Much of the work done on active and passive constrained layer beams is done with mathematical models proposed by Kerwin and extended by DiTaranto, Mead and Markus, and others. The mathematics proposed by these early researchers was tailored to fit the damping treatments in use at that time: thin foil damping tapes applied to panels for noise reduction. A key assumption was that all layers had identical transverse displacements. While these assumptions are reasonable when the core layer, normally a soft viscoelastic material(VEM), is thin and the constraining layer is weak in bending, there are many situations in industry and in the literature where the ``Mead and Markus'' (MM) assumptions should be questioned. An important consequence of the MM modeling assumptions is that the strain energy in the VEM core is dominated by shear strain, and this in turn means that only the shear modulus is of primary importance. This is fortunate since only the shear modulus is available to engineers for viscoelastic materials used for layered damping treatments. It is a common practice in industry and academia to simply make an educated guess of the value of Poisson's ratio. It is shown in the dissertation that this can result in erroneous predictions of damping, particularly in partial-coverage configurations. Finite element analysis is used to model both the MM assumptions and a less-restrictive approach commonly used in industry. Predictions of damping from these models are compared against models with elements from C0 elements and a C1-capable element that matches tractions at material interfaces. It is shown that the time-honored modal strain energy method is a good indicator of modeling accuracy. To assess the effects of the MM assumptions on an active PZT used as a constraining layer, closed-loop damping versus gain is determined using both the MM and higher order elements. For these analyses, the time-dependent properties of the viscoelastic material are represented by a Maxwell model using internal variables. Finally, the basic MM premise that all layers share the same transverse displacement is disproved by experiment. / Ph. D.

<p> A detailed synopsis of the state-of-the-art in the field of the Structural Analysis of sandwich beams is presented. Deficiencies, inaccuracies, lack of clarity, and the imposition. of unnecessary assumptions of behaviour found -in the related bibliography are presented in a comparative fashion. A method of analysis with obvious advantages over the others studied in this thesis is derived, and its use is suggested. The presentation of all methods of analysis is made under the most general cases of dimensions and loadings to make them as applicable as possible to the common cases encountered in sandwich components for the building industry. </p> <p> Experimental work carried out on several materials with some potential to be used in sandwich members for buildings and the tests carried out on some sandwich beams and beam-columns are reported. </p> / Thesis / Master of Engineering (MEngr)

No description available.

<p> A detailed synopsis of the state-of-the-art in the field of the Structural Analysis of sandwich beams is presented. Deficiencies, inaccuracies, lack of clarity, and the imposition of unnecessary assumptions of behaviour found in the related bibliography are presented in a comparative fashion. A method of analysis with obvious advantages over the others studied in this thesis is derived, and its use is suggested. The presentation of all methods of analysis is made under the most general cases of dimensions and loadings to make them as applicable as possible to the common cases encountered in sandwich components for the building industry.</p> <p> Experimental work carried out on several materials with some potential to be used in sandwich members for buildings and the tests carried out on some sandwich beams and beam-columns are reported.</p> / Thesis / Master of Engineering (MEngr)

Sandwich beams are composite systems having high stiffness-to-weight and strength-to-weight ratios and are used as light weight load bearing components. The use of thin, strong skin sheets adhered to thicker, lightweight core materials has allowed industry to build strong, stiff, light, and durable structures. Due to the use of viscoelastic polymer constituents, sandwich beams can exhibit time-dependent behavior. This study examines and predicts the time-dependent behavior of sandwich beams driven by the viscoelastic foam core. Governing equations of the deformation of viscoelastic materials are often represented in differential form or hereditary integral form. A single integral constitutive equation is used to model linear viscoelastic materials by means of the Boltzmann superposition principle. Based on the strength of materials approach, the analytical solution for the deformation in a viscoelastic sandwich beam is determined based on the application of the Correspondence Principle and Laplace transform. Finite element (FE) method is used to analyze the overall transient responses of the sandwich systems subject to a concentrated point load at the midspan of the beam. A 2D plane strain element is used to generate meshes of the three-point bending beam. User material (UMAT) subroutine in ABAQUS FE code is utilized to incorporate the viscoelastic constitutive model for the foam core. Analytical models and experimental data available in the literature are used to verify the results obtained from the FE analysis. The stress, strain, and deformation fields during creep responses are analyzed. Parameters such as the viscosity of the foam core, the ratio of the skin and core thicknesses, the ratio of the skin and core moduli, and adhesive layers are varied and their effect on the timedependent behavior of the sandwich system is examined.

