Vibration Analysis Of Sandwich Plates Research Articles

Three-Dimensional Free Vibration Analysis of Sandwich Plates with VSCL Face Sheets and Porous Functionally Graded Core

Three-Dimensional Free Vibration Analysis of Sandwich Plates with VSCL Face Sheets and Porous Functionally Graded Core

Nonlinear bending and vibration analysis of sandwich plate with graphene reinforced micro composite facing sheets and auxetic honeycomb core in thermal environment

Nonlinear bending and vibration analysis of sandwich plate with graphene reinforced micro composite facing sheets and auxetic honeycomb core in thermal environment

Free vibration analysis of sandwich plates with cut-outs: An experimental and numerical study with artificial neural network modelling

This article presents a comprehensive study on the free vibration and damping behaviour of sandwich plates with cut-outs based on experimental and numerical approaches. The effects of the shape, size, and position of the cut-outs on the dynamic response of the sandwich plates under various boundary conditions are explored. Subsequently, artificial neural network (ANN) models are developed utilizing the obtained experimental and numerical data to predict the sandwich plate's natural frequencies and modal loss factors for different cut-outs configurations. The ANN models are trained and tested using a large dataset, and their accuracy is evaluated using various statistical measures. Moreover, a graphical user interface (GUI) is designed using the developed ANN models to provide a user-friendly tool for predicting the modal characteristics of the sandwich plate with cut-outs. The developed ANN models demonstrated high accuracy in predicting the free vibration properties of the sandwich plates under different boundary conditions and cut-out configurations. The combination of experimental and numerical analyses with ANN models and a user-friendly GUI provides a practical and efficient solution for evaluating the dynamic behaviour of sandwich plates with cut-outs, which can be useful for design optimization and structural health monitoring in engineering applications.

Free vibration analysis of sandwich plates

Laminated sandwich plates consisting of a soft core bounded by two relatively thin and stiff faces exhibit excellent strength to weight and stiffness to weight ratios. This makes them very suitable for applications where weight saving is a major concern, such as in aerospace and automotive structures. Piezoelectric layers or patches, due to their simple electro-mechanical properties, can easily be integrated with sandwich composites. The objective of integrating piezoelectric patches is to use them as sensors and actuators in order to control the excessive deformations and vibrations of the structure. Such a structure will have self-correcting capabilities against external loads and is called a smart structure. This further reduces the weight of the structure without compromising on strength or stiffness and becomes a very suitable choice for aerospace applications. Since these structures are often subjected to high dynamic loadings, it becomes important to have an insight of their free vibration characteristics. The work presented includes a study of the free vibration response of laminated sandwich plates using different core materials. From the study it was found that the material of the core significantly influences the free vibration behaviour of the plate, the natural frequency increases with the increase in density of the core material and also with an increase in mode number. The investigation will help in acquiring a better insight of the dynamic behaviour of sandwich plates with surface bonded piezoelectric patches. The efficiency and accuracy of the used elements is established by validation of the results with the published literature.

Nonlinear vibration analysis of sandwich plates with honeycomb core and graphene nanoplatelet-reinforced face-sheets

Nonlinear vibration analysis of sandwich plates with honeycomb core and graphene nanoplatelet-reinforced face-sheets

Navier solution for static and free vibration analysis of sandwich plate with auxetic honeycomb core resting on pasternak elastic foundation

This study investigates the bending behaviour and free vibration response of a rectangular sandwich plate with auxetic honeycomb core and functionally graded material (FGM) face sheets. Governing equations are established from Hamilton’s principle in the framework of the first-order deformation theory (FSDT). The Navier solution has been utilized to determine the deflection and the natural frequency of the simply supported sandwich plate. The reliability and accuracy of the proposed model have been validated via verification studies. The numerical investigations are conducted to investigate the influence of geometric parameters of auxetic material, volume fraction index of FGM, the thickness ratio of layers, and elastic foundation stiffness on deflection and fundamental frequency of the FG-Auxetic sandwich plate.

Carrera unified formulation for bending and free vibration analysis of sandwich plate with FG-CNT faces considering the both soft and stiff cores

In this article, the bending and free vibration behavior of sandwich plates reinforced with functionally graded carbon nanotube (FG-CNT) were investigated based on the Carrera unified formulation(CUF). CUF is a technique which can handle a large category of plate models in a unified way. For FG-CNT, variable kinematic method was used to apply the properties of functionally graded CNTs, which reduce the degrees of freedom and increase the accuracy of the results. Accuracy and efficiency of the presented solution procedure are demonstrated by comparing the obtained results for the sandwich panel with the solution are available. It can be seen that the CUF is the robust method for modeling the sandwich plate with every configuration of CNTs. It must be mentioned, one of the capability of the CUF is that allows us to study the soft core considering the flexibility of the core which not reported in the literature. Therefore, results indicate that the CUF is a suitable model for analysis of the FG-CNT sandwich panels with both stiff and soft cores. A detailed numerical study is performed to examine the influence of soft and hard cores, different plate thickness ratios, different volume fractions of the CNTs, core to face sheet thickness, and also different types of nanotube configurations FG-X, FG-O, FG-VΛ, and FG-ΛV.

