Analysis of sandwich beam structures using kriging based higher order models

Functionally graded composite materials can provide continuously varying properties, which distribution can vary according to a specific location within the composite. More frequently, functionally graded materials consider a through thickness variation law, which can be more or less smoother, possessing however an important characteristic which is the continuous properties variation profiles, which eliminate the abrupt stresses discontinuities found on laminated composites. This study aims to analyze the transient dynamic behavior of sandwich structures, having a metallic core and functionally graded outer layers. To this purpose, the properties of the particulate composite metal-ceramic outer layers, are estimated using Mod-Tanaka scheme and the dynamic analyses considers first order and higher order shear deformation theories implemented though kriging finite element method. The transient dynamic response of these structures is carried out through Bossak-Newmark method. The illustrative cases presented in this work, consider the influence of the shape functions interpolation domain, the properties through-thickness distribution, the influence of considering different materials, aspect ratios and boundary conditions. (C) 2014 Elsevier Ltd. All rights reserved.

Dynamic behaviour of soft core sandwich beam structures using kriging-based layerwise models

Sandwich structures with soft cores are widely used in applications where a high bending stiffness is required without compromising the global weight of the structure, as well as in situations where good thermal and damping properties are important parameters to observe. As equivalent single layer approaches are not the more adequate to describe realistically the kinematics and the stresses distributions as well as the dynamic behaviour of this type of sandwiches, where shear deformations and the extensibility of the core can be very significant, layerwise models may provide better solutions. Additionally and in connection with this multilayer approach, the selection of different shear deformation theories according to the nature of the material that constitutes the core and the outer skins can predict more accurately the sandwich behaviour. In the present work the authors consider the use of different shear deformation theories to formulate different layerwise models, implemented through kriging-based finite elements. The viscoelastic material behaviour, associated to the sandwich core, is modelled using the complex approach and the dynamic problem is solved in the frequency domain. The outer elastic layers considered in this work may also be made from different nanocomposites. The performance of the models developed is illustrated through a set of test cases. (C) 2015 Elsevier Ltd. All rights reserved.

Refined sandwich model for the vibration of beams with embedded shear piezoelectric actuators and sensors

This work extends a previously presented refined sandwich beam finite element (FE) model to vibration analysis, including dynamic piezoelectric actuation and sensing. The mechanical model is a refinement of the classical sandwich theory (CST), for which the core is modelled with a third-order shear deformation theory (TSDT). The FE model is developed considering, through the beam length, electrically: constant voltage for piezoelectric layers and quadratic third-order variable of the electric potential in the core, while meclianically: linear axial displacement, quadratic bending rotation of the core and cubic transverse displacement of the sandwich beam. Despite the refinement of mechanical and electric behaviours of the piezoelectric core, the model leads to the same number of degrees of freedom as the previous CST one due to a two-step static condensation of the internal dof (bending rotation and core electric potential third-order variable). The results obtained with the proposed FE model are compared to available numerical, analytical and experimental ones. Results confirm that the TSDT and the induced cubic electric potential yield an extra stiffness to the sandwich beam. (C) 2007 Elsevier Ltd. All rights reserved.

Multimodal passive vibration control of sandwich beams with shunted shear piezoelectric materials

This work presents a performance analysis of multimodal passive vibration control of a sandwich beam using shear piezoelectric materials, embedded in a sandwich beam core, connected to independent resistive shunt circuits. Shear piezoelectric actuators were recently shown to be more interesting for higher frequencies and stiffer structures. In particular, for shunted damping, it was shown that equivalent material loss factors of up to 31% can be achieved by optimizing the shunt circuit. In the present work, special attention is given to the design of multimodal vibration control through independent shunted shear piezoelectric sensors. In particular, a parametric analysis is performed to evaluate optimal configurations for a set of modes to be damped. Then, a methodology to evaluate the modal damping resulting from each shunted piezoelectric sensor is presented using the modal strain energy method. Results show that modal damping factors of 1%-2% can be obtained for three selected vibration modes.

