Curved Sandwich Beams Research Articles

Nonlinear Dynamic Analysis of a Curved Sandwich Beam with a Time-Dependent Viscoelastic Core Using the Generalized Differential Quadrature Method (GDQM)

This paper focuses on the geometrically nonlinear dynamic analyses of a three-layered curved sandwich beam with isotropic face layers and a time-dependent viscoelastic core. The boundary conditions and equations of motion governing the forced vibration are derived by using Hamilton’s principle. The first-order shear deformation theory is used to obtain kinematic relations. The spatial discretization of the equations is achieved using the generalized differential quadrature method (GDQM), and the Newmark-Beta algorithm is used to solve the time variation of the equations. The Newton–Raphson method is used to transform nonlinear equations into linear equations. The validation of the proposed model and the GDQM solution’s reliability are provided via comparison with the results that already exist in the literature and finite element method (FEM) analyses using ANSYS. Then, a series of parametric studies are carried out for a curved sandwich beam with aluminum face layers and a time-dependent viscoelastic core. The resonance and cancellation phenomena for the nonlinear moving-load problem of curved sandwich beams with a time-dependent viscoelastic core are performed using the GDQM for the first time, to the best of the authors’ knowledge.

Finite element model for stability and vibration analyses of bi-directional FG curved sandwich beams

Finite element model for stability and vibration analyses of bi-directional FG curved sandwich beams

Dynamic and electrical responses of a curved sandwich beam with glass reinforced laminate layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact

Dynamic and electrical responses of a curved sandwich beam with glass reinforced laminate layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact

Flexural behavior evaluation of a foam core curved sandwich beam

In this study, curved sandwich beams (CSBs) with glass fiber-reinforced polymer (GFRP) and polyethylene terephthalate (PET) foam core were initially fabricated. Experiments in three-point bending were then performed to understand the flexural behaviors including failure modes, load-bearing capacities, and load–displacement curves. The effects of various geometrical parameters including facesheets and core thicknesses, two different types of cores, and curvature radius were clarified. It was found that the utilization of PET foam in CSBs resulted in a prevention of core shearing failure and a gradual decrease in load–displacement response. Moreover, the results showed that the ultimate load-bearing capacity and stiffness of the CSBs decreased by 17.7 % and 61.8 %, with a curvature decreased from 1500 to 300 mm, respectively. An analytical model was performed to accurately estimate the experimental failure modes and load-bearing capacities of CSBs. Failure maps were also developed to investigate the various failure modes caused by different geometric parameters of curved sandwich beams. The failure maps offer valuable guidance for the design of lightweight structures.

Manufacturing and mechanical testing of curved sandwich beams with zero‐Poisson's ratio honeycomb cores

AbstractIn this research, free curling property of the over‐expanded honeycomb (OH) with zero Poisson's ratio was utilized to design and manufacture curved carbon fiber‐reinforced composite (CFRC) sandwich beams by hot compression molding technique and co‐curing process. Three‐point bending experiments were conducted to reveal the failure mechanism of these OH‐based curved sandwich beams with various curvatures. The results reveal that in this research no matter what the curvature is, the shearing fracture of the OH core controls the initial failure of the curved structure, which is followed by upper skin fracture, lower skin delamination and fracture. With the increase of curvature, the ultimate bearing capacity and flexural rigidity of the curved beams will increase. No debonding was observed in the experiments.Highlights Curved sandwich beams with zero‐Poisson's ratio honeycomb‐core was designed. Deformation process from arc, flattening to anti‐arc was revealed by testing. Strength of curved sandwich beams depends on shear strength of the honeycomb. Beams with smaller curvature have greater bearing capacity and stiffness.