Free vibration of three-layer sandwich plate with viscoelastic core modelled with fractional theory

In the present study, natural frequencies and damping behavior of three-layer sandwich plates with viscoelastic core modelled with fractional theory are studied. Governing equations of motion are derived using Lagrange's equation and then solved via Rayleigh-Ritz method. In the first section of the analysis, the coefficients of the fractional and classical viscoelastic models are determined utilizing the curve fitting method on existed experimental data in the literature, and the best viscoelastic model is selected for free vibration analysis of sandwich plate. The method of least squares for fitting smooth curves to experimental data is applied. The results show that the fractional Zener model gives the best fit curve to the experimental data. After that, the effects of some geometrical parameters such as length to width ratio and viscoelastic core thickness on the natural frequency and loss factor of the sandwich plate with viscoelastic core are investigated, and some conclusions are drawn.

Post-Yield characteristics of electrorheological fluids in nonlinear vibration analysis of smart sandwich panels

The present study deals with the nonlinear free vibration analysis of sandwich plates containing electrorheological (ER) fluid as the core layer. Since yield stress of the ER fluid is relatively low, the fluid widely operates in the post-yield region in which the shear stress and shear strain relation is no longer linear. This study employs an equivalent linearized complex shear modulus to quantify the storage and loss moduli of the fluid in different levels of shear strain amplitude and electric field intensity. Also, Classical Plate Theory (CPT) along with von Kármán kinematic formulations are incorporated to extract governing equations of motion of the ER based sandwich plates, in a finite element formulation. The nonlinear governing equations of motion of the structure are solved using a displacement control strategy to evaluate the resonant frequencies and corresponding loss factors of the sandwich plate. Then, the primary attention is focused on the effect of post-yield characteristics of ER fluid on the nonlinear dynamic behavior of the ER based sandwich structure. Furthermore, the effect of applied electric field, boundary conditions and plate parameters such as core layer thickness on the natural frequencies and damping of the structure are comprehensively investigated.

Post-yield characteristics of magnetorheological fluids; from modelling to large-amplitude vibration analysis of sandwich plates using nonlinear finite element method

The present study concerns with post-yield characterization of magnetorheological (MR) fluid and development of a phenomenological model representing the linearized equivalent storage and loss moduli of the fluid in the nonlinear region. It also investigates the nonlinear vibration behaviour of MR based sandwich plates undergoing large amplitude oscillation. To this end, using a magneto-rheometer, the equivalent storage and loss moduli associated with the first harmonic of the measured nonlinear stress-strain data are evaluated under varying shear strain amplitude and magnetic flux intensity. A simple phenomenological model is subsequently proposed to quantify the post-yield moduli of the MR fluid in terms of shear strain magnitude and applied magnetic field. Using the developed model combined with the classical plate theory (CPT), von Karman's formulation and Hamilton's principle, the nonlinear governing equations of motion of the sandwich panel incorporating MR fluid as the core layer have been developed in the finite element form. Displacement control strategy is used to solve the nonlinear equations and identify dynamic characteristics of the structure in terms of natural frequency and loss factor. The results are then compared with those available in literature to validate the developed model. Finally, the developed model has been employed to investigate the effects of post-yield characteristics of the MR fluid, maximum vibration amplitude and applied magnetic field on the nonlinear dynamic characteristics of the MR sandwich panels.

An analytical solution for vibration analysis of sandwich plates reinforced with graphene nanoplatelets

In this study, the free vibration of a composite sandwich plate reinforced with graphene nanoplatelets (GPLs) enclosed by piezoelectric layers is investigated using an analytical solution. In the framework of the first-order shear deformation plate theory, multilayer functionally graded graphene platelets-reinforced composite plate is assumed. Applying modified Halpin–Tsai model and rule of mixtures, the effective Young’s modulus, mass density and Poisson’s ratio of nanocomposites are predicted. In each individual layer, the weight fraction of GPL nanofillers illustrates a layer-wise variation along the thickness direction either uniformly or non-uniformly GPLs dispersed. Based on Maxwell’s equation, the electric potential in a piezoelectric layer is considered for open and closed circuit boundary conditions. Coupled governing equations of motion and boundary conditions are derived by using the Hamilton’s principle. Four auxiliary scalar functions are introduced to decouple the governing equations of motion and boundary conditions, which are solved analytically by employing Levy-type boundary conditions. The effects of GPLs weight fraction, GPLs distribution patterns, number of layers and aspect ratio are examined in detail. The results show that the best way to predict the most effective reinforcement is to distribute more GPLs with a larger surface area near the top and bottom surfaces of the plate. Besides, adding a small amount of GPLs as reinforcing nanofillers can significantly improve the stiffness of the plate.

