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The present research applies a 2D refined plate theory and isogeometric analysis (IGA) for free vibration analysis of functionally graded (FG) sandwich plates, whose governing equations are treated based on a unified formulation (UF), and nonuniform rational Lagrange (NURL)-based IGA technique. The constitutive model of FG materials is approximated via a Voigt’s rule of mixture based on an equivalent single-layer (ESL) theory. The present framework offers several advantages, including high precision of vibration response by employing higher-order plate theory and the capability of NURL basis functions to capture the exact form of plate geometries. Moreover, higher-order theories postulated by the UF are exempt from the Poisson locking phenomenon and do not require a shear correction factor. Additionally, by employing UF, the effect of thickness stretching on vibration response is considered. Furthermore, higher-order NURL basis functions effectively mitigate shear locking. A large numerical investigation shows the accuracy of results and investigates the effects of several key parameters, such as gradient index, thickness-to-length ratios, layer-to-thickness ratios, and boundary conditions, on the vibration response of FG sandwich plates.

This work is devoted to studying the combined action of periodic in-plane load and tangential subsonic flow on the nonlinear mechanism of the out-plane deformation of the functionally graded composite plate. Three distribution functions are proposed to investigate the distribution of the transverse shear strains and stresses across the thickness of the plates. By using Hamilton’s variational principle, the equations governing the plate instability boundaries are formulated. A nonlinear differential equation describing the first mode of the plate dynamic instability behavior by employing Galerkin’s method. The method of multiple time scales is used to obtain a periodic one-mode solution, which directly leads to the solvability condition. The different resonance cases for the interaction between the frequency of out- plane deformation and the external forces are discussed to discover the extent of the sandwich functionally graded material (FGM) rectangular plate resistance in the presence of external influences. Various bifurcation diagrams for different cases of resonance are obtained versus the basic parameters. In view of this study, we could get a deeper look at the complexity of frequency components in resonance responses of the sandwich FGM rectangular plate. The results could provide some suggestions for the sandwich plate’s vibration reduction design or fault diagnosis field or design fault diagnosis.

Sandwich panels can be manufactured in many ways like lamination press, closed mold fabrication, and vacuum bag compaction. During manufacturing, the core and the sheets are attached under certain applied pressure and temperature, associated with a deformation and stress remaining in the sandwich core. This study presents an evaluation of the compressive residual stress effect of the core which occurs during the localized shock loading at the mid-span of a clamped sandwich plate. We simulate such a square lattice core sandwich plate by commercial finite element code, ABAQUS/Explicit. We apply uniform distributed loading on upper face sheet and temperature difference occurred during the manufacturing process is taken here before the impact simulation step. These loadings induce certain amount of residual stresses in core structure of sandwich panel. The computational result from non-residual stress case is verified by comparing with the results of published experimental data on similar investigation. In addition, the effect of existing residual stress at core is analyzed. We also compare the dynamic responses of two clamped sandwich plates with and without pre-stressed core. And impact resistance of sandwich panel is explained in the view of energy capacity. Results show that the shock loading behavior of sandwich panel depends on its manufacturing process and panels with compressive residual stresses have less deformation and high impact energy absorption characteristics.

Nonlinear dynamics of a sandwich plate with viscoelastic soft core in supersonic flow are investigated by considering the in-plane periodic loading. Using Reddy’s third-order shear deformation theory and von Karman’s nonlinearity, the governing partial differential equations are derived by Hamilton’s principle and then truncated into a set of ordinary differential equations by Galerkin method. The critical speed for flutter is discussed by employing the linear theory. Further, the method of multiple scales is used in the nonlinear dynamical analysis of the truncated system. The Poincaré map is numerically calculated to identify dynamical behaviors. The bifurcation diagrams are presented for varying the dimensionless in-plane loading fluctuation amplitude and the Mach number related dimensionless parameter while other parameters are unchanged.

Mathematical models for multilayer sandwich plates consisting of alternating stiff and compliant layers are derived. Two main types of models are described. First an initial model (analogous to the three-layer Rao–Nakra model) is derived under Kirchhoff plate assumptions for the stiff layers and Mindlin shear-deformable displacement assumptions for the compliant layers. The second type of model can be obtained from the original model by dropping the in-plane and rotational inertia. The resulting model is a generalization of the well-known model of Mead and Markus. Well-posedness and continuous parameter dependence results are described. Some variations of the initial model corresponding to thin compliant layers are described and shown to be regular perturbations of the initial model.