Uumajäykistetyt sandwich-rakenteet

Tässä työssä tutkittiin uumajäykistettyä sandwich-rakennetta. Tutkimuksen tavoitteena oli kehittää kuormitetulle uumajäykistetylle sandwich-elementille taipuman analyyttinen laskentamenetelmä. Sellaisen kehitykselle oli tarve, koska kyseisen tyyppiselle sandwich-rakennetyypille ei ole standardisoitua taipuman laskentamenetelmää. Uumajäykistetyn sandwich-elementin taipuma on kiinnostava, koska käyttörajatilan mukainen taipumaraja on tärkein rakennetta mitoittava tekijä. Työn soveltavassa osiossa kehitettiin uumajäykistetyn sandwich-elementin taipuman analyyttinen laskentamenetelmä. Taipuman analyyttinen laskentamenetelmä kehitettiin sandwich-palkkiteorian perusteella. Keskeisimpiä ongelmia oli uumajäykisteiden taivutus- ja leikkausjäykkyyden huomioonottaminen laskennassa. Analyyttisen laskennan tuloksia verrattiin uumajäykistetylle sandwich-elementille suoritettujen taivutuskokeiden tuloksiin sekä FE-analyysin tuloksiin. Tutkimustulosten perusteella voitiin todeta kehitetyn uumajäykistetyn sandwich-elementin taipuman analyyttisen laskentamenetelmän soveltuvan taipuman laskentaan tutkitulle uumajäykistetylle sandwich-elementille. Laskentamenetelmän luotettavuuden ja toimivuusrajojen määrittämiseksi uumajäykistetty sandwich-rakenne vaatii jatkotutkimuksia.

Performance Assessment of Sandwich Structures with Debonds and Dents

A sandwich construction is a special form of the laminated composite consisting of light weight core, sandwiched between two stiff thin face sheets. Due to high stiffness to weight ratio, sandwich construction is widely adopted in aerospace industries. As a process dependent bonded structure, the most severe defects associated with sandwich construction are debond (skin core bond failure) and dent (locally deformed skin associated with core crushing). Reasons for debond may be attributed to initial manufacturing flaws or in service loads and dent can be caused by tool drops or impacts by foreign objects. This paper presents an evaluation on the performance of honeycomb sandwich cantilever beam with the presence of debond or dent, using layered finite element models. Dent is idealized by accounting core crushing in the core thickness along with the eccentricity of the skin. Debond is idealized using multilaminate modeling at debond location with contact element between the laminates. Vibration and buckling behavior of metallic honeycomb sandwich beam with and without damage are carried out. Buckling load factor, natural frequency, mode shape and modal strain energy are evaluated using finite element package ANSYS 13.0. Study shows that debond affect the performance of the structure more severely than dent. Reduction in the fundamental frequencies due to the presence of dent or debond is not significant for the case considered. But the debond reduces the buckling load factor significantly. Dent of size 8-20% of core thickness shows 13% reduction in buckling load capacity of the sandwich column. But debond of the same size reduced the buckling load capacity by about 90%. This underscores the importance of detecting these damages in the initiation level itself to avoid catastrophic failures. Influence of the damages on fundamental frequencies, mode shape and modal strain energy are examined. Effectiveness of these parameters as a damage detection tool for sandwich structure is also assessed

Effective Electromechanical Coupling Coefficients of Piezoelectric Adaptive Structures: Critical Evaluation and Optimization

This work presents a critical analysis of methodologies to evaluate the effective (or generalized) electromechanical coupling coefficient (EMCC) for structures with piezoelectric elements. First, a review of several existing methodologies to evaluate material and effective EMCC is presented. To illustrate the methodologies, a comparison is made between numerical, analytical and experimental results for two simple structures: a cantilever beam with bonded extension piezoelectric patches and a simply-supported sandwich beam with an embedded shear piezoceramic. An analysis of the electric charge cancelation effect on the effective EMCC observed in long piezoelectric patches is performed. It confirms the importance of reinforcing the electrodes equipotentiality condition in the finite element model. Its results indicate also that smaller (segmented) and independent piezoelectric patches could be more interesting for energy conversion efficiency. Then, parametric analyses and optimization are performed for a cantilever sandwich beam with several embedded shear piezoceramic patches. Results indicate that to fully benefit from the higher material coupling of shear piezoceramic patches, attention must be paid to the configuration design so that the shear strains in the patches are maximized. In particular, effective square EMCC values higher than 1% were obtained embedding nine well-spaced short piezoceramic patches in an aluminum/foam/aluminum sandwich beam.

