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The objective of this study is to investigate the post-buckling of sandwich beams possessing functionally graded material (FGM) faces and functionally graded porous (FGP) cores in thermal environment. Thus, the critical buckling temperature and the deformation of such sandwich beams are determined and discussed in detail for three main types of temperature distributions which are uniform, linear and nonlinear temperature rises. An improved third-order shear deformable theory based on more rigorous kinematics of displacements is employed with von Kármán nonlinearity for constructing the energy equations of the problem. A Jacobi–Ritz method cooperating with the direct iteration procedure and Newton–Raphson technique is utilized to carry out the solutions of the sandwich beams associated with several parameters of material composition, porous coefficient, geometrical ratio and others. Based on the results, it can be disclosed that the beams can withstand the deformation due to thermal loadings if they have more pores inside the core. The resistance to deformation brought on by thermal loadings is significantly improved by increasing the sandwich thickness ratio.

Elastic metamaterials (EMs) are a new kind of artificial composite medium composed of complex micro-structural elements, which have unique dynamic properties and elastic wave regulation ability that their constituent materials do not possess. The existing researches on EMs mainly focus on wave characteristics in two-dimensional and three-dimensional infinite domains. However, actual EM structures are always in the form of finite structures such as rods, beams and plates, so it is more important for engineering applications to understand and master their natural and forced vibration characteristics. Therefore, it is necessary to establish an effective simplified solution method and framework with certain accuracy for the vibration analysis of such structures. In the early stage, we have studied the natural and forced vibration characteristics of EM beams from this point of view, and presented a simplified solution process. In this paper, a kind of sandwich beam structure with EMs as the core is further constructed, the simplified solution process is extended to such more practical model analysis, and the free and steady forced vibration analysis processes of the finite-size sandwich beam are given. The vibration characteristics different from the traditional sandwich beam are investigated, and some interesting and useful phenomena are revealed, including the absence of natural frequencies within bandgap (BG), the gathering of natural frequencies in the vicinity of band edges, and the particular modal correspondence before and after BG. Then, the corresponding formation mechanisms are explained from the perspective of wave propagation.

The four-point bending tests were performed first on the sandwich beam with glass/polypropylene faces and aluminum foam cores. The face thickness, core height, and angle-ply directions were considered as the variables to prepare the specimens. The effects of these variables on the bending strengths and the failure modes of the studied sandwich beams were experimentally analyzed using an MTS 810 material testing system and a four-point bending jig. Experimental results show that four failure modes, i.e. face-sheet failure, local indentation, and two types of core shear failure, were observed for the specimens with various experimental variables. The theoretical strengths for the four failure modes were proposed based on the mechanical strengths of the faces and cores. Among the four theoretical strengths, the lowest one is selected as the predicted strength and the corresponding mode is the predicted failure mode. The comparison results between the predicted and experimental strengths and failure modes were provided in the study. Assessment results show that the prediction errors are found to be below 30% for most specimens.

The two-stage cumulative flexural fatigue behavior of sandwich beams with glass/polypropylene (PP) faces and aluminum (Al) foam core was experimentally analyzed to study the loading sequence effect of the studied innovative sandwich composites subjected to variable-amplitude cyclic loading. The constant amplitude load–life curve was established first for reference. Subsequently, the two-stage cumulative fatigue tests were performed, and the high/low loading sequence and cycle ratio of the first stage were used as experimental variables in the cumulative fatigue tests. Experimental results showed that the sum of the cycle ratios of the two stages for all cases was approximately 1.3. Furthermore, the loading sequence effect was slight. Because the interaction of damage evolution for the two stages was nonsignificant, the different failure modes for the high- and low-loading levels contributed to the high sums of cycle ratios.

Free vibration and buckling of laminated sandwich plate having soft core is studied by using an efficient C⁰ continuous finite element (FE) model based on higher-order zigzag theory (HOZT). In this theory, the in-plane displacement field for both the face sheets and the core is obtained by superposing a global cubically varying displacement field on a zigzag linearly varying displacement field with a different slope in each layer. The transverse displacement is assumed to be quadratic within the core while it remains constant in the faces beyond the core. The proposed model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the plate. The nodal field variables are chosen in an efficient manner to overcome the problem of C¹ continuity requirement of the transverse displacement. Numerical examples on free vibration and buckling covering different geometric and material features of laminated composite and sandwich plates are presented. Many new results are also presented which should be useful for future research.