The dynamic instability of composite and sandwich laminates with interfacial slips is studied in this paper. An efficient finite element model recently developed by the authors is used for the purpose. The plate model is based on a refined higher-order shear deformation theory, where the transverse shear stresses are continuous at the layer interfaces with stress free conditions at plate top and bottom. A linear spring-layer model is used to model the interfacial slips by introducing in-plane displacement jump at the interfaces. Some interesting new results are presented in this paper, which are useful to understanding of the behavior of laminated composite materials.

This paper presents the low-velocity impact tests on the sandwich plates with aluminum foam core and aluminum skins at elevated temperatures. A furnace, attached to an Instron Dynatup 9250 HV drop hammer system, was designed to accomplish the penetration tests at temperatures up to 500°C. In order to process the experimental data accurately, the numerical vibration analysis was conducted to determine the threshold frequencies of the fast Fourier transform (FFT) filter for the original impact data. The experimental results showed that the failure modes of the sandwich, peak load and absorbed energy varied obviously with temperatures. Furthermore, the results showed that the failure modes of the top skin and metal foam core showed minor changes with respect to temperatures. Whereas the failure mode of the bottom skin and peak loads changed significantly with respect to temperatures. Also, the absorbed energy revealed a three-stage variation with the change of temperature.

In this paper, buckling analysis of isotropic, orthotropic, laminated composite and sandwich plates utilizing trigonometric shear deformation theory and meshless method based on the finite point formulation using thin plate, polynomial and inverse multiquadric radial basis function is presented. The convergence of the present method is studied for isotropic and laminated composite plates for different radial basis functions with optimal value of shape parameter. Numerical examples of laminated and sandwich plates subjected to various types of in-plane loads are solved to demonstrate accuracy and applicability of present method. Several new results for variety of composite and sandwich plates are presented. The present results are observed to be in good agreement with those available in literature. The effects of orthotropy ratio of material, span to thickness ratio, number of layers, core thickness and lamination scheme on the critical load of plates are also presented.

Two higher-order analytical models based on a new higher-order theory for sandwich plates with flexible cores are developed considering the effect of the core material density and skin-to-core-stiffness-ratio (SCSR). The main difference between the two models is the role of the flexible core in the dynamic response of sandwich plates with cores of different stiffnesses. Firstly, the governing equations of a simply supported sandwich plate with a flexible core are derived based on the two models, and the analytical solutions are determined by using Navier’s approach. Then, the free vibration, static, dynamic bending and stress field characteristics of the sandwich plates with different SCSRs are investigated. The results obtained by the proposed method are compared with other published results. In particular, an accuracy assessment of the present dynamic models is conducted for different SCSRs. Finally, conclusions on the applicability of the proposed method and other theories on sandwich plates with different SCSRs are drawn.

In the present study, free vibration and buckling characteristics of a sandwich functionally graded material (FGM) plate resting on the Pasternak elastic foundation have been investigated. The formulation is based on non-polynomial higher-order shear deformation theory with inverse hyperbolic shape function. A new modified sigmoid law is presented to compute the effective material properties of sandwich FGM plate. The governing equilibrium equations have been derived using Hamilton’s principle. Non-dimensional frequencies and critical buckling loads are evaluated by considering different boundary conditions based on admissible functions satisfying the desired primary and secondary variables. Comprehensive parametric studies have been performed to analyze the influence of geometric configuration, volume fraction exponent, elastic medium parameter, and non-dimensional load parameter on the non-dimensional frequency and critical buckling load. These parametric studies have been done for various boundary conditions and different configurations of the sandwich plate. The computed results can be used as a benchmark for future comparison of sandwich S-FGM plates.

The free and forced vibration characteristics of three-layered sandwich plates with thin isotropic faces and Leptadenia pyrotechnica rheological elastomer (LPRE) core are studied in this investigation. The LPRE core is fabricated and experimented to determine its shear storage modulus and loss modulus. It is observed that the stiffness and damping characteristics of the LPRE core is significantly higher than those of the room-temperature vulcanized silicone rubber elastomer (RTVE) core. The governing equation of motion for the sandwich plate is derived by the Lagrange principle and given in finite element form. The natural frequencies and loss factors of the three-layered sandwich plate are studied by varying the thicknesses of the core and the constraining isotropic layer, and material of the constraining layer with different boundary conditions. The results are compared with those of similar structures with different core materials and boundary conditions. In addition, a LPRE-based sandwich plate is fabricated and its fundamental frequency is determined experimentally and compared with the finite element result. The forced vibration response of the three-layered sandwich plate is also explored under a harmonic excitation force. This study provides supports for the application of the LPRE-based sandwich plates potentially to the passive vibration suppression of structures.