Experimental analysis of active-passive vibration control using viscoelastic materials and extension and shear piezoelectric actuators

Hybrid active-passive damping treatments combine the reliability, low cost and robustness of viscoelastic damping treatments and the high-performance, modal selective and adaptive piezoelectric active control. Numerous hybrid damping treatments have been reported in the literature. They differ mainly by the relative positions of viscoelastic treatments, sensors and piezoelectric actuators. In this work we present an experimental analysis of three active-passive damping design configurations applied to a cantilever beam. In particular, two design configurations based on the extension mode of piezoelectric actuators combined with viscoelastic constrained layer damping treatments and one design configuration with shear piezoelectric actuators embedded in a sandwich beam with viscoelastic core are analyzed. For comparison purposes, a purely active design configuration with an extension piezoelectric actuator bonded to an elastic beam is also analyzed. The active-passive damping performance of the four design configurations is compared. Results show that active-passive design configurations provide more reliable and wider-range damping performance than the purely active configuration.

Dimensionless analysis of constrained damping treatments

One of the most effective ways of controlling vibrations in plate or beam structures is by means of constrained viscoelastic damping treatments. Contrary to the unconstrained configuration, the design of constrained and integrated layer damping treatments is multifaceted because the thickness of the viscoelastic layer acts distinctly on the two main counterparts of the strain energy the volume of viscoelastic material and the shear strain field. In this work, a parametric study is performed exploring the effect that the design parameters, namely the thickness/length ratio, constraining layer thickness, material modulus, natural mode and boundary conditions have on these two counterparts and subsequently, on the treatment efficiency. This paper presents five parametric studies, namely, the thickness/length ratio, the constraining layer thickness, material properties, natural mode and boundary conditions. The results obtained evidence an interesting effect when dealing with very thin viscoelastic layers that contradicts the standard treatment efficiency vs. layer thickness relation; hence, the potential optimisation of constrained and integrated viscoelastic treatments through the use of properly designed thin multilayer configurations is justified. This work presents a dimensionless analysis and provides useful general guidelines for the efficient design of constrained and integrated damping treatments based on single or multi-layer configurations. (C) 2012 Elsevier Ltd. All rights reserved.

On the use of particle swarm optimization to maximize bending stiffness of functionally graded structures

Functionally graded materials are a type of composite materials which are tailored to provide continuously varying properties, according to specific constituent's mixing distributions. These materials are known to provide superior thermal and mechanical performances when compared to the traditional laminated composites, because of this continuous properties variation characteristic, which enables among other advantages, smoother stresses distribution profiles. Therefore the growing trend on the use of these materials brings together the interest and the need for getting optimum configurations concerning to each specific application. In this work it is studied the use of particle swarm optimization technique for the maximization of a functionally graded sandwich beam bending stiffness. For this purpose, a set of case studies is analyzed, in order to enable to understand in a detailed way, how the different optimization parameters tuning can influence the whole process. It is also considered a re-initialization strategy, which is not a common approach in particle swarm optimization as far as it was possible to conclude from the published research works. As it will be shown, this strategy can provide good results and also present some advantages in some conditions. This work was developed and programmed on symbolic computation platform Maple 14. (C) 2013 Elsevier B.V. All rights reserved.

Proposta de construção de um amortecedor de vibração ajustável, TVA, utilizando fluido magnetoreológico

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dynamic analysis for different finite element models of beams with viscoelastic damping layer

Many new viscoelastic materials have been developed recently to help improve noise and vibration levels in mechanical structures for applications in automobile and aeronautical industry. The viscoelastic layer treatment applied to solid metal structures modifies two main properties which are related to the mass distribution and the damping mechanism. The other property controlling the dynamics of a mechanical system is the stiffness that does not change much with the viscoelastic material. The model of such system is usually complex, because the viscoelastic material can exhibit nonlinear behavior, in contrast with the many available tools for linear dynamics. In this work, the dynamic behavior of sandwich beam is modeled by finite element method using different element types which are then compared with experimental results developed in the laboratory for various beams with different viscoelastic layer materials. The finite element model is them updated to help understand the effects in the damping for various natural frequencies and the trade-off between attenuation and the mass add to the structure.

