Natural Frequencies Of Sandwich Plates Research Articles

Natural Frequencies of Soft-Core Composite Sandwich Plates Reinforced by FG Graphene Platelets

Superior mechanical properties such as ultrahigh stiffness and strength along with amazing physical properties have led to the use of nano graphene platelets (GPLs) as a reinforcement in polymer composite structures such as sandwich plates. In this research, free vibration analysis of rectangular sandwich plates with functionally graded (FG) GPL-reinforced face sheets and a soft core is investigated. A high-order three-layer accurate sandwich plate theory is employed to model the soft-core sandwich structure. Third order shear deformable plate theory is applied for functionally graded graphene nano-composite face sheets while second and third order polynomials are used for displacements of the soft core. In this theory, the transverse flexibility of the core as well as the continuity conditions of transverse shear stresses are assumed. Hamilton’s principle is applied to extract the motion equations and the corresponding analytical solutions are presented. The effects of materials properties and geometrical parameters on the natural frequencies of the sandwich plates are studied. A comparison of the present results in particular cases with those of published studies confirms the accuracy of the present analysis. Results show that the natural frequencies of the sandwich plates are enhanced by reinforcing the face sheets with GPLs.

Free vibration behaviours of composite sandwich plates with reentrant honeycomb cores

The free vibration behaviours of carbon fiber composite sandwich plates with reentrant honeycomb cores were explored by experiment, theory and finite element method (FEM) in present study. The composite sandwich plates with reentrant honeycomb cores were designed and fabricated through hot-press and secondary forming technology. The modal characteristics of composite auxetic honeycomb sandwich plates were tested under simply supported boundary conditions. Furthermore, the influences of relative densities and dimensions on the natural frequencies of composite auxetic honeycomb sandwich plates were studied. The equivalent moduli of the unit cell of reentrant hexagonal core were deduced. The free vibration control equation was derived to gain the natural frequencies of the sandwich plates by Zig-Zag theory. The theoretical results of the natural frequencies were obtained and compared with the experimental results and finite element calculation results. The results showed that the theory and FEM could estimate the natural frequencies of this kind of sandwich plates accurately. The natural frequencies of the sandwich plates raised as the increasing of relative densities and influenced by dimensions of the core.

Free Vibrational Analysis of a Functionally Graded Five-Layer Sandwich Plate Resting on a Winkler Elastic Foundation in a Thermal Environment

The effect of adhesive layers bonding to the core of functionally graded (FG) surface layers is investigated using the free vibration of a five-layer sandwich composite plate resting on a Winkler elastic foundation in a thermal environment. It is assumed that all layers are experiencing a steady-state temperature ΔT. The layer-wise theory is used to derive the governing equations with the help of Hamilton’s principle. The Navier solution is employed to obtain the closed-form solutions. The numerical results obtained using the present theory are compared with three-dimensional finite elements implemented by ABAQUS software. The results show that the proposed theory is not only accurate but also efficient in predicting the natural frequencies of sandwich plates resting on Winkler foundations.

A simple and efficient analytical model for the natural frequencies of sandwich plates made of flexible core and composite face sheets with embedded pre‐strained shape memory alloy wires

AbstractTwo main goals are followed in the present work. The first objective is the development of a simple analytical model based on piecewise low‐order shear deformation theory (PLSDT) for the natural frequencies of sandwich plates made of flexible core with temperature‐dependent mechanical properties and laminated composite face