Three-layer Beam Research Articles

Elastic buckling of a sandwich beam with variable mechanical properties of the core

This paper deals with the analytical and numerical studies of elastic buckling of a three-layered beam with metal foam core. Mechanical properties of the core are variable along the z-axis. There are two schemes of displacement of the faces and core of the beam: a broken line hypothesis and a non-linear hypothesis. The mathematical models for both types of displacements are presented. The governing differential equations of the sandwich beam are derived. Numerical analysis of sandwich beams is conducted in ANSYS environment. The finite elements analysis has been performed using a linear elastic buckling model. The analysis with constant and variable Young׳s modulus of the core of the beam is carried out. The values of the critical load obtained by the analytical and numerical (FEM) methods are compared.

Multilayered and FGM structural elements under mechanical and thermal loads. Part I: Comparison of finite elements and analytical models

Nowadays modern composites with various internal structures are used for manufacturing of structural parts of airplanes and in other branches of engineering. They have a layered structure or can be produced as functionally graded materials (FGM). For specific applications some porosity is necessary to satisfy technological process requirements.In this paper several numerical models of structural parts of airplanes made of different composites were elaborated. The finite element (FE) analysis and the mechanical response of the structural elements were compared with previously formulated simplified analytical models [1,2]. The calculations concern estimation of deformation states in:–a layered exhaust pipe covered by thermal barrier coating (TBC) subjected to an internal pressure and a temperature gradient,–a two-layered plate under thermal loading,–three-layered beams subjected to bending with non-symmetrical cross-section,–a FGM beam element subjected to bending load,–a FGM two-layered rod subjected to uniaxial tension.For each considered case a good correlation of the results using both methods – analytical and numerical ones – was obtained, which proves correctness of the theoretical derivations, [1,2]. The paper provides also own general procedure for modelling of FGM in the ABAQUS.

Analytical solutions of three-layer beams with interlayer slip and step-wise linear interface law

A new formulation to solve the equilibrium problem of three-layer beams with interlayer slip is proposed. Each layer is modelled as a linearly elastic Euler–Bernoulli beam. Connections between layers are assumed to be perfect in the transverse direction while to have finite stiffness in the longitudinal direction (only interlayer slips are allowed). Interface behaviors in the longitudinal direction are described through linear non proportional relationships relating shear traction and slip between two layers. A novel closed form solution is then obtained and explicit expressions for all static and kinematic variables are derived. This analytical solution can be employed to simulate the response of composite beams for different boundary and loading conditions generating interfacial tractions that induce an irreversible process of progressive interfacial debonding. A numerical example is considered to investigate the influence of a post-elastic interface behavior on the global response of the composite beam when the layers are still elastic.

Analytical solution for a heterogeneous Timoshenko beam subjected to an arbitrary dynamic transverse load

This paper presents the analytical solution for dynamic response of a simply supported heterogeneous Timoshenko beam. Elastic constants and material density are assumed to vary in the thickness direction according to an arbitrary even function. First, the governing equations are established and the dependence of Timoshenko shear coefficient on material functions is derived for rectangular cross-section. Once the equations of motion are derived, they are solved using the classical integral transform method and the Laplace transforms of the beam deflection and of the slope of the beam are presented for an arbitrary type of dynamic load. Then a particular impact problem of a three-layered beam is solved and the analytical results obtained by means of the numerical inverse Laplace transform are confronted with the results of numerical simulations. The correctness and the validity of derived analytical solution are then discussed based on this comparison. Analysis made show that using the presented solution the response of symmetric laminate and functionally graded beams and of symmetric layered beams with functionally graded layer(s) to an arbitrary dynamic load, impact included, can be investigated. The presented approach is suitable for solving the optimisation problems due to its efficiency. • The analytical solution for dynamic response of a heterogeneous beam is derived. • The problem was solved for arbitrary type of transverse load, impact included. • The shear correction factor significantly depends on the beam composition. • Results can be used for symmetric laminate, functionally graded and layered FG beams. • Presented approach is very effective and suitable for solving optimisation problems.

