the stresses on longitudinal beam, a revised curved for maximum stresses is provided. For the curves of plate stresses in the longitudinal and transverse directions at the center of the panels, the orthotropic plate theory provides conservative values when compared with the values of FEM models. The orthotropic plate method only provides curves for unstiffened plate under clamped boundary condition. Numerical curves for reinforced panels with clamped boundary condition are provided. Analogies are made between the solution provided by the orthotropic theory for a reinforced panel with an infinite virtual aspect ratio = , longitudinal edges clamped and transverse edges simply supported. Additionally, analytical results based on grillage theory were compared with the values provided by the numerical curves for clamped reinforced panels, obtaining a consistent results and a good correlation. This analysis provides a critic overview of the applicability and limitations of the orthotropic plate method for the analyses of reinforced panels with simply supported boundary condition. The study also provides new numerical solutions for reinforced panels with clamped boundary condition.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2014-10-21T20:53:51Z No. of bitstreams: 5 Dissertação - Ana Larissa dal Piva Argenta - 2013 - Parte 01.pdf: 20230731 bytes, checksum: 56aa4f90641e87e6081a5e3e9319bd24 (MD5) Dissertação - Ana Larissa dal Piva Argenta - 2013 - Parte 02.pdf: 10802505 bytes, checksum: 4e34e2a114366cce38898dda48f31144 (MD5) Dissertação - Ana Larissa dal Piva Argenta - 2013 - Parte 03.pdf: 14680983 bytes, checksum: e7a40859c186d5c2130a3debfec64edd (MD5) Dissertação - Ana Larissa dal Piva Argenta - 2013 - Parte 04.pdf: 11913507 bytes, checksum: 73e7928267b0b902da703843e18b2919 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Jaqueline Silva (jtas29@gmail.com) on 2014-10-22T19:05:17Z (GMT) No. of bitstreams: 5 Dissertação - Ana Larissa dal Piva Argenta - 2013 - Parte 01.pdf: 20230731 bytes, checksum: 56aa4f90641e87e6081a5e3e9319bd24 (MD5) Dissertação - Ana Larissa dal Piva Argenta - 2013 - Parte 02.pdf: 10802505 bytes, checksum: 4e34e2a114366cce38898dda48f31144 (MD5) Dissertação - Ana Larissa dal Piva Argenta - 2013 - Parte 03.pdf: 14680983 bytes, checksum: e7a40859c186d5c2130a3debfec64edd (MD5) Dissertação - Ana Larissa dal Piva Argenta - 2013 - Parte 04.pdf: 11913507 bytes, checksum: 73e7928267b0b902da703843e18b2919 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-10-22T19:05:17Z (GMT). No. of bitstreams: 5 Dissertação - Ana Larissa dal Piva Argenta - 2013 - Parte 01.pdf: 20230731 bytes, checksum: 56aa4f90641e87e6081a5e3e9319bd24 (MD5) Dissertação - Ana Larissa dal Piva Argenta - 2013 - Parte 02.pdf: 10802505 bytes, checksum: 4e34e2a114366cce38898dda48f31144 (MD5) Dissertação - Ana Larissa dal Piva Argenta - 2013 - Parte 03.pdf: 14680983 bytes, checksum: e7a40859c186d5c2130a3debfec64edd (MD5) Dissertação - Ana Larissa dal Piva Argenta - 2013 - Parte 04.pdf: 11913507 bytes, checksum: 73e7928267b0b902da703843e18b2919 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-06-13 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Circular cylindrical shells are widely used structures in several engineering areas and have great capacity to withstand both axial and lateral loads. However, they may present a complex dynamic behavior. Thus, a detailed study of the behavior of cylindrical shells subjected to different loading and support conditions as well as the influence of material characteristics and geometric relations evaluation is justified. In this work the influence of geometry and orthotropy on the nonlinear dynamic behavior of orthotropic simply supported cylindrical shells subjected to both axial and lateral time depending loads is studied. To model the shell, the Donnell nonlinear shallow shell theory, neglecting the effects of shear deformations, is used. It is considered the shell in three different situations: empty, filled with static fluid and subjected to internal flow of incompressible and non-viscous fluid, whose motion is isentropic and irrotational. The radial displacements are described as an expansion with eight degrees of freedom which satisfies the boundary conditions. The Galerkin method is applied to obtain a set of nonlinear equations of motion, which are in turn solved by the Runge-Kutta method. A detailed analysis is performed to study the influence of material orthotropy and geometric relations such as length-radio (L/R) and radio-thickness (R/h) on the natural frequencies, critical loads, critical flow velocities, post-critical paths, frequency-amplitude relations, instability boundaries, bifurcation diagrams and resonance curves. Obtained results display the strong influence of both material orthotropy and geometric relations on the linear and nonlinear behavior of the shells and, depending on these characteristics, the shell can display softening or hardening behavior. / Cascas cilíndricas são estruturas com diversas aplicações em várias áreas da engenharia e têm grande capacidade para resistir a carregamentos axiais e a pressões laterais. Entretanto, são estruturas que podem apresentar um complexo comportamento dinâmico. Assim, um estudo detalhado do comportamento das cascas cilíndricas submetidas a diferentes condições de carregamento bem como a avaliação da influência do material e da geometria se justifica plenamente. Este trabalho tem como objetivo estudar a influência da ortotropia do material e da geometria no comportamento dinâmico não linear das cascas cilíndricas ortotrópicas simplesmente apoiadas e submetidas a carregamentos axiais e laterais variáveis com o tempo. Para modelar a casca é utilizada a teoria não linear de Donnell para cascas abatidas desprezando-se os efeitos das deformações cisalhantes. Considera-se a casca em três situações distintas: vazia, preenchida com fluido estático e submetida ao escoamento interno de fluido incompressível e não viscoso, cujo movimento é isentrópico e irrotacional. O deslocamento radial da casca é descrito, de maneira geral, por uma expansão com oito graus de liberdade que satisfaz as condições de contorno. O método de Galerkin é utilizado para obter o sistema discreto de equações diferencias não lineares de movimento, que são resolvidas através do método de Runge-Kutta de quarta ordem. Uma análise detalhada é realizada visando observar a influência das características do material e das relações geométricas comprimento-raio (L/R) e raio-espessura (R/h) nas frequências naturais, cargas críticas, velocidades críticas do fluido bem como nos caminhos pós-críticos, relações frequência-amplitude, fronteiras de instabilidade, diagramas de bifurcação e curvas de ressonância das cascas. Os resultados obtidos permitem observar a forte influência que a geometria e as propriedades dos materiais exercem no comportamento linear e não linear das cascas cilíndricas ortotrópicas e, dependendo de certas características, verifica-se que a casca pode ter comportamentos com ganho ou perda de rigidez.

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.