Free vibration analysis of sandwich plates with compressible core in contact with fluid

In this paper, the extended higher-order sandwich plate's theory (EHSAPT) is used to analyze the free vibration of the sandwich plate with compressible core and different boundary conditions in contact with fluid. First-order shear deformation theory is adopted for the top and bottom face sheets, while the in-plane and transverse displacements of the core are considered to be cubic and quadratic functions of the transverse coordinate, respectively. A single series is considered with two-variable orthogonal polynomials as a set of admissible functions satisfying the boundary conditions. Besides, the fluid is considered to be irrotational, inviscid and incompressible. By taking into account the boundary conditions and compatibility conditions, the fluid velocity potential is acquired. The natural frequencies of the system are calculated by the Rayleigh-Ritz method. An excellent accuracy is obtained between the results in the available literature and the present method. Finally, the effects of various parameters including boundary conditions, side-to-thickness ratio, thickness of the core to thickness of the face sheets ratio, face sheet to core flexural modulus ratio, dimensions of the container, and aspect ratios on the natural frequencies of the sandwich plate are presented and discussed in detail.

TheFinite Element Modeling and Experimental Study of Sandwich Plates with Frequency-Dependent Viscoelastic Material Model.

Athree-layer composite plate element is developed for finite element modeling and vibration analysis of sandwich plate with frequency-dependent viscoelastic material core. The plate element is quadrilateral element bounded by four-node with 7-degree-of-freedom per node. The frequency-dependent characteristics of viscoelastic material parameters are described using the Biot model. The method of identifying the parameters of the Biot model is given. By introducing auxiliary coordinates, the Biot model is combined with the finite element equation of the viscoelastic sandwich plate. Through a series of mathematical transformations, the equation is transformed into a standard second-order steady linear system equation form to simplify the solution process. Finally, the vibration characteristics of the viscoelastic sandwich plate are analyzed and experimentally studied. The results show that the method in this paper is correct and reliable, and it has certain reference and application value for solving similar engineering vibration problems.

Bending and free vibration analysis of sandwich plates with functionally graded soft core, using the new refined higher-order analysis model

This study presents a new higher-order refined analysis model for static and free vibration analysis of a sandwich plate with soft functionally graded material core. The governing equations are derived from equilibrium differential equations of motions. The accuracy and convergence of the present model and numerical solution are validated versus available results. Variable length width ratios, thickness ratios between skins and core and span-to-thickness of sandwich plates have been studied. Obtained results show that suggested model can achieve greater accuracy for sandwich plates with soft functionally graded material core, as compared to existing functionally graded sandwich plate analysis models and models based on finite element method. Finally, parametric study has been carried out to investigate influence of volume fraction distribution, thickness to side ratio and material properties on the plate bending and free vibration.

Vibration analysis of sandwich plates with carbon nanotube-reinforced composite face-sheets

A layer-wise sandwich model is employed for vibration analysis of symmetric sandwich plates with two thin carbon nanotube-reinforced composite (CNTRC) face-sheets, in which a new polynomial refined plate theory is proposed for the core and the classical plate theory is adopted for the face-sheets. By virtue of symmetry, the in-plane displacements are neglected. By maintaining the displacement continuity conditions at the interfaces, the displacement fields are expressed with only two transverse displacement components, which are given in summations of products of beam characteristic functions in one direction and unknown functions in the other. Then, the multi-term Kantorovich-Galerkin method (MTKGM) is extended to obtain semi-analytical solutions for vibration response of symmetric CNTRC sandwich plates resting on elastic foundation. Non-dimensional natural frequencies are obtained for CNTRC sandwich plates, and the effects of the number of approximate terms, boundary conditions, sandwich configurations, volume fractions of carbon nanotube, plate aspect ratio, core-to-skin thickness ratio, and foundation stiffness are examined. The new polynomial refined plate theory presented provides an improved yet relatively simple model for vibration analysis of sandwich structures.