This paper investigates the free vibration and elastic buckling of sandwich beams with a stiff core and functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets within the framework of Timoshenko beam theory. The material properties of FG-CNTRCs are assumed to vary in the thickness direction, and are estimated through a micromechanical model. The governing equations and boundary conditions are derived by using Hamilton's principle and discretized by employing the differential quadrature (DQ) method to obtain the natural frequency and critical buckling load of the sandwich beam. A detailed parametric study is conducted to study the effects of carbon nanotube volume fraction, core-to-face sheet thickness ratio, slenderness ratio, and end supports on the free vibration characteristics and buckling behavior of sandwich beams with FG-CNTRC face sheets. The vibration behavior of the sandwich beam under an initial axial force is also discussed. Numerical results for sandwich beams with uniformly distributed carbon nanotube-reinforced composite (UD-CNTRC) face sheets are also provided for comparison.

This paper demonstrates that a sandwich beam with the continuous harmonic distribution of geometrical and physical parameters can be adjusted to yield the desired response. The facial layer thickness and core layer modulus of the sandwich beam are considered as the harmonic distribution. The frequency responses and response spectral densities of the finite harmonic sandwich beam with supported mass under stochastic support motion excitations are studied for improving the performance. The partial differential equations for the horizontal and vertical coupling motions of the harmonic sandwich beam are derived and converted into the ordinary differential equations for the multi-mode coupling vibration. The modal stiffness, mass and excitation coefficients are functions of the harmonic distribution parameters (HDPs). The vibration responses including resonances and anti-resonances can be adjusted by the harmonic parameter wave numbers and amplitudes. The frequency responses and response spectral densities of the harmonic sandwich beam are obtained. The single and two-mode vibrations are analyzed to demonstrate that the response resonance and anti-resonance can be adjusted via the HDPs of the beam. The substantially improved vibration response characteristics and the influence of the HDPs on the response spectral densities are illustrated with numerical results.

By using a high order sandwich beams theory which is modified by considering the transverse flexibility of the core, free vibration characteristics of two models of sandwich beams are studied in this paper. In type-I, functionally graded layers coat a homogeneous core, and in type-II, an FG core is covered by homogeneous face sheets. To increase the accuracy of the model of the FGM properties, even and uneven porosity distributions are applied, and all materials are considered temperature-dependent. Nonlinear Lagrange strain and thermal stresses of the face sheets and in-plane strain of the core are considered. To obtain the governing equations of motion, Hamilton’s principle is used and a Galerkin method is used to solve them for simply supported and clamped boundary conditions. To verify the results of this study, they are compared with the results of literatures. Also, the effect of variation of temperature, some geometrical parameters and porosities on the frequency are studied.

In this study, dynamic instability of a sandwich beam made of an isotropic core and functionally graded (FG) graphene platelets-reinforced composite (GPLRC) face sheets is investigated for the first time. A Frostig theory for soft core and third-order shear deformation theory (TSDT) for sheets are used. Hamilton’s principle is used to derive the governing equations of motion, and by applying Bolotin’s approach, the dynamic instability regions (DIRs) are investigated. A comprehensive investigation is conducted to assess the effects of different weight fractions of nanofiller, various GPL patterns, boundary conditions, slenderness ratio, the thickness of face sheet and static load factors on the DIRs of the beam.

In the dynamic study of sandwich structures, the analysis of forced vibrations of these structures is particularly important. Also, no exact solution can be found from the forced vibrations of sandwich beams, and mainly by numerical methods, the dynamic response of sandwich beams has been obtained. Also, there is no coupling solution for this type of structure with an exact solution. Therefore, the present work aims to present a method by which an accurate solution to the dynamic response of sandwich beams can be obtained to eliminate the computational error in numerical methods. Hence, the model is a five-layer sandwich beam with a constant moving load. Carbon nanotubes (CNTs) are used as functionally graded (FG) distributions as reinforcements for the core. Mantari’s higher-order shear deformation theory is also used for displacement fields. The governing equations were derived using the Hamilton principle. The Laplace method is used to obtain the exact solution of the dynamic response of the sandwich beam in both longitudinal and transverse directions. For validation, the natural frequency is compared with previous research. In the following, parameters such as voltage, thickness ratio, the volume fraction of CNTs, and velocity of moving load on the dynamic response of piezoelectric sandwich beams in transverse and axial displacement are investigated.