Effect of Thickness of Damping Material on Vibration Control of Structural Vibration in Constrained Layer Damping Treatment

The reduction of noise and vibration is a major requirement for performance of any vibratory system. Passive damping technology using viscoelastic materials is classically used to control vibrations. Viscoelastic material among the damping materials is widely used to dissipate the structural vibration energy. Three-layer sandwich beams, made of two elastic outer layers and a viscoelastic layer sandwiched between them, are considered as damping structural elements. This paper presents the effect of thickness of constrained damping material on modal loss factor of vibrating structures. Measurements are performed on sandwich beam structure. In order to understand the effectiveness of the sandwich structures, the dynamics of beam with constrained viscoelastic layers are investigated. Comparisons of the experimental and the Numerical results confirm that the damping levels and the natural frequencies of damped structures are well corroborated.

Static and Dynamic Interfacial Stresses Analysis for Three-Layer Beam Structures Using Spectral Element Method

As the structural integrity at the interfaces of a three-layer structure certainly depends on the shear and normal (peeling) stress concentrations near the free ends of the cover plate, it is very important to predict the static and dynamic interfacial stresses in an accurate and efficient way for successful designs of three-layer beam-type structures subject to various loading conditions. Thus, this paper presents a frequency-domain spectral element method by which both static and dynamic interfacial stresses can be accurately predicted. To that end, the governing equations of motion for three-layer beam-type structures are derived by using Hamilton's principle and then the spectral element model is formulated in the frequency domain by using the variational method. The high accuracy of the present spectral element model is verified in due course. Numerical studies are then conducted to investigate static and dynamic interfacial stresses for an example three-layer beam subjected to various loadings.

Study on the Generating Performance of a Novel Piezoelectric Generator with Multilayer Cantilevers

In order to improve the generating performance of piezoelectric generator, a novel piezoelectric generator with multilayer cantilever beams is designed, and the finite element model with three-layer cantilever beams is established based on ANSYS 12.0 for static analysis and modal analysis. The results of the simulation show that the piezoelectric cantilever beams have a consistent stress and vibration rule and conform to structural characteristics of the typical cantilever beam. On the basis of this, electromechanical coupling model is established to analyze the nephogram and fluctuation curve of voltage with outside incentive load on the fixed end(base) of each layer of cantilever beam. Physical device with three-layer beams is manufactured to test the stress, natural frequency and output voltage. It can be found that the experimental results coincide well with the simulation ones. Generating performance influence on piezoelectric unimorph cantilever with different vibration frequency and amplitude is investigated by experimental and simulated methods. The results indicate that the novel piezoelectric generator with multilayer cantilever has the optimal generating performance with an environmental vibration frequency of 38 Hz and amplitude of 1.25 mm.

413 2種類の粒径のフィラーを充填した接着剤を用いた三層構造はりの減衰特性評価

413 2種類の粒径のフィラーを充填した接着剤を用いた三層構造はりの減衰特性評価

Equation of a layered packet with transverse shears and compression taken into account

The equations describing a layered packet with transverse shears and compression taken into account in all layers are constructed in this paper. The layer material is assumed to be elastic and transversely isotropic. The generalized Timoshenko kinematic hypotheses are used to take into account the transverse shears and compression. The equations in generalized forces, moments, and displacements are obtained, and the equations for characteristic functions in terms of which all variables describing the stress-strain state in the layered packet can be expressed are derived. The deformation problem for a three-layer beam is considered as an example.

FEM Analysis of a Cantilever Sandwich Beam with MR Fluid Based on ANSYS

The study covers the modeling three-layered beam incorporating a magnetorheological (MR) fluid. The beam finite element model was created using the ANSYS software. The beam comprises two outer layers made of aluminium and MR fluid layer in between, sealed with silicone rubber. Interactions of the magnetic field are taken into account by varying the parameters of the finite elements. Data required for identification were collected from results of measurement of the beams free vibrations. The identification procedure assumes the good agreement between the frequencies of the beams free vibrations and dimensionless damping coefficients obtained from research and computation data. The validity of proposed beams finite element model was also investigated. Finally some numerical results were presented.