Vibration analysis of sandwich plates with lattice truss core

ABSTRACTAn effective methodology is developed to investigate the vibration of the sandwich plate with pyramidal lattice core. Equation of motion of lattice sandwich plate is established by Hamilton's principle. Displacement fields are expressed with a simple method, and the natural frequencies of the lattice sandwich plate are conveniently calculated. The correctness of the analytical method is verified by comparing the present results with published literatures. The effects of structural and material parameters on the vibration characteristics of lattice sandwich plate are analyzed. The present method will be useful for vibration analysis and design of lattice sandwich plates.

High-order free vibration analysis of FGM sandwich plates with non-monotonically graded flexible core

Free vibration analysis of sandwich plates with non-monotonically graded flexible core is studied using a high-order sandwich panel theory. The non-monotonically graded flexible core is considered as two monotonically graded flexible core layers. In this high-order theory, the first-order shear deformation theory is used for the face sheets and a 3D-elasticity solution of weak core is employed for each single core layer. The laminated two-layered core is analyzed and formulated by the mixed layer-wise theory. Based on the continuity of the displacements and transverse stresses at the interfaces of the face sheets and the core, equations of motion are derived by Hamilton’s principle. The accuracy of the present approach is validated by comparing with the numerical results obtained from finite element method and good agreements are reached. Parametric study is also conducted to investigate the effect of distribution of functionally graded material properties, the monotonically graded core thickness ratio, and the thickness-to-side ratio on the vibration frequency.

Free vibration Analysis of Sandwich Plates with cutout

This paper presents the free vibration analysis of sandwich plates with cutouts. Cutouts are inevitable in structural applications and the presence of these cutouts in the structures greatly influences their dynamic characteristics. A finite element model has been developed here using the ANSYS 15.0 software to study the free vibration characteristics of sandwich plates in the presence of cutouts. Shell 281 element, an 8-noded element with six degrees of freedom suited for analyzing thin to moderately thick structures is considered in the development of the model. Block Lanczose method is adopted to extract the mode shapes to obtain the natural frequency corresponding to free vibration of the plate. The effects of parametric variation on the natural frequency of the sandwich plates with cutout are studied and results are presented.

Postbuckling and postbuckled vibration analysis of sandwich plates under non-uniform mechanical edge loadings

Postbuckling and postbuckled vibration characteristics of sandwich plate subjected to non-uniform in-plane loadings is investigated in this article. The core compressibility effects are considered in the model by assuming fourth and fifth order expansions for the transverse and tangential displacement of the core. The exact stress distributions within the panel are determined by panel prebuckling analysis for the applied parabolic and partial edge loadings. Multi-term Galerkin's method is employed to reduce the governing partial differential equation to a set of non-linear ordinary differential equations in the case of dynamic analysis and to a set of non-linear algebraic equations in the case of static stability analysis. Newton-Raphson method in conjunction with Riks approach is used to trace the postbuckling path. Free vibration frequencies of the sandwich plate about a static equilibrium state are obtained by solving the associated linear eigenvalue problem. From numerical study it is observed that the postbuckling path becomes more softening type with increase of aspect ratio. Moreover, unloaded fixed edge of SCSC sandwich plate gives more rigidity than unloaded simply supported edge of CSCS. The prebuckling and postbuckling frequency increases with increase in edge restraint, and in postbuckling range, frequency increases with increase of in-plane load.

Free vibration analysis of sandwich plate with a transversely flexible core and FG-CNTs reinforced nanocomposite face sheets subjected to magnetic field and temperature-dependent material properties using SGT

In this research, the free vibration analysis of a sandwich plate with a transversely flexible core and functionally graded – carbon nanotubes (FG-CNTs) reinforced nanocomposite face sheets subjected to magnetic field and temperature-dependent material properties is presented based on high-order sandwich plate theory (HSAPT). The governing equations of motion are derived using Hamilton's principle. Classical plate theory (CPT) is used for modeling the face sheets and the effective properties of them are defined based on the extended mixture rule. Mechanical properties of the core such as Young's and shear modulli are assumed to be function of temperature. The influences of aspect and side ratios, temperature changes, core-to-face sheet thickness ratio, distribution types and volume fraction of carbon nanotubes are presented. The size-dependent mathematical formulation of the face sheets is developed based on the strain gradient theory (SGT). The results show that with increasing the aspect ratio, the non-dimensional natural frequency increases, however the side ratio has a reverse effect. As the temperature of the system increasing, the non-dimensional natural frequency decreases while by applying the magnetic field, the frequency parameter increases. Also it is concluded that the sandwich plate with X distribution type of carbon nanotubes in the face sheets, has higher frequency compared with the other types. Finally it is observed that by considering the size effect and introducing the material length scale parameters, the frequency of the sandwich plate increases. Employing FG-CNTs in face sheets, magnetic field, and size dependent effect leads to increase stiffness of nanostructures, thus the use of this sandwich plate has a prominent role in modern engineering applications.