In this study, the instability regions of a honeycomb sandwich plate are investigated for different end conditions under periodic in-plane loading. The core layer of the sandwich plate is made of carbon nanotube (CNT)/glass fiber-reinforced honeycomb and the face layers of CNT/glass fiber- reinforced laminated composite. The governing equations are derived using classical laminated plate theory (CLPT) and solved numerically by using finite element formulation. The effectiveness of the developed finite element formulation is demonstrated by comparing the results in terms of natural frequencies with those available in the literature. The effects of CNT wt.% on the core material, CNT wt.% on the skin material, ply orientation and various end conditions on the variation of natural frequencies, loss factors and instability regions are studied. Finally, some inferences for the effects of CNT reinforcement on the honeycomb sandwich plate subjected to the periodic in-plane loads are discussed.

The research work presented in this paper is focused on the investigation of dynamic characteristics and optimum design of rotating laminated composite multi-walled carbon nanotubes-reinforced magnetorheological elastomer (MWCNT-MRE) sandwich plate. Higher-order shear deformation theory (HSDT) and finite element (FE) formulations are employed to derive the governing equations of the composite MWCNT-MRE sandwich plate. The performance of the derived numerical model is validated by comparing it with the results available in the published literature. The free and forced vibrations of the composite MWCNT-MRE sandwich plate are examined at different magnetic fields and rotating speeds. Also, the optimal ply orientations of the MWCNT-MRE sandwich plate are identified using the developed numerical model coupled with a genetic algorithm (GA) to enhance the natural frequencies and loss factors.

This study examined the transient or dynamic response of sandwich plates with a functionally graded porous core under the action of time-dependent loads. The plates had two isotropic faces at the top and bottom layers, and the middle layer was made of an open-cell material with functionally graded internal pores. By using the first-order shear deformation theory, the equations of motion used to describe the dynamic behavior of the plates were applied to generate accurate results with less computational effort. To solve the equations of motion, the Ritz method based on the Jacobi polynomials for the admissible displacements, cooperating with the time integration of Newmark, was used to find out the dynamic response of the plates. The results of the numerical experiments revealed that the plates carrying a larger number of internal pores at the middle zone of the core had a great improvement in flexural stiffness, providing less deflection under dynamic loads. The observed results of the plates’ dynamic behavior related to the effects of the porosity coefficient, plate’s geometrical ratio, dynamic loading types, porous distributions of the core, etc. are shown in the form of graphs and tables, which can be used as a benchmark for future research.

Sandwich plates are popular in the research field of vibration damping and are widely used in numerous engineering domains. Sandwich plates have been studied extensively for their excellent performances by a large number of researchers. Due to the interaction between the out-of-plane and in-plane vibrations of the layers of sandwich plates, it is difficult to solve the displacements of each layer in all directions analytically. To deal with this problem conveniently and accurately, a novel analytical method is presented in this study for coupled out-of-plane and in-plane vibrations of sandwich plates, which can be applied to both free and forced vibrations of sandwich plates with arbitrary boundaries. In this method, the core plate is treated as a three-dimensional (3D) problem, and it is assumed that the displacement of the core plate varies linearly along the thickness. Based on the Kirchhoff hypothesis, the displacement solutions of the base and constrained plates of the sandwich plate in the $x$, $y$ and $z$ directions are expressed as a superposition of one-dimensional (1D) and two-dimensional (2D) Fourier series, respectively. By comparison to the published analytical solutions and numerical results of the finite element method, the proposed method achieves excellent accuracy and reliability. In addition, the influence of out-of-plane and in-plane vibrations of sandwich plates on each other is studied, and the effects of geometrical and material parameters on the dynamic behaviors of a sandwich plate are investigated. The result shows that the out-of-plane vibration affects the in-plane vibration significantly, which means that the coupling effect of the out-of-plane and in-plane vibrations must be taken into account when analyzing in-plane vibration.

Advanced automated fiber placement technologies enable variable angle tow sandwich structures possible, which provides an extended flexibility in stiffness tailoring to design lightweight sandwich structures with superior performance. However, complex-shaped openings within this new type of sandwich structures bring great challenges when dealing with vibration problems. In this paper, an isogeometric analysis (IGA) formulation based on a novel high-order sandwich plate theory is developed for the first time to the study of free vibration of variable stiffness sandwich plates with complex-shaped cutouts. The proposed new high-order sandwich plate model is formulated based on the idea of layerwise modeling, that is, the first-order shear deformation theory is employed to characterize the kinematics of the two skins, while the high-order theory based on hierarchic Legendre polynomials is applied to describe the kinematics of the core. The weak-form governing equations for free vibration problems of the perforated sandwich plates are first derived from the virtual work principle, and then the IGA formulation based on the non-uniform rational B-splines (NURBS) is applied to obtain the eigenfrequencies and the corresponding eigenmodes. The novelty of this work lies in that the introduction of hierarchic Legendre polynomials enables the kinematics of the core to be enriched to any desired expansion order, which shows great superiority over its traditional counterpart such as extended high-order sandwich panel theory (EHSAPT). On the other hand, the developed IGA procedure based on the novel high-order sandwich plate theory is applicable to a general sandwich plate even with complex-shaped cutouts. The accuracy and effectiveness of the developed IGA procedure are validated by comparing against the results available in the literature and those obtained using ABAQUS. Effects of cutout size, boundary condition and fiber angle on the vibration characteristics of the perforated sandwich plates are discussed in numerical examples. The results presented herein may be beneficial for the design of variable stiffness sandwich plates with complex-shaped cutouts.