Investigation of simply supported Multilayer sandwich beams with symmetrical loading and of Multipier shear walls with arbitrary horizontal loadings. The analysis contains the influence of normal deformation of the layers and piersrespectively. / Thesis / Master of Engineering (ME)

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-10-16T10:52:39Z No. of bitstreams: 1 tamaradecarvalhofreitas.pdf: 4928276 bytes, checksum: 9de5596b41afe271cb80f81cfe1197a6 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-10-16T14:32:24Z (GMT) No. of bitstreams: 1 tamaradecarvalhofreitas.pdf: 4928276 bytes, checksum: 9de5596b41afe271cb80f81cfe1197a6 (MD5) / Made available in DSpace on 2018-10-16T14:32:24Z (GMT). No. of bitstreams: 1 tamaradecarvalhofreitas.pdf: 4928276 bytes, checksum: 9de5596b41afe271cb80f81cfe1197a6 (MD5) Previous issue date: 2018-09-05 / Sistemas passivos de controle para a atenuação de vibrações em estruturas apresentam grande diversidade de concepções, pois resultam de projetos criativos voltados para cada problema específico. Em geral, são mecanicamente robustos e se mostram como alternativas mais eficientes, sob o ponto de vista dinâmico estrutural, do que as técnicas usuais e conservadoras de enrijecimento da estrutura. Dentre estes sistemas, podem-se destacar aqueles que utilizam materiais viscoelásticos (MVE) como núcleo amortecedor, como por exemplo os sistemas tipo sanduíche. Estes materiais têm propriedades mecânicas dependentes da temperatura e, principalmente, da frequência de vibração, trazendo dificuldades adicionais às já complexas formulações teóricas do problema. Neste trabalho, as formulações usadas para modelar sistemas sanduíches viscoelásticos GHM (Golla-Hughes-MacTavish); ADF (Anelastic Displacement Field); e DF (Derivadas de Ordem Fracionária) são tomadas como base para as simulações computacionais analisadas. Partindo de experimentos de caracterização de materiais desenvolvidos, as formulações supracitadas foram adotadas para estimar o comportamento dinâmico de estruturas sanduíche. Por fim, estratégias voltadas para o projeto de estruturas sanduíches com MVE são propostas, baseadas no desempenho de cada uma das formulações avaliadas no que se refere às suas respectivas capacidades de simular os experimentos realizados. / Passive control systems for vibration control in structures demonstrate a wide variety of conceptions, as they are results of creative projects focused on specific problems. Usually, they are robust mechanisms and are shown as more efficient alternatives than ordinary and conservative techniques of structural stiffening. Among these systems, it is possible to highlight the ones that use viscoelastic materials (VEM) as damping core, such as sandwich systems. These materials have mechanical properties depending on temperature and, mainly, on the vibration frequency, introducing additional difficulties to the already complex theoretical formulations of the problem. In this work, formulations used to model viscoelastic sandwich systems, such as GHM (Golla-Hughes-MacTavish); ADF (Anelastic Displacement Field); and DF (Fractional Order Derivatives) are taken as basis for the computational simulations considered. Based on the experimental characterization of the VEM’s, the formulations previously mentioned were used to estimate the dynamic behavior of sandwich structures. Finally, strategies aimed at design of sandwich VEM structures are indicated, based on the performance of each of the evaluated formulations, regarding to their ability to simulate the experiments performed.

This study focuses on assessing the accuracy of the Euler-Bernoulli beam theory as computational bases to calculate strain and deflection of composite sandwich beam subjected to three-point and four-point bending. Two groups of composite sandwich beams tests results will be used for comparison purposes. Mechanical properties for the laminated skin are provided by researchers from University of Mississippi (Ellen Lackey et al., 2000). Mechanical properties for the balsa wood core are provided by Alcan Baltek Corporation. Appropriate material properties and test geometries are then used in the Euler-Bernoulli-based algorithm in order to generate analytical data for comparison to experimental data provided by researchers from University of New Orleans (UNO, 2005). The resulting single material cross section is then analyzed in the traditional manner using the Euler-Bernoulli beam theory. In general, the Euler-Bernoulli beam theory provides an appropriate analytical approach in predicting flexural behavior of composite sandwich beams.

