Multilayer Beam Research Articles

Design and fabrication of multilayer dichroic beam splitter

Beam splitters are primarily used for applications like avionic displays, optical storage, fluorescence applications, optical interferometry, semiconductor instrumentation where some of the information needs to be reflected as well as transmitted. They operate on the principle of light being reflected and transmitted by various interfaces where it is split by percentage of overall intensity or wavelength. In this study, design and fabrication of a dichroic optical beam splitter for filtering of red and green light from a white light source has been presented. Here, a symmetric dielectric multilayer stack with 15 alternating layers of alumina and silica are deposited on BK-7 glass using e-beam evaporation technique. High and low refractive indices of 1.63 and 1.46 respectively are used with quarter-wave optical thicknesses of layers. The beam splitter is designed for 45 ̊ angle of incidence using FilmstarTM design software. Transmission spectrum obtained from UV-Vis-NIR double beam spectrophotometer shows reflectance of ~54% at 660 nm (red wavelength region) and transmittance of ~88% at 550 nm (green wavelength region). The coated sample is further subjected to adhesion and hardness test according to MIL standard and no peel off or scratch is observed indicating excellent durability of the coating. The modelled and measured results closely agree with one another over visible spectral regions. Copyright © 2017 VBRI Press.

Dynamic response analysis of multi-span bridge-track structure system under moving loads

Based on the finite Fourier series and the energy variation principle, an analytical calculation method for the dynamic response of multi-span bridge-track structure systems under the action of moving load series is proposed. The applicability of this method is verified by the comparison of the results with the analytical and numerical approaches. Based on the proposed method, the dynamic response of double-layer and four-layer beam models, commonly used in railway bridge systems is solved, and the calculation formulas of resonance and vibration cancelation velocity of multi-layer beam systems are proposed. The influence of the span number of simply supported beams and the length of subgrade sections on the dynamic response of the four-layer beam system is investigated. The results show that the deflection of the dynamic response of double-layer and four-layer beam systems reaches the maximum value near the mid-span. These two systems have multiple critical speeds under moving loads. When the resonance and vibration cancelation of the multi-beam system occur simultaneously, the vibration cancelation plays a leading role. The span number of simply supported beams and length of subgrade sections influence the dynamic response of the four-layer beam system but have no significant effect on the critical velocity of resonance and vibration cancelation. At present, there is a lack of research on analytical or semi-analytical methods for the dynamic response of multi-span bridge-track structure systems. This research may provide a theoretical basis for the planning, design, operation, and maintenance of bridge-track structure systems to a certain extent.

Thermally induced deformations in multi-layered polymeric struts

Stimulus activated structures that deform from a reference to target configurations are used in various fields such as soft robotics, smart materials, and actuators. Examples of stimuli include electric and magnetic fields, swelling, and temperature. The design of stimulus activated structures requires a comprehensive understanding of the relations between geometry, material properties, structure composition, and the influence of the chosen stimulus. With the aim of better understanding these relations, this work employs moderate rotations theory to model the thermo-mechanical response of multi-layered polymeric struts in a wide range of temperatures. In particular, the transition from a glassy to a rubbery state is explicitly discussed. Implicit equations that relate the material properties and the geometry to the thermally-induced deformation are developed. To illustrate the merit of the model, we investigate the thermo-mechanical behavior of homogeneous and heterogeneous multi-layered struts under two boundary conditions - free-standing and pinned. We show that multi-layered beams with a mismatch in the thermal and elastic properties bend as a result of temperature change. Interestingly, the glass-transition temperature can result in the reversal of bending direction. We follow with simulations of thermally-activated polymer-based bi-layer struts with typical properties to demonstrate the applicability of the proposed design. This framework can be used as a guideline and an inverse design tool for the selection of materials and geometries for thermally-activated shape-morphing lattice-based structures that are capable of achieving multiple shape-shifts with a single stimulus. Additionally, this work can be readily extended to other stimuli and thus serves as a foundation for the effective design of stimulus activated structures capable of polymorphism.