The vibration and buckling characteristics of the sandwich plate with a honeycomb core and functionally graded material (FGM) face sheet have been evaluated in this paper. The honeycomb core, also known as conventional honeycomb and auxetic honeycomb, is modeled based on positive and negative Poisson’s ratio. Material properties of face sheets varied according to simple power-law functionally graded material (P-FGM). Hamilton’s principle has been employed to derive the equation of motion, and Navier’s method is used to solve the plate problem. Three different plate configurations are used to study the effect of the thickness layer. In addition, the outcome based on span-to-thickness ratio, aspect ratio, geometric parameters, and volume fraction exponent of honeycomb structure on frequency parameter and critical buckling load is examined and exhibited for three different plate configurations. The validation of the present formulation is ascertained by comparing it with other available results. Some novel results are presented for different angles of the unit cell that can be useful as a validation study for the forthcoming research on sandwich honeycomb rectangular plates. It is observed that the thickness of the honeycomb layer plays a significant role in affecting the behavior of the sandwich plate. Besides, the auxetic structure is highly sensitive to high excitation frequency applications compared to the conventional honeycomb structure.

In this paper, the dynamic compressive response of metal sinusoidal corrugated core sandwich plates is investigated. The analytical model for the reaction forces of top and bottom face sheets subjected to constant velocity are developed. Finite element (FE) method is carried out to predict the dynamic collapse of metal sinusoidal corrugated cores. Several collapse modes of cores are found in terms of different impact velocity and relative core density. The analytical predications are compared with numerical results, and the analytical model captures numerical results for reaction forces reasonably. The collapse mechanism maps are constructed for sinusoidal corrugated cores with elastic-perfectly plastic material and strain hardening plastic material. The effect of strain rate sensitive on the collapse response is discussed. It is demonstrated that the strain hardening of the metal material increases the dominant deformation mode of the collapse mechanism maps.

This research presents theoretical investigation to analyze vibration of axially moving sandwich plate floating on fluid. This plate is composed of balsa wood core and two nanocomposite face sheets where the three layers vibrated as an integrated sandwich. The fluid–structure interaction (FSI) effects on the stability of moving plate are considered for both ideal and viscous fluid. Halpin–Tsai model is utilized to determine the material properties of two-phase composite consist of uniformly distributed and randomly oriented carbon nanotubes (CNTs) through the PmPV (poly{(m-phenylenevinylene)-co-[(2,5-dioctoxy-p-phenylene)vinylene]}) matrix. The governing equations are derived based on sinusoidal shear deformation plate theory (SSDT) which is more accurate than the conventional theories, and significantly, it does not require a shear correction factor. Employing Hamilton’s principle, the equations of motion are obtained and solved by the semi-analytical method. Results indicated that the dimensionless frequencies of moving sandwich plate decrease rapidly with increasing the water level and they are almost independent of fluid level when it is higher than 50% of the plate length. The results of this investigation can be used in design and manufacturing of marine vessels and aircrafts.

Thermal buckling of graphene platelets (GPLs) reinforced sandwich functionally graded porous (SWFGP) plate with temperature-dependent (TD) properties is investigated. The studied plate is composed of two homogeneous face layers and one functionally graded porous core. Two types of porosity distribution with uniformly distributed GPL reinforcement are included. Based on the first-order shear deformation plate theory, Hamilton principle and Galerkin procedure are employed to build the analytical framework. Uniform, linear, and nonlinear thermal loads along the thickness direction are considered. Subsequently, an iterative procedure is introduced to find out the critical buckling temperature of the plate with the temperature dependence considered. Verifications are conducted to demonstrate the accuracy of the proposed method. Several parametric analyses are investigated in detail where the effects of porosity, GPL weight fraction, geometric configuration, and the boundary condition on the thermal buckling of the plates are discussed.