Sandwich constructions are the most commonly used structures in aircraft and navy industries, traditionally. These structures are made up of the face sheets and the core, where the face sheets will be taking the load and is connected to other structural members, while the soft core material, will be used to absorb energy during impact like situation. Thus, sandwich constructions are mainly employed in light weight structures where the high energy absorption capability is required. Generally the face sheets will be thin, made up of either metallic or composite material with high stiffness and strength, while the core is light in weight, made up of soft material. Cores generally play very crucial role in achieving the desired properties of sandwich structures, either through geometric arrangement or material properties or both. Foams are in extensive use nowadays as core material due to the ease in manufacturing and their low cost. They are extensively used in automotive and industrial field applications as the desired foam density can be fabricated by adjusting the mixing, curing and heat sink processes. Modeling of sandwich beams play a crucial role in their design with suitable finite elements for face sheets and core, to ensure the compatibility between degrees of freedom at the interfaces. Unless the mathematical model simulates the physics of the model in terms of kinematics, boundary and loading conditions, results predicted will not be accurate. Accurate models helps in obtaining an efficient design of sandwich beams. In Structural Health Monitoring studies, the responses under the impact loading will be captured by carrying out the wave propagation analysis. The loads applied will be for a shorter duration (in the orders of micro seconds), where higher frequency modes will be excited. Wavelengths at such high frequencies are very small and hence, in such cases, very fine mesh generally is employed matching the wavelength requirement of the propagating wave. Traditional Finite element softwares takes enormous time and computational e ort to provide the solution. Various possible models and modeling aspects using the existing Finite element tools for wave propagation analysis are studied in the present work. There exists a huge demand for an accurate, efficient and rapidly convergent finite elements for the analysis of sandwich beams. E orts are made in the present work to address these issues and provide a solution to the sandwich user community. Super convergent and Spectral Finite sandwich Beam Elements with metallic or composite face sheets and soft core are developed. As a philosophy, the sandwich beam finite element is constructed with the combination of two beams representing the face sheets (top and bottom) at their neutral axis. The core effects are captured at the interface boundaries in terms of shear stress and normal transverse stress. In the case of wave propagation analysis, the equations are coupled in time domain and spatial domain and solving them directly is a difficult task. In Spectral Finite Element Method(SFEM), the displacement functions are derived by solving the transformed governing equations in the frequency domain. By transforming them and forces from time domain to frequency domain, the coupled partial differential equations will become coupled ordinary differential equations. These equations in frequency domain, can be solved exactly as they are normally ordinary differential equation with constant coefficients with frequency entering as a parameter. These solutions will be used as interpolating functions for spectral element formulation and in this respect it differs from conventional FE method wherein mostly polynomials are used as interpolating functions. In addition, SFEM solutions are expressed in terms of forward and backward moving waves for all the degrees of freedom involved in the formulations and hence, SFEM provides faster and efficient solutions for wave propagation analysis. In the present work, strong form of the governing differential equations are derived for a given system using Hamilton's principle. Super Convergent elements are developed by solving the static part of the governing differential equations exactly and hence the stiffness matrix derived is exact for point static loads. For wave propagation analysis, as the mass is not exactly represented, these elements are required in the optimal numbers for getting good results. The number of these elements required are generally much lesser than the number of elements required using traditional finite elements since the stiffness distribution is exact. Spectral elements are developed by solving the governing equations exactly in the frequency domain and hence the dynamic stiffness matrix derived is exact for the dynamic loads. Hence, one element between any two joints is enough to solve the whole system under impact loads for simple structures. Developing FE for sandwich beams is quiet challenging. Due to small thickness, the face sheets can be modeled using 1D idealization, while modeling of large core requires 2-D idealization. Hence, most finite or spectral elements requires stitching of these two idealizations into 1-D idealization, which can be accomplished in a variety of ways, some of which are highlighted in this thesis. Variety of finite and spectral finite elements are developed considering Euler and Timoshenko beam theories for modeling the sandwich beams. Simple element models are built with rigid core in both the theories. Models are also developed considering the flexible core with the variation of transverse displacements across depth of the core. This has direct influence on shear stress variation and also transverse normal stress in the core. Simple to higher order models are developed considering different variations in shear stress and transverse normal stress across depth of the core. Development of super convergent finite Euler Bernoulli beam elements Eul4d (4 dof element), Eul10d (10 dof element) are explained along with their results in Chapter 2. Development of different super convergent finite Timoshenko beam elements namely Tim4d (4 dof), Tim7d (7 dof), Tim10d (10 dof) are explained in Chapter 3. Validation of Euler Bernoulli and Timoshenko elements developed in the present work is carried out with test cases available in the open literature for displacements and free vibration frequencies are presented in Chapter 2 and Chapter 3. The results indicates that all developed elements are performing exceedingly well for static loads and free vibration. Super convergence performance for the elements developed is demonstrated with related examples. Spectral elements based on Timoshenko theory STim7d, STim6d, STim6dF are developed and the wave propagation characteristics studies are presented in Chapter 4. Euler spectral elements are derived from Timoshenko spectral elements by enforcing in finite shear rigidity, designated as SEul7d, SEul6d, SEul6dF and are presented. E orts were made in this present work to model the horizontal cracks in top or bottom face sheets using the spectral elements and the methodology is presented in Chapter 4. Wave propagation analysis using general purpose software N AST RAN and the super convergent as well as spectral elements developed in this work, are discussed in detail in Chapter 5. Modeling aspects of sandwich beam in N AST RAN using various combination of elements available and the performance of four possible models simulated were studied. Validation of all four models in N AST RAN, Super convergent Euler, Timoshenko and Spectral Timoshenko finite elements was carried out by simulating a homogenous I beam by comparing the longitudinal and transverse responses. Studies were carried out to find out the response predictions of a sandwich beam with soft core and all the predictions were compared and discussed. The responses in case of cracks in top or bottom face sheets under the longitudinal and transverse loading were studied in this chapter. In Chapter 6, Parametric studies were carried out for bringing out the sensitiveness of the important specific parameters in overall behaviour and performance of a sandwich beam, using Super convergent and Spectral elements developed. This chapter clearly brings out the various aspects of design of sandwich beam such as material selection of core, geometrical configuration of overall beam and core. Effects of shear modulus, mass density on wave propagation characteristics, effects of thick or thin cores with reference to the face sheets and dynamic effects of core are highlighted. Wave propagation characteristics studies includes the study of wave numbers, group speeds, cut off frequencies for a given configuration and identification of frequency zone of operations. The recommendations for improvement in design of sandwich beams based on the parametric studies are made at the end of chapter. The entire thesis, written in seven Chapters, presents a unified treatment of sandwich beam analysis that will be very useful for designers working in the area.

