This investigation is concerned with the flexural response of linear viscoelastic plates of constant thickness. Fundamental equations for both quasi-static and dynamic response of such plates are developed and solved for important cases of each. The term quasi-static ls used to indicate that Inertia forces due to deformation are neglected. These are included, of course, in the dynamic analysis. Solutions of the quasi-static equation are compared with experimental results obtained by measuring the deflection of a test plate made of Plexiglas. The basic viscoelastic stress-strain relations used in the derivation of the fundamental plate equations are taken in the form of a differential time operator equation. Use of this equation leads to results that are In a convenient form for reduction to a particular material such as a Kelvin or a Maxwell plate. Using a generalized virtual work principle based upon irreversible thermodynamic considerations the fundamental plate equation, including shear effects, ls established. The procedure involved ls that of determining a stationary value of a certain operational invariant by means of the calculus of variations. A simplified form of this equation, omitting the shear effects, is deduced and solutions for various load conditions obtained. An extended version of this simplified form which includes inertia effects due to deformation is developed by the principle of correspondence. This is used to study free vibrations of rectangular viscoelastic plates simply supported on all edges. Solutions of the simplified form of the fundamental equation for the case of so-called proportional loading, I.e. when the load function is the product of a space function multiplied by a time function, are given in terms of the equivalent elastic solution multiplied by a function of time. For more general types of loading the deflection and the load are expanded Into suitable infinite series and these series representations are inserted directly into the previously mentioned variational expression of the generalized virtual work principle. This leads to a set of ordinary differential situations in time the unknowns of which are the coefficients of the deflection expansion. These equations, as were the similar ones arising in the case of proportional loading, are solved by the Laplace transform method of the operational calculus. As an example of such a general loading the case of a moving line load on a rectangular plate is worked out. As a means of establishing a correlation between the deflection predicted by the analytical solution and actual deflections of Inelastic plates a set of static load tests were carried out on a square plate made or Plexiglas. The results are plotted and a comparison of the theoretical and experimental values given. The problem of determining the dynamic response of viscoelastic plates is treated using the method given above for solving the case of general loading for the quasi-static deflection. Under the assumption of incompressibility of the plate material explicit solutions in terms of the physical parameters involved are presented and discussed. For compressible plate materials methods are developed to give approximate solutions the accuracy of which depends on the degree of approximation used in determining the roots of certain cubics appearing in the transformed form of the governing dynamics equation. Conditions for the dynamic solutions to be oscillatory are indicated. / Ph. D.

An experimental study is made to investigate the feasibility of determining a viscoelastic stress-strain law for two (or three) dimensional stress conditions by means of one dimensional tests. The conclusions are based upon comparison of theory and experiment for a creep test of a lead plate, subjected to biaxial tension. The stress-strain law that was selected is given by S_ij = B σ²/σt² e_ij + c σ/σt e_ij to cover ehear effects and by σ_ii = κε_ii for hydrostatic tension or compression. S_ij and e_ij are respectively the stress deviator and σ_ii and ε_ii are the stress and strain tensors. Uniaxial test data was used to evaluate the constants in the above laws. The Lapplace transform technique was used to obtain the analytical solution for the strain in the plate as a function of time. Agreement between theory and experiment or the duration of the test, 1200 minutes, was quite good. / Master of Science