Optimización de la densidad de energía en vigas de material compuesto (PRF) sometidas a flexión pura

Las necesidades energéticas actuales requieren el desarrollo de tecnologías eficaces y eficientes en producción, transporte y distribución de energía. Estas necesidades han impulsado nuevos desarrollos en el ámbito energético, entre los cuales se encuentran sistemas de almacenamiento de energía. El avance en ingeniería de materiales permite pensar en la posibilidad de almacenamiento mediante deformación elástica de vigas. Concretamente se parte de un concepto de mecanismo acumulador de energía basado en la deformación elástica de resortes espirales a torsión. Dichos resortes se pueden considerar como elementos vigas sometidos a flexión pura y grandes deflexiones. Esta Tesis de centra en el diseño y optimización de estos elementos con el fin de maximizar la densidad de energía que son capaces de absorber. El proceso de optimización comienza con la identificación del factor crítico del que depende dicho proceso, en este caso de trata de la densidad de energía. Dicho factor depende de la geometría de la sección resistente y del material empleado en su construcción. En los últimos años ha existido un gran desarrollo de los materiales compuestos de tipo polimérico reforzados con fibras (PRF). Estos materiales están sustituyendo gradualmente a otros materiales, como los metales, debido principalmente a su excelente relación entre propiedades mecánicas y peso. Por otro lado, analizando las posibles geometrías para la sección resistente, se observó que la más adecuada es una estructura tipo sándwich. Se implementa así un procedimiento de diseño de vigas sándwich sometidas a flexión pura, con las pieles fabricadas en materiales compuestos tipo PRF y un núcleo que debe garantizar el bajo peso de la estructura. Se desarrolla así un procedimiento sistemático que se puede particularizar dependiendo de los parámetros de entrada de la viga, y que tiene en cuenta y analiza la aparición de todos los posibles modos de fallo posibles. Así mismo se desarrollan una serie de mapas o ábacos de diseño que permiten seleccionar rápidamente las dimensiones preliminares de la viga. Finalmente se llevan a cabo ensayos que permiten, por un lado, validar el concepto del mecanismo acumulador de energía a través del ensayo de un muelle con sección monolítica, y por otro validar los distintos diseños de vigas sándwich propuestos y mostrar el incremento de la densidad de energía con respecto a la alternativa monolítica. Como líneas futuras de investigación se plantean la investigación en nuevos materiales, como la utilización de nanotubos de carbono, y la optimización del mecanismo de absorción de energía; optimizando el mecanismo de absorción a flexión pura e implementando sistemas que permitan acumular energía mediante la deformación elástica debida a esfuerzos de tracción-compresión. ABSTRACT Energy supply requires the development of effective and efficient technologies for the production, transport and distribution of energy. In recent years, many energy storage systems have been developed. Advances in the field of materials engineering has allowed the development of new concepts as the energy storage by elastic deformation of beams. Particularly, in this Thesis an energy storage device based on the elastic deformation of torsional springs has been studied. These springs can be considered as beam elements subjected to pure bending loads and large deflections. This Thesis is focused on the design and optimization of these beam elements in order to maximize its density of stored energy. The optimization process starts with the identification of the critical factors for the elastic energy storage: the density. This factor depends on the geometry of the cross section of the beam and the materials from which it is made. In the last 20 years, major advances in the field of composite materials have been made, particularly in the field of fiber reinforced polymers (FRP). This type of material is substituting gradually metallic materials to their excellent weight-mechanical properties ratio. In the other side, several possible geometries are analyzed for its use in the cross section of the beam; it was concluded that the best option, for maximum energy density, is using a sandwich beam. A design procedure for sandwich beams with skins made up with FRP composites and a light weight core is developed. This procedure can be particularized for different input parameters and it analyzes all the possible failure modes. Abacus and failure mode maps have been developed in order to simplify the design process. Finally several tested was made. Firstly, a prototype of the energy storage system which uses a monolithic composite beam was tested in order to validate the concept of the energy storage by elastic deformation. After that sandwich beam samples are built and tested, validating the design and showing the increase of energy density with respect to the monolithic beam. As futures research lines the following are proposed: research in new materials, as carbon nanotubes; and the optimization of the energy storage mechanism, that means optimizing the pure bending storage mechanism and developing new ones based on traction-compression mechanisms.

Damping energy dissipated by interfaces in beam and plate supports and in sandwich cores.

"Materials Laboratory, Contract no. AF 33(616)-5426, Project no. 7360."

Optically Induced Modulation of a Laser Beam in Nematic Liquid Crystals Structures

In this paper we report the experimental results obtained when an He-Ne laser beam crosses an MBBA homeotropic sandwich structure and is modulated by the influence of another laser beam, in our case an Ar+ laser, crossing through the same region. We extend some results previously reported by us1 2 concerning the influence of the ratio of the diameters of the laser beams on the modulation characteristics. A theoretical model, based on the one reported in Ref6 , shows good agreement with the experimental results. If the Ar+ laser is intensity chopped, the resulting He-Ne diffracted image is also intensity modulated. The highest frequency observed has been 500 p. p. s.