Unsymmetric three-layer laminate with soft core for photovoltaic modules

Unsymmetrical laminates are designed for the use in new lightweight construction of photovoltaic modules. One feature of the laminate is relatively thin and compliant polymeric core layer for embedding solar cells. To assess mechanical properties of the core a three-layer beam is proposed as a model structure. For the structural analysis a layer-wise beam theory is developed. Robust relationships between the maximum deflection, the transverse shear strain of the core layer and the applied force in a three-point-bending test of laminated beam samples are derived. Furthermore, a three-dimensional finite element analysis is performed to verify the assumptions of the beam theory. Three-point-bending tests for laminated beams are performed. The experimentally obtained load–deflection curves are compared with the theoretical results.

Analysis of post-buckling and delamination in laminated composite St. Venant–Kirchhoff beams using CZM and layer-wise TSNDT

A layer-wise third order shear and normal deformable plate/shell theory (TSNDT) incorporating a cohesive zone model (CZM) is used to study the initiation and growth of delamination in straight and curved laminated beams. Upon satisfaction of the delamination criteria at a point on the interface between two layers, displacements there of two abutting points on the interface between the two layers are made discontinuous. Delaminations under mode-I, mode-II and mixed-mode static and transient loadings have been studied. All geometric nonlinearities, including the von Karman nonlinearity, are considered. The material of each layer is assumed to be St. Venant–Kirchhoff for which the second Piola–Kirchhoff stress tensor is a linear function of the Green-St. Venant strain tensor. Example problems studied also include delamination growth during axial buckling of a three-layer beam. It is found that the consideration of inertia forces noticeably delays the buckling load and significantly affects the deformed shape of an axially compressed laminated beam.

Investigation of Flexural Behavior of Geocell Reinforcement Using Three-Layered Beam Model Testing

The study presented in this paper aimed to investigate the flexural behavior of geocell reinforcement by means of three-layered beam model testing. The geocell reinforcement was assumed to be a continuous beam sandwiched between two identical polywood beams. An analytical analysis was conducted to derive the closed-form solution to calculate the deflection of the three-layered beam model. A series of four-point bending tests using dead weights were carried out to test the three-layered beam models. Two geocell products of different dimensions and two types of infill materials, crushed stone and silty sand were tested in this study. Deflections of the layered beam models were measured along with the increment of applied loads. Testing results showed that the geocell reinforcement provides considerable resistance to flexural deformation, especially at higher load levels. The geocell with greater cell height to cell length ratio exhibited overall greater resistance to flexural deflection, especially when crushed stone was used as infill materials. Geocell reinforcements filled by crushed stone showed less flexural deformation than the geocells filled by silty sand. The modulus of the geocell reinforcement was calculated based on the closed-form solution and deflection measurements from the four-point bending tests. Ranges of elastic modulus were presented for the geocell reinforcement filled with compacted crushed stone and silty sand, which can be used as reference values for material property inputs in mechanistic-empirical design of geocell-reinforced pavements.

A precise integration method for solving coupled vehicle–track dynamics with nonlinear wheel–rail contact

A new method is proposed as a solution for the large-scale coupled vehicle–track dynamic model with nonlinear wheel–rail contact. The vehicle is simplified as a multi-rigid-body model, and the track is treated as a three-layer beam model. In the track model, the rail is assumed to be an Euler-Bernoulli beam supported by discrete sleepers. The vehicle model and the track model are coupled using Hertzian nonlinear contact theory, and the contact forces of the vehicle subsystem and the track subsystem are approximated by the Lagrange interpolation polynomial. The response of the large-scale coupled vehicle–track model is calculated using the precise integration method. A more efficient algorithm based on the periodic property of the track is applied to calculate the exponential matrix and certain matrices related to the solution of the track subsystem. Numerical examples demonstrate the computational accuracy and efficiency of the proposed method.