Effect of porosity distribution on vibration and damping behavior of inhomogeneous curved sandwich beams with fractional derivative viscoelastic core

PurposeThe purpose of this paper is to parametrically investigate the vibration and damping characteristics of a functionally graded (FG) inhomogeneous and porous curved sandwich beam with a frequency-dependent viscoelastic core.Design/methodology/approachThe FG material properties in this study are assumed to vary through the beam thickness by power law distribution. Additionally, FG layers have porosities, which are analyzed individually in terms of even and uneven distributions. First, the equations of motion for the free vibration of the FG curved sandwich beam were derived by Hamilton's principle. Then, the generalized differential quadrature method (GDQM) was used to solve the resulting equations in the frequency domain. Validation of the proposed FG curved beam model and the reliability of the GDQ solution was provided via comparison with the results that already exist in the literature.FindingsA series of studies are carried out to understand the effects on the natural frequencies and modal loss factors of system parameters, i.e. beam thickness, porosity distribution, power law exponent and curvature on the vibration characteristics of an FG curved sandwich beam with a ten-parameter fractional derivative viscoelastic core material model.Originality/valueThis paper focuses on the vibration and damping characteristics of FG inhomogeneous and porous curved sandwich beam with frequency dependent viscoelastic core by GDQM – for the first time, to the best of the authors' knowledge. Moreover, it serves as a reference for future studies, especially as it shows that the effect of porosity distribution on the modal loss factor needs further investigation. GDQM can be useful in dynamic analysis of sandwich structures used in aerospace, automobile, marine and civil engineering applications.

Bending, buckling and free vibration analyses of shallow-to-deep FG curved sandwich beams using a global–local refined shear deformation theory

This paper investigates the bending, vibration, and buckling behaviour of functionally graded (FG) curved sandwich beams using a global–local refined shear deformation theory. Material properties of these beams are varied through the thickness according to the power-law distribution. A beam element with a combination of Hermite cubic and quadratic Lagrange shape functions is developed to solve the problems. The obtained results are compared with the results from finite element software (ABAQUS), and other higher-order beam theories. It can be observed that the present model can predict accurately static, vibration, and buckling responses of both shallow and deep FG sandwich beams with arbitrary boundary conditions.

Design and nonlinear dynamics of FG curved sandwich beams with self-adapted auxetic 3D double-V meta-lattice core

The functionally graded (FG) curved sandwich beams with the self-adapted auxetic 3D double-V meta-lattice core and GRC (graphene reinforced composite) facesheets are designed, modeled, and analyzed to reveal their linear vibration and nonlinear dynamic behaviors. The 3D double-V meta-lattices with negative Poisson’s ratio (NPR), developed from the 2D double arrowed honeycombs, are designed that can be self-adapted to meet the spatial requirements of curved sandwich beams. Through micromechanical modeling according to the extended Halpin-Tsai model, the material properties are determined for GRC facesheets, which are further designed to have different distributions of graphene sheets along the structural radial direction, to make the whole sandwich beams possess FG configurations. By linear vibration analysis, the distinct influences of FG configurations on the fundamental natural frequencies are presented. Results from full-scale FE modeling and nonlinear analysis have shown the significant effects of structural curvature radii. The influences of beam lengths, strut radii, thicknesses of the core layer and facesheets, and charge parameters of the blast loadings are followed.

Dynamic response of multilayer curved aluminum honeycomb sandwich beams under low-velocity impact

In this paper, the dynamic response of multilayer curved aluminum honeycomb sandwich beams under low-velocity impact is investigated experimentally. The deformation process and final failure modes of multilayer curved aluminum honeycomb sandwich beams are observed and analyzed. The numerical calculation is conducted, and the numerical results are in good agreement with experimental ones. The effects of core thickness, core-thickness gradient, and gradient of inscribed circle diameters in upper and lower honeycombs on the load-carrying capacity and energy absorption of multilayer curved aluminum honeycomb sandwich beams are explored. It is shown that the multilayer curved sandwich beam has the best energy absorption capacity when the thicknesses of upper and lower cores are same. The total energy absorption of the specimen with the lower layer of 30 mm and the upper layer of 10 mm is 63.7% of that of the specimen with upper and lower layers of same thickness, and the total energy absorption of the specimen with the lower layer of 10 mm and the upper layer of 30 mm is 53.5% of that of the specimen with upper and lower layers of same thickness, respectively, under 40 J impact energy. In the range of curvature angle from 20°to 60°, the energy absorption capacity and mitigation ability of the multilayer curved sandwich beam can be effectively improved. Also, increasing the face-sheet thickness can effectively improve the energy absorption capability of multilayer curved sandwich beams.