Failure modes for sandwich beams of GFRP laminate skins and Nomex honeycomb core are investigated. Theoretical models using honeycomb mechanics and classical beam theory are described. A failure mode map for loading under 3-point bending, is constructed, showing the dependence of failure mode and load on the ratio of skin thickness to span length and honeycomb relative density. Beam specimens are tested in 3-point bending. The effect of honeycomb direction is also examined. The experimental data agree satisfactorily with the theoretical predictions. The results reveal the important role of core shear in a sandwich beam's bending behaviour and the need for a better understanding of indentation failure mechanism. High order sandwich beam theory (HOSBT) is implemented to extract useful information about the way that sandwich beams respond to localised loads under 3-point bending. 'High-order' or localised effects relate to the non-linear patterns of the in-plane and vertical displacements fields of the core through its height resulting from the unequal deformations in the loaded and unloaded skins. The localised effects are examined experimentally by Surface Displacement Analysis of video images recorded during 3-point bending tests. A new parameter based on the intrinsic material and geometric properties of a sandwich beam is introduced to characterise its susceptibility to localised effects. Skin flexural rigidity is shown to play a key role in determining the way that the top skin allows the external load to pass over the core. Furthermore, the contact stress distribution in the interface between the central roller and the top skin, and its importance to an indentation stress analysis, are investigated. To better model the failure in the core under the vicinity of localised loads, an Arcan- type test rig is used to test honeycomb cores under simultaneous compression and shear loading. The experimental measurements show a linear relationship between the out-of-plane compression and shear in honeycomb cores. This is used to derive a failure criterion for applied shear and compression, which is combined with the high order sandwich beam theory to predict failure caused by localised loads in sandwich beams made of GFRP laminate skins and Nomex honeycomb under 3-point bending loading. Short beam tests with three different indenter's size are performed on appropriately prepared specimens. Experiments validate the theoretical approach and reveal the nature of pre- and post-failure behaviour of these sandwich beams. HOSBT is used as a compact computational tool to reconstruct failure mode maps for sandwich panels. Superposition of weight and stiffness contours on these failure maps provide carpet plots for design optimisation procedures.