On damping vibrations of three-layered beam containing magnetorheological elastomer

In this article, we present the results of investigations of viscoelastic properties of magnetorheological elastomer containing carbonyl iron particles. Frequencies of natural vibrations of three-layered beam, supporting constructions of which are made from aluminum, and the inner layer—from magnetorheological elastomer—are calculated, and the dependence of vibrations on induction of the applied magnetic field is obtained. Nonstationary vibrations of the beam at pulse impact of magnetic field are found.

Deformation of a three-layer elastoplastic beam on an elastic foundation

We study the thermal force bending of an elastoplastic three-layer beam with a rigid filler; the beam is connected with an elastic foundation. The broken normal hypothesis is adopted to describe the kinematics of a packet nonsymmetric with respect to the thickness. The foundation reaction is described by Winkler’s model. The system of equilibrium equations and its exact solution in displacements are obtained and numerical results for a three-layer metal-polymeric beam are presented.

Analysis of the vibrationally induced dissipative heating of thin-wall structures containing piezoactive layers

A strongly non-linear dynamic problem of thermomechanics for multilayer beams is formulated based on the Kirchhoff–Love hypotheses. In the case of harmonic loading, a simplified formulation is given using a single-frequency approximation and the concept of complex moduli to characterise the non-linear cyclic properties of the material. As an example, the problem of forced vibrations and dissipative heating of a roller-supported layered beam containing piezoactive layers is solved. Different aspects of thermal, mechanical and electric responses to the mechanical and electric excitations are addressed. Dissipative heating due to electromechanical losses in the three-layer beam with piezoelectric layers is studied. It is assumed that the structure fails if the temperature exceeds the Curie point for piezoceramics. Using this criterion, the fatigue life of the structure is estimated. Limitations of the approximate monoharmonic approach are also specified.

Dynamic Instability of MRE Embedded Soft Cored Sandwich Beam with Non-Conductive Skins

In this work the governing temporal equations of motions with complex coefficients have been derived for a three-layered unsymmetric sandwich beam with nonconductive skins and magnetorheological elastomer (MRE) embedded soft-viscoelastic core subjected to periodic axial loads using higher order sandwich beam theory, extended Hamilton's principle, and generalized Galerkin's method. The parametric instability regions for principal parametric and combination parametric resonances for first three modes have been determined for various end conditions with different shear modulus, core loss factors, number of MRE patches and different skin thickness. This work will find application in the design and application of sandwich structures for active and passive vibration control using soft core and MRE patches.

Simplified monoharmonic approach to investigation of forced vibrations of thin wall multilayer inelastic elements with piezoactive layers under cyclic loading

A coupled dynamic problem of electromechanics for thin wall multilayer elements is formulated based on the Kirchhoff–Love hypotheses. In the case of harmonic loading, a simplified formulation is given using the monoharmonic approach and the concept of complex moduli to characterize the cyclic properties of the material. The problem of forced vibrations of three-layer beam, whose outer layers are made of a viscoelastic piezoactive material, and, the inner layer of a passive physically nonlinear material, is considered as an example to demonstrate the possibility of the technique elaborated. The possibility of damping the forced vibrations of a structure with the help of harmonic voltages applied to the external piezoactive layers is studied. Results obtained for the transient response of the beam using the complete model are compared with data found using the simplified model. Limitations on the simplified model application are specified.

Modeling of an Adaptive Beam with MR Fluid

This paper is devoted to modeling of a three-layered cantilever beam filled with magnetorheological (MR) fluid. The beam consists of two aluminium outer layers and an MR fluid layer placed between them. The study covers description of MR fluid behavior in the pre-yield regime, analysis of strain and internal forces, formulation of differential equations of motion and finite element model (FEM) and numerical calculations. The aim of the study is to determine maximal amplitudes up to which the MR fluid operates in the pre-yield regime.