Assessment of four-variable refined shear deformation theory for low-velocity impact analysis of curved sandwich beams

In this paper, the accuracy of the four-variable refined global-local (FRGL) shear deformation theory in the prediction of dynamic responses of curved sandwich beams under low-velocity impact has been investigated. The governing equations of motion of the curved sandwich beams are derived by employing a finite element (FE) model based on FRGL shear deformation theory. By using the method of truncated superimposition of modes, the size of the total dynamic system is firstly reduced. Then, the resulting dynamic system is solved via the state-space (SS) approach. For validation, curved sandwich beams with various deepness ratios and different boundary conditions are analyzed using the proposed model. Different materials and lay-up configurations were assumed for the face-sheets. The obtained results are validated through comparison with the results of ABAQUS simulations and other analytical and numerical results reported in the open literature. The comparisons show that the FRGL shear deformation theory in conjunction with the truncated reduced modal SS approach is a precise and computationally low-cost model for solving the dynamic problems of curved sandwich beams under impact loads.

Two-dimensional low-velocity impact analysis of curved sandwich beams with FG-CNTRC face sheets and porous core

The dynamic responses of curved sandwich beams with functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets and porous core subjected to a low velocity impactor is studied. In order to accurately simulate the dynamic behavior of the sandwich curved beams, a layerwise-finite element approach based on the two-dimensional elasticity theory is employed. The contact force is estimated based on the modified Hertz law. Equivalent mechanical properties of the FG-CNTRC face sheets are determined using a refined rule of mixture approach. After validating the approach, some parametric studies are carried out to examine the influences of carbon nanotube distribution patterns, impactor velocity, the curved beam opening angle, length-to-thickness ratio and core-to-face sheet thickness ratio on the responses of the sandwich curved beams under investigation.

On the finite element analysis of functionally graded sandwich curved beams via a new refined higher order shear deformation theory

In the present paper, a novel refined shear deformation beam theory is proposed and applied, for the first time, to investigate the bending behavior of functionally graded (FG) sandwich curved beam. The present theory is exploited to satisfy parabolic variation of shear stress distribution along the thickness direction thereby obviating the use of any shear correction factors. The material properties of FG sandwich beam change continuously from one surface to another according to a power-law function. Three common configurations of FG beams are considered for the study, namely: (a) single layer FG beam; (b) sandwich beam with FG face sheets and homogeneous core and (c) sandwich beams with homogeneous face sheets and FG core. The governing equations derived herein are solved by employing the finite element method using a two-noded beam element, developed for this purpose. A wide range of comparative studies is carried-out to establish the robustness and the performance of the present finite element model. A comparison study shows that the proposed model is: (a) accurate and comparable with the literature; b) of fast rate of convergence to the reference solution; c) excellent in terms of numerical stability and d) valid for both thin and thick FG sandwich curved beams. Moreover, comprehensive numerical results are presented and discussed in detail to investigate the effects of volume fraction index, radius of curvature, material distributions, length-to-thickness ratio, face-to-core- thickness ratio, loadings and boundary conditions on the static response of FG curved sandwich beam. New referential results for thin and thick FG sandwich curved beam are offered, in which can be used to establish benchmarks for future research.

A three-unknown refined shear beam element model for buckling analysis of functionally graded curved sandwich beams

A three-unknown refined shear beam element model for buckling analysis of functionally graded curved sandwich beams

Exact free vibration of symmetric three-layered curved sandwich beams using dynamic stiffness matrix

Exact free vibration of symmetric three-layered curved sandwich beams using dynamic stiffness matrix

Analysis of low velocity impact on curved sandwich beams with FML face sheets and flexible core

In this article, the dynamic response of the curved Fiber-Metal-Laminate sandwich beam with flexible core, under low-velocity impact on the top of the face sheet, is investigated. Higher order shear deformation theory is used and strain-displacement, stress-strain equations, and compatibility conditions between the core and face sheets are applied to obtain the displacement field of the core. The results of model are compared with the results of ABAQUS simulation and the latest researches. The effects of beam curvature angle, core thickness, and its modulus of elasticity, mass and velocity of impactor on radial displacements and contact force histories are reviewed.