The main focus of this dissertation was on characterizing the viscoelastic behavior of a set of four flexible slabstock water-blown polyurethane foams with varying hard segment content as well as solid plaques made from these foams. Three viscoelastic tests; tensile stress relaxation, compression load relaxation, and compression creep, were utilized to evaluate the behavior of these materials at constant temperature and/or relative humidity, RH. The tensile stress relaxation tests were performed at a 25 percent strain level. The majority of the compression load relaxation tests were conducted at a 65 percent level since this is the strain level used for the common indentation load deflection test for flexible foams and the relaxation behavior was rather independent of strain at this level. Over a three hour testing period, a near linear relationship for the log of tensile stress or compressive load versus log time is observed for most conditions. The slope from this linear relationship in tension or the stress decay rate is similar for all the foams and their respective plaques; thus indicating that the tensile stress relaxation of these materials is governed by the solid portion of the foams and is therefore independent of the cellular textures. In addition, the rates of relaxation for rather linear behavior in tension and compression are also comparable for these foams and this implies that the relaxation in compression is mostly independent of the cellular texture of the foams at a 65 percent strain level. After a short induction period, the compressive creep behavior exhibits rather linear behavior for linear strain vs log time over a three hour period. The slope of this relationship is dependent on the initial strain level and goes through a maximum with initial strain at 40 percent. This maximum is believed to be due to the buckling of the foam’s struts. The results for the creep behavior were evaluated at a 65 percent initial strain since the creep behavior is believed to be mostly independent of the cellular texture of the foam at this level and greater. A greater amount of viscoelastic decay, i.e. tensile stress relaxation, compression load relaxation and com- pression creep is observed for the higher hard segment foams. Temperature has a similar effect on the results obtained from the three viscoelastic tests. Likewise, relative humidity at a constant temperature also has a similar effect on the viscoelastic behavior of the three tests. Up to 100°C, temperature accelerates the viscoelastic decay of these foams over a three hour time period. For all three viscoelastic tests, a significant increase in the viscoelastic decay at temperatures greater than 100°C is observed. The FTIR thermal analysis of the plaques indicated that this significant increase is due to additional hydrogen bond disruption as well as possible degradation in the urea and urethane links. Increasing relative humidity at a given temperature does bring about a steady decrease in the initial load or initial stress as well as a small increase in the rate of viscoelastic decay. Overall, the effects of temperature are greater on the viscoelastic decay than humidity. The morphology and the viscoelastic behavior of another set of flexible slabstock foams were characterized. These additional foams are rather unique in that some of their morphological features, the urea aggregate structure in particularly, are altered by adding a small amount of LiCl to the formulation. As discussed within the body of this dissertation, these observed changes in morphology are believed to have a significant effect on the viscoelastic nature. / Ph. D.

As new materials are developed and further concerns on green alternatives and serviceability arise, understanding material behavior during the entire span of their lifetime becomes crucial to engineering applications. Moreover, many problems display a significant dependence to time and loading effects which, by varying across multiple time scales, require material models that incorporate these effects into any valid characterization and prediction. This dissertation aims at proposing a new approach to analyze and predict viscoelastic materials that deteriorate during multiple loading conditions. The model is constructed from mechanical and mathematical basis while satisfying physical laws. In this work, the proposed constitutive law is used for the analysis of the mechanical properties of ice. The mechanical behavior, biaxial envelop and multiple loading types demonstrate the validity of the model when compared to experimental results and other ice models available in the literature. A rigorous calibration scheme for the viscoelastic and damage parameters is also presented. Moreover, as material deterioration or damage is modeled in standard Finite Elements software, it is commonly known that computational results can be dependent on the spatial discretization or mesh. That is, damage zone and energy dissipation are dependent on the selection of the mesh yielding a disappearing damage zone and energy dissipation upon refinement. This non-physical behavior is corrected by the novel regularization approach proposed in this document, which introduces a length scale of the material and produces results that are no longer sensitive to the mesh selection. The nonlocal damage model is finally used in the analysis of asphalt concrete viscoelastic behavior and cracking prediction. As presented in the ice case, a rigorous calibration approach is presented first followed by the validation to experimental data available in the literature under different loading conditions. The coupled viscoelastic and damage model is compared to other model and their Finite Elements implementations are highlighted in terms of computational efficiency. A nonlinear coupled system for solving this problem is programmed as a User Element in a commercial Finite Element analysis software.

This thesis focuses on the micromechanical modeling of particulate viscoelastic composite materials in the quasi-static frequency domain to approximate macroscopic damping behavior and has two main objectives. The first objective is the development of a robust frequency dependent multiscale model. For this purpose, the self-consistent (SC) mean-field micromechanical model introduced by Cherkaoui et al [J. Eng. Mater. Technol. 116, 274-278 (1994)] is extended to include frequency dependence via the viscoelastic correspondence principal. The quasi-static model is then generalized using dilute strain concentration tensor formulation and validated by comparison with complex bounds from literature, acoustic and static experimental data, and established models. The second objective is SC model implementation as a tool for the design of high loss materials. This objective is met by integrating the SC model into a Compromise Decision Support Protocol (CDSP) to explore the microstructural design space of an automobile windshield. The integrated SC-CDSP design space exploration results definitively indicate that one microstructural variable dominates structure level acoustic isolation and rigidity: negative stiffness. The work concludes with a detailed description of the fundamental mechanisms leading to negative stiffness behavior and proposes two negative stiffness inclusion designs.