Exact Solutions for Time-Varying Bending Behavior of Multilayer Orthotropic Beams Bonded by Viscoelastic Interlayers

This study proposed exact solutions for the purpose of investigating and understanding the time-varying bending behavior of a multilayer orthotropic beam bonded by viscoelastic interlayers. In the analytical model, each orthotropic layer involved four independent elastic constants and was modeled on the basis of the two-dimensional (2D) elasticity theory. The interlayer exhibited viscoelastic properties and was described by the standard linear solid model. By means of Fourier series expansion, the general solutions of stresses and displacements were derived with unknown coefficients, which were analytically determined by interfacial and loading conditions, in which the convolution was converted by the Laplace transform. The results of numerical examples showed that the present solutions converged rapidly and were consistent with the finite element solutions. Comparison of the present 2D solutions with the one-dimensional (1D) solutions based on the Euler–Bernoulli beam theory indicated that the 1D solutions were inaccurate for thick beams. The effects of viscoelastic material and orthotropic constants on the long-term stresses and displacements in the beam were thoroughly examined. These results provided a reference for the optimization of a multilayer orthotropic beam design.

ON IMPROVING THE METHOD OF ELECTRON-BEAM DEPOSITION

The paper deals with improvement of the electron-beam additive forming of metal products using a vertically fed filler wire in vacuum with two electron beams as a heating source. We compared the importance of the power of the heat source required for fusing the layers with each other and the calculated power of the heat source required to melt the filler wire and the surface of the product. Within the experimental conditions of the multilayer electron beam deposition using side wire feeding, the electron beam power of 2.4 kW was required to ensure fusion without the defect formation between the layers during the deposition of Ti-6Al-4V titanium alloy. At the same time, approximate calculations of the minimum power of the heat source required to melt the filler wire and the surface of the product showed a level of 730 W.

Experimental and numerical study on the compressive behaviour of partially accessible concrete columns strengthened by a layer of high-performance concrete

In this paper, a novel reinforcement system for partially accessible concrete columns is studied experimentally and numerically. This technique involves the application of a layer of high-performance mortar only on one side of the existing concrete columns with built-in shear connectors that, together with the concrete-mortar interface, transfer the load between the two components. In the experimental campaign, three different fibre-reinforced high-performance mortars have been used for the reinforcement of a concrete column. The influence of the thickness and the material of the reinforcement layer on the increase of the bearing capacity of the columns have been assessed. In addition, a novel finite-element formulation for a multi-layer beam allowing for plastic deformation (and failure) of the layers and mixed-mode delamination between them is proposed to model the reinforced columns. The model has been capable of simulating the complex structural behaviour of the experimental testing with low computational burden and robust solution procedure, allowing to conclude that the amount of the interlayer relative displacements strongly influences the effectiveness of the reinforcement technique.

Multi-layer polymer beam reinforced by graphene platelets on low velocity impact response

PurposeThe purpose of this paper is to investigate the effect of graphene platelets (GPLs) on the low-speed contact between a mass and surface of a multi-layer polymer beam.Design/methodology/approachThis problem is primarily organized by first-order shear deformation beam theory and nonlinear Hertz rule. GPLs are distributed along the beam thickness direction. The Halpin–Tsai micromechanics model is applied for computing the effective Young’s modulus of the GPLs/polymer composites. In the formulation process, the principle of conservation of energy is first used and the histories of results are extracted using the separation of variables and Runge–Kutta method.FindingsIn comparing the responses with the available data, a good agreement is observed. The effects of the weight fraction and distribution pattern on the impact response of polymer beam reinforced with GPLs are studied. Results show that contact force is increased, contact time and beam recess are decreased with increasing of weight fraction of GPLs. Also, among the different distribution patterns, the contact force depended on value of GPLs at the point of contact.Originality/valueThe effects of GPLs addition on the multi-layer polymer beam has a novelty in impact problems.