A novel approach for in-plane vibration and damping analysis of arbitrarily curved laminated composite and sandwich beams

This study presents a novel approach for the vibration and damping analysis of arbitrarily curved n-layered sandwich beams. The governing equations are derived using Hamilton’s principle and solved by the generalized differential quadrature method (GDQM). Results are compared with the ones that exist in the literature for various types of curved beams either laminated composite or sandwich with a viscoelastic core. In addition, the results of an in-house finite element (FE) solver are added to the comparisons and a very good agreement between the results is observed. Finally, a spiral curved sandwich beam with a parametric mid-section curve and a frequency-dependent viscoelastic core is studied. The effects subtended angle and the core thickness on the vibration and damping behavior are analyzed in detail.

Vibration analysis of curved composite sandwich beams with viscoelastic core by using differential quadrature method

This paper focuses on the vibration analysis of three-layered curved sandwich beams with elastic face layers and viscoelastic core. First, the equations of motion that govern the free vibrations of the curved beams together with the boundary conditions are derived by using the principle of virtual work, in the most general form. Then, these equations are solved by using the generalized differential quadrature method in the frequency domain, for the first time to the best of the authors’ knowledge. Verification of the proposed beam model and the generalized differential quadrature solution is carried out via comparison with the results that already exist in literature and the ANSYS finite element solution combined with the modal strain energy method. The effect of system parameters, i.e. layer thicknesses, the lamination angle of layers and the curvature on the vibration and damping characteristics of a curved sandwich beam with laminated composite face layers and a frequency dependent viscoelastic core is investigated in detail.

Free vibration analysis of a debonded curved sandwich beam

Abstract In this paper, a high order theory is developed to study the free vibration response of a debonded curved sandwich beam. Since the real contact condition at the debonded region is nonlinear, two linear “with contact” and “without contact” models are employed. The Lagrange's principle and the Rayleigh-Ritz method are employed to derive and solve the governing equations. The model regards the radial and circumferential rigidities of the core. For this purpose, quadratic polynomial distributions across the core's height are proposed for its displacement components. The high order model is validated by finite element simulation in ANSYS Workbench. It will be shown that the quadratic distributions can effectively be used for a debonded curved beam comparing to other possible distributions such as a linear pattern which has been previously suggested for an undamaged beam. The analyses demonstrate that curvature angle and boundary conditions play important roles in the vibration response of a curved beam. Also, the results show that the debond effect on natural frequencies is approximately identical for flat and curved beams.

Critical buckling load of curved sandwich beams with composite skins subjected to uniform pressure load

The critical buckling load of curved composite sandwich beam under a uniform pressure load is analyzed in this research. Derivation of equations for face sheets is accomplished via the classical theory of curved beam, whereas for the flexible core, the elasticity equations in polar coordinates are implemented. Employing the von Karman-type geometrical nonlinearity in strain–displacement relations, nonlinear governing equations are resulted. Linear pre-buckling analysis is performed neglecting the rotation effects in pre-buckling state. Stability equations are concluded based on the adjacent equilibrium criterion. Considering the movable simply supported type of boundary conditions, suitable trigonometric solutions are adopted which satisfy the assumed edge conditions. The critical uniform load of the beam is obtained as a closed-form solution. Numerical results cover the effects of various parameters on the critical buckling load of the beam.

A theoretical investigation on low-velocity impact response of a curved sandwich beam

In this paper, two different theoretical approaches are applied to study the low-velocity impact behavior of a curved sandwich beam. At first, a new high order model is developed for curved sandwich beams. Then, the accuracy of this high order model in evaluating the dynamic response and stress results is verified by the layerwise theory. The Ritz method is used to discretize the governing equations and the Runge–Kutta numerical integration method is applied to solve the set of discretized equations. Studies show that the effect of curvature angle is in conjunction with boundary conditions. For a simply supported beam with circumferentially free ends, the contact force decreases and contact time and maximum deflection increase when the curvature angle increases. While this scenario is completely reverse for a beam with circumferentially fixed ends in which the beam becomes stiffer by increasing the curvature angle.