In order to study suspensions of deformable particles, a hybrid numerical technique was developed that combined a lattice-Boltzmann (LB) fluid solver with a finite element (FE) solid-phase solver. The LB method accurately recovered Navier-Stokes hydrodynamics, while the linear FE method accurately modeled deformation of fluid-filled elastic capsules for moderate levels of deformation. The LB/FE technique was extended using the Message Passing Interface (MPI) to allow scalable simulations on leading-class distributed memory supercomputers. An extensive series of validations were conducted using model problems, and the LB/FE method was found to accurately capture proper capsule dynamics and fluid hydrodynamics. The dilute-limit rheology was studied, and the individual normal stresses were accurately measured. An extension to the analytical theory for viscoelastic spheres [R. Roscoe. J. Fluid Mech., 28(02):273-93, 1967] was proposed that included the isotropic pressure disturbance. Single-body deformation was found to have a small negative (tensile) effect on the particle pressure. Next, the rheology and microstructure of dense suspensions of elastic capsules were probed in detail. As elastic deformation was introduced to the capsules, the rheology exhibited rapid changes. Moderate amounts of shear thinning were observed, and the first normal stress difference showed a rapid increase from a negative value for the rigid case, to a positive value for moderate levels of deformation. The particle pressure also demonstrated a decrease in compressive stresses as deformation increased. The corresponding changes in microstructure were quantified. Changes in particle self-diffusivity were also noted.

Thesis (Ph. D.)--Mississippi State University. Department of Aerospace Engineering. / Title from title screen. Includes bibliographical references.

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Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2017-04-04T10:35:10Z No. of bitstreams: 2 Dissertação - Guilherme de Oliveira Andrade - 2017.pdf: 3342486 bytes, checksum: f35bb27c1451d7b8969dbf1fe3332a30 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-04-04T10:35:40Z (GMT) No. of bitstreams: 2 Dissertação - Guilherme de Oliveira Andrade - 2017.pdf: 3342486 bytes, checksum: f35bb27c1451d7b8969dbf1fe3332a30 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-04-04T10:35:40Z (GMT). No. of bitstreams: 2 Dissertação - Guilherme de Oliveira Andrade - 2017.pdf: 3342486 bytes, checksum: f35bb27c1451d7b8969dbf1fe3332a30 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-03-10 / Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG / In order to attenuate unwanted vibrations, coming from mechanical systems, are increasing research in developing efficient products in the vibrant energy dissipation, being carried out in this line, full characterization of viscoelastic materials for the identification of its main phenomena and effectiveness check, reliability and security. The non-linear behavior of viscoelastic materials, when subjected to cyclic loading, is due to their microstructural characteristics, where it is possible that an effective vibration attenuation occurs. However, the complexity of the proposed problem suggests the implementation of numerical-computational procedures, the So that the deformation rates can be evaluated through harmonic analysis, so that the temperature variations can be defined and the phenomena associated with the material can be analyzed. With this, based on the dissipative characteristics of the material, the present work aims at the application of the same in the automotive area, being applied on the vehicular structure of utility vehicles aiming at the attenuation of the vibrations that arrive to the passenger compartment. To prove the efficacy of the material, the structural modeling of the viscoelastic was carried out in a computer environment (MatLab®) and then the material was inserted into the vehicle structure in the finite element software (Ansys®), where the structural and modal harmonic analysis , Thus verifying attenuations of the order of 8.746% for the second vibrating mode of the structure. However, due to the safety involved in automotive projects, it was necessary to analyze the computational effectiveness of these materials on the wide range of operational and environmental factors in which utility vehicles are submitted, thus guaranteeing the necessary reliability to the project. / Com o objetivo de atenuar as vibrações indesejadas, oriundas de sistemas mecânicos, são crescentes as pesquisas nas áreas de desenvolvimento de produtos eficientes na dissipação de energia vibrante, sendo realizados nesta linha, a caracterização completa de materiais viscoelásticos visando a identificação de seus principais fenômenos e verificação de eficácia, confiabilidade e segurança. O comportamento não-linear de materiais viscoelásticos, quando submetido a carregamentos cíclicos, é devido a suas características microestruturais, onde é possível que ocorra uma eficaz atenuação de vibrações. Entretanto, a complexidade do problema proposto sugere a implementação de procedimentos numérico-computacionais, a fim de que se avalie as taxas de deformações através de analises harmônicas, para que desta forma possam ser definidos as variações de temperaturas e analisados os fenômenos associados ao material. Com isso, tendo como base as características dissipativas do material, o presente trabalho visa a aplicação do mesmo na área automotiva, sendo aplicado sobre a estrutura veicular de automóveis utilitários objetivando a atenuação das vibrações que chegam até o habitáculo. Para comprovação da eficácia do material, primeiramente foi realizada a modelagem estrutural do viscoelástico em ambiente computacional (MatLab®) e em seguida realizada a inserção do material na estrutura veicular no software de elementos finitos (Ansys®), onde foram realizadas a análise harmônica estrutural e modal, verificando assim atenuações da ordem de 8,746 % para o segundo modo de vibrar da estrutura. Porém, vale ressaltar, que devido a segurança envolvida em projetos automotivos, foi necessário que se analisasse computacionalmente a eficácia destes materiais sobre a ampla faixa de fatores operacionais e ambientais na qual veículos utilitários estão submetidos, garantindo assim a confiabilidade necessária ao projeto.