Experimental and Simulation Analysis of the Evolution of Residual Stress Due to Expansion via CMAS Infiltration in Thermal Barrier Coatings

The failure behavior of thermal barrier coatings (TBCs) involves multilayered systems infiltrated with calcium–magnesium–alumino-silicates (CMAS). The metastable tetragonal phase is mainly composed of 7YSZ (7 mol.% Y2O3-stabilized ZrO2), and it destabilizes into the Y-lean tetragonal phase, which may be induced by CMAS infiltration, and transforms into a monoclinic phase during cooling. The phase transformation leads to volume expansion around the CMAS-rich layer. Furthermore, it is shown that the spalling of the coating system emerges when the surface of the coating system is subjected to significant residual stress. In this study, a double-cantilever beam model is established to describe the macroscopic phenomenon of thermal buckling induced via CMAS. The result of the buckle height is used to demonstrate the consistency of the experiment and finite element simulation. The experimental parameters are imported into a multilayer cantilever beam model to analyze the interfacial stresses due to CMAS infiltration. The finite element results indicate that the phase transformation leads to damage in the coating system wherein the interfacial stresses due to phase transformation are 27% higher than those in the model without phase transformation.

Influence of Loading History on Delamination in Multilayered Beam with Creep

The present paper deals with an analytical study of the time-dependent delamination in a multilayered inhomogeneous cantilever beam with considering of the loading history. The multilayered beam exhibits creep behaviour that is treated by using a non-linear stress-strain-time relationship. The material properties are continuously distributed along the thickness and length of the layers. The external loading is applied in steps in order to describe the loading history. The analysis reveals that during each step of the loading, the strain energy release rate increases with time. The influences of crack length and location on the time-dependent strain energy release rate are also investigated.

Energy Dissipation in Viscoelastic Multilayered Inhomogeneous Beam Structures: An Analytical Study

The present work is concerned with analysis of the dissipated energy in viscoelastic multilayered inhomogeneous beam structure. The layers of the beam are continuously inhomogeneous along the thickness. The Maxwell mechanical model is used for treating the viscoelastic behaviour of the beam. The moduli of elasticity and the coefficients of viscosity vary continuously along the thickness of each layer. The dissipated energy is obtained by integrating of the unit dissipated energy in the volume of the beam. A parametric investigation of the dissipated energy is carried-out by applying the solution derived in order to evaluate the influence of various factors.

Investigation of electronic transport in InAs/GaAs samples. A study using the metaheuristic self-adaptive differential evolution method

This manuscript presents the study of electronic transport on a set of five multilayer molecular beam epitaxy-grown InAs/GaAs semiconductor samples. We developed an automated switch system to carry out electronic transport measurements of mobility and carrier concentration using the van der Pauw technique. Measurements were carried out as a function of temperature within the range of 260 K to 310 K. To identify which scattering mechanisms most contributed to mobility limitation, It was necessary to use the Self-adaptive Differential Evolution meta-heuristic method. This method allowed the determination of the main scattering mechanisms limiting the electronic mobility and identified as scattering by dislocations and phonons. Dislocations consist of the dominant defects in this lattice mismatch structure. Therefore, to increase carrier mobility, we propose some strategies: a change in the sample growth parameters such as substrate temperature and InAs/GaAs layer thickness. Alternatively, annealing of the samples could also be considered to improve sample mobility.

Delamination analysis of multilayered beams exhibiting creep under torsion

A delamination analysis of a multilayered inhomogeneous beam structure under linear creep is developed. A viscoelastic model that consists of an arbitrary number of linear springs and linear dashpots is used. The cross-section of the beam is a circle. The beam is made of concentric longitudinal layers. Each layer is continuously inhomogeneous in thickness and length directions. Therefore, the shear moduli and the coefficients of viscosity of the viscoelastic model are distributed continuously along the thickness and length of each layer. Two concentric delamination cracks are located arbitrary between layers. The beam is loaded in torsion. Time-dependent solutions to the strain energy release rate for the two delaminations are derived by using the time-dependent strain energy in the beam. The strain energy release rates are derived also by the compliance method for verification. The variation of the strain energy release rate with time due to creep is evaluated. The effects of material inhomogeneity, external loading and delamination length on the strain energy release rate are investigated.

Dynamic Analysis of Multi-layer Beam Structure of Rail Track System Under a Moving Load Based on Mode Decomposition

Dynamic Analysis of Multi-layer Beam Structure of Rail Track System Under a Moving Load Based on Mode Decomposition

Refined orthotropic beam models based on Castigliano’s theorem and an approximate solution of the compatibility equation

This paper presents an extension of Castigliano’s second theorem for orthotropic beams. The notion “extension” in this context means to find more accurate results not only for the vertical deflection, but also for the horizontal deflection and the rotation angle. For this purpose the Airy stress function is calculated for an orthotropic rectangular strip based on the iterative approximation method from Boley-Tolins when distributed loads or shear tractions are assumed as surface loads. Hence all stress components can be derived from the stress function and may be inserted into the complementary strain energy. Computing the partial derivative of the complementary strain energy with respect to a scalar dummy parameter, the weighted displacement field components over the cross section are obtained. Finally the analytical results from the extended Castigliano theorem (ECT) are verified by two-dimensional (2D) analytical results for an orthotropic cantilever and a clamped-hinged beam and the outcome is also compared to Bernoulli–Euler and to Timoshenko results. The accuracy of the derived results is higher than that derived by the Timoshenko theory because the normal stress in thickness direction is properly taken into account. Moreover it is demonstrated that this lower order normal stress which is caused by distributed loads yields a mean horizontal elongation or shrinkage that is not considered by the Timoshenko beam theory. Hence, highly accurate formulations for laminated composite beams, involving sandwich-structures or multi-layered beams with imperfect bonding, may be derived from the present orthotropic beam model in the future.

Delamination analysis of multilayered viscoelastic beam exposed to chemical degradation

Delamination of multilayered viscoelastic non-homogeneous beam structure subjected to chemical degradation is analysed in this paper. The creep behaviour is treated by using a linear viscoelastic model. The influence of chemical degradation is taken into account by decreasing the elasticity modulus and the coefficient of viscosity with time. The time-dependent delamination fracture under chemical degradation is studied by analysing the strain energy release rate. The strain energy is used to obtain the strain energy release rate that accounts for the creep and for the chemical degradation. The solution is verified by applying the compliance method with considering of the chemical degradation.

Free vibration and dynamic transient response of functionally graded composite beams reinforced with graphene nanoplatelets (GPLs) resting on elastic foundation in thermal environment

In this article, free vibration and dynamic transient response of a multilayer polymer nanocomposite beam resting on elastic foundation reinforced by graphene platelets (GPLs) non-uniformly distributed through the thickness direction in thermal environment is investigated. Theoretical formulations are derived based on Hamilton’s principle, Timoshenko beam theory relationships. The effective Young’s modulus of the GPL/polymer composite is estimated by Halpin–Tsai micromechanics model to account for the effects of GPL geometry and dimensions. The vibration frequencies of the beam are obtained numerically by generalized differential quadrature method (GDQM). The influences of the distribution pattern, weight fraction, the number of layers, thermal environment, slenderness ratio of the beam, boundary conditions, and types of elastic foundations on the free vibration behavior and transient response are presented. The results show that adding a very small amount of GPLs into polymer matrix as reinforcements together with the elastic foundation, significantly increases the natural frequencies of the beam. Placing more GPLs near the top and bottom surfaces of the beam are the most effective ways to strengthen the beam stiffness and increase the natural frequencies. Besides, with the increasing of foundation’s stiffness, the displacement amplitude of the functionally graded composite beam reinforced by GPLs subjected to impulsive load decreases.

Stress calculation method of bending multilayer structural element when bending moment acts in the planes that do not coincident with principal planes

This paper presents stress calculationmethod of bending multilayer structural element when bending moment acts in the planes that do not coincident with principal planes, and cross section is symmetric or asymmetric. Carrying the computation of occurring stress values in multilayer beam layers it is necessary to identify coordinates of cross-section stiffness centre, direction of principal axes, and coordinates of specific points regarding principal axes. Having this information and equation which is valid for stress calculation of bending multilayer beams it is possible to identify normal stress values at any point of the beam cross section under skew bending. It is deduced that stress values and the nature of their changes are influenced by the shape of beam cross-section, its asymmetry degree, and the direction of appliedmoment.

An analytical solution to the problem of thermoelastic bending of a multilayer beam with different temperature of longitudinal faces

An exact analytical solution of the quasistatic problem of thermoelasticity is presented for a section of a narrow multilayer beam with different temperatures of the longitudinal lower and upper faces and a heat flow of arbitrary height across the sections through the lateral faces. The solution was obtained for the entire package of layers by sequentially solving the heat equation for an inhomogeneous beam, taking into account the ideal thermal contact of the layers and the system of equations of the plane problem of the theory of elasticity under the assumption of a rigid connection of the layers. To take into account the inhomogeneity of the beam, a continuum approach is used, in which the multilayer material is considered continuous with variable physical and mechanical characteristics. The resulting relations take into account the orthotropy of the physico-mechanical properties of the materials of the layers and their compliance with the transverse shear and compression strains. An example of implementation of a solution for a five-layer beam with combined rigid and articulated fastening of the ends is given.

The problem of plane bending a direct composite beam of arbitrary cross-section and the prerequisites for its approximate analytical solution

The approach to the reduction of the spatial problem of plane bending a composite discrete-inhomogeneous beam of arbitrary cross-section to the approximate two-dimensional bending problem of the equivalent multilayer beam has been discussed here. The result is represented in the form of relations for determination the characteristics of the equivalent multilayer structure by physical and mechanical materials characteristics of the original beam’s phases and the system of static, geometric and physical relations of the corresponding two-dimensional problem. The obtained equations are similar to the plane problem equations of the elasticity theory, but instead of stresses, they contain internal efforts consolidated to the main plane of the beam. The equations of the approximate two-dimensional problem were used to solve the problem of static bending a composite console of arbitrary structure with a load on the free end, taking into account the uniform change of the temperature field. The given system of equations and relations is the starting point for the construction of non-classical deformation models and solving a wide range of problems concerning the deformation of a direct composite beams.

Electro-structural analysis and optimization studies of laminated composite beam energy harvester

Modern ambient energy harvesters meet the micropower demands of the industrial sensors and communication hardware. Optimum design of such systems to maximize the power output is, therefore, of vital importance. This paper presents a multi-objective optimization methodology of smart laminated composite beam energy harvester by considering different geometric parameters. A typical multilayer carbon-epoxy composite beam with unimorph piezoelectric configuration is analyzed with finite element model. The coupled electro-mechanical effects are considered and the resultant free vibration solution is validated with that of a three-dimensional model. The structural response and power density of the base excited beam are obtained by varying thickness ratio of piezo layer, composite lamination sequence, number of layers, circuit resistance, piezoelectric materials, and so on. The most influencing design variables are identified using analysis of variance (ANOVA). By minimization of the frequency band gap between first two modes and maximization of output power density simultaneously, optimum solution is obtained from grey relation analysis technique. The results are validated with a surrogate model employing multilayer perceptron (MLP) neural network in conjunction with multi-objective genetic algorithms. The structural dynamic response and electrical power output characteristics of optimized configuration are found to be improved.