In this paper, critical buckling analysis and nonlinear load-deflection curve for sandwich beam with functionally graded material are presented based on refined zigzag theory (RZT). By using the variational principle, the equilibrium equations in buckling analysis are given based on the RZT formulations as well as the nonlinear strain-displacement relations. The solutions are also derived for eigenvalue problems in critical buckling load calculations and for load-deflection relations with initial geometric imperfection. The solutions are presented analytically, and the mathematical properties during the derivation process have been proven in order to keep the mathematical rigor. The present analytical RZT critical buckling loads are validated by the RZT FEM, which is the finite element solutions of the sandwich beam meshed by the beam elements based on RZT. These solutions are also compared by commercial software ANSYS, resulting that this approach can obtain an accurate critical buckling load. Various parameters such as aspect ratio, thickness ratio and modulus ratio are considered to investigate their effects on the critical buckling loads. The present results are compared to the beams with higher-order shear deformation theory (HSDT). From the comparisons of the RZT and the HSDT results, it is seen that both theories approach to CBT for slender beam. The results show that the HSDT overestimates the stiffness in the load-deflection curve. It is shown that the RZT exhibits the zigzag displacements at high accuracy, resulting in accurate calculation in critical buckling loads, mode shapes and nonlinear load-deflection curves than HSDT. The superiority of the RZT solutions is presented especially for the case of FGM sandwich beam with soft middle layer.

Being widely used in engineering, the optimization of sandwich beams to achieve greater stiffness-to-weight ratio is of great research interest. In this paper, the optimization process was carried to obtain minimum weight designs in three-point bending based on prescribed stiffness index. Results indicate that honeycomb-cored sandwich beams possess smaller minimum weight index in comparison with metal foam-cored beams. In addition, failure mechanisms of the optimized designs were also investigated to reveal that the sandwich-cored beams were more prone to face wrinkling than metal foam-cored beams. In the optimization process, five different core topologies and four different parent materials were investigated under a given load index. It was found for low prescribed load values where bending is dominant, unidirectional lattice composite sandwich beams bear loads more efficiently than steel cored beams. However, the primary mode of failure for high prescribed load index is core shear, thus implying no significant advantage in lattice composite sandwich beams over other materials. Comparing the different materials, that laminate lattice composite sandwich beams possess the best bending performance for varying levels of prescribed load index, making it suitable for applications in the aerospace field.

A yield criterion for physically asymmetric sandwich cross-sections is proposed in this paper. Using the yield criterion, analytical solutions for the large deflections of fully clamped asymmetric slender sandwich beams transversely loaded by a flat punch at the midspan are derived considering the core strength effect and interaction of bending and axial stretching. Finite element (FE) method is employed to predict the large deflection behavior of the sandwich beams. Good agreement is achieved between the analytical predictions and FE results. Effects of asymmetric factor, core strength and loading punch size are also discussed. It is demonstrated that core strength and loading punch size have significant influences on the load-carrying and energy absorption capacities of physically asymmetric metal sandwich beams while the asymmetry effect could be neglected when the deflection exceeds sandwich beam depth.

This paper experimentally investigates the behavior of sandwich beam with auxetic core subjected to low-velocity impact loading. Two types of sandwich beams with different topologies of auxetic cellular cores were produced. Furthermore, a test procedure involving a cylindrical impactor was developed, and a parametric study was designed and performed. The results revealed that, at the same level of impact energy, the peak load decreased by increasing the re-entrant angle would make the auxetic sample with the highest re-entrant angle an ideal candidate for protective applications. However, in other applications where the structure needs to be protected from damage at a higher level of impact energy, the auxetic sample with the lowest re-entrant angle exhibited the best performance due to the highest amount of failure energy. Finally, the results showed that once the core structure changed from the conventional to auxetic, the energy level leading to damage to the structure increased so that it was escalated by a factor of 2 in the auxetic sample compared to the conventional sample. This is due to the negative Poisson’s ratio effect of structure that makes unit cells be drawn into the projectile impact area and, in turn, the structure is strengthened.

A beam embedded piezoelectric layers is widely used as actuator to excite or control the vibrations of machines and structures. It is also applied as sensor to measure their vibrations. By using the hypothesis of Euler-Bernoulli in beam theory and assuming the distribution of the electric potential in the z-direction, this paper derives the governing equations for sandwich beams coupled with piezoelectric layers. The frequency equation of the free vibration is then obtained and numerical results are presented to demonstrate the availability of the presented theory.