Inverse problems are problems where causes for desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development, including radar/sonar, medical imaging, geophysical exploration, invisibility cloaking and remote sensing, to name just a few. In this thesis, we focus on the theoretical study and applications of some intriguing inverse problems. Precisely speaking, we are concerned with two typical kinds of problems in the field of wave scattering and nonlocal inverse problem, respectively. The first topic is on the geometric structures of eigenfunctions and their applications in wave scattering theory, in which the conductive transmission eigenfunctions and Laplacian eigenfunctions are considered. For the study on the intrinsic geometric structures of the conductive transmission eigenfunctions, we first present the vanishing properties of the eigenfunctions at corners both in R2 and R3, based on microlocal analysis with the help of a particular type of planar complex geometrical optics (CGO) solution. This significantly extends the previous study on the interior transmission eigenfunctions. Then, as a practical application of the obtained geometric results, we establish a unique recovery result for the inverse problem associated with the transverse electromagnetic scattering by a single far-field measurement in simultaneously determining a polygonal conductive obstacle and its surface conductive parameter. For the study on the geometric structures of Laplacian eigenfunctions, we separately discuss the two-dimensional case and the three-dimensional case. In R2, we introduce a new notion of generalized singular lines of Laplacian eigenfunctions, and carefully investigate these singular lines and the nodal lines. The studies reveal that the intersecting angle between two of those lines is closely related to the vanishing order of the eigenfunction at the intersecting point. We provide an accurate and comprehensive quantitative characterization of the relationship. In R3, we study the analytic behaviors of Laplacian eigenfunctions at places where nodal or generalized singular planes intersect, which is much more complicated. These theoretical findings are original and of significant interest in spectral theory. Moreover, they are applied directly to some physical problems of great importance, including the inverse obstacle scattering problem and the inverse diffraction grating problem. It is shown in a certain polygonal (polyhedral) setup that one can recover the support of the unknown scatterer as well as the surface impedance parameter by finitely many far-field patterns. Our second topic is concerning the fractional partial differential operators and some related nonlocal inverse problems. We present some prelimilary knowledge on fractional Sobolev Spaces and fractional partial differential operators first. Then we focus on the simultaneous recovery results of two interesting nonlocal inverse problems. One is simultaneously recovering potentials and the embedded obstacles for anisotropic fractional Schrödinger operators based on the strong uniqueness property and Runge approximation property. The other one is the nonlocal inverse problem associated with a fractional Helmholtz equation that arises from the study of viscoacoustics in geophysics and thermoviscous modelling of lossy media. We establish several general uniqueness results in simultaneously recovering both the medium parameter and the internal source by the corresponding exterior measurements. The main method utilized here is the low-frequency asymptotics combining with the variational argument. In sharp contrast, these unique determination results are unknown in the local case, which would be of significant importance in thermo- and photo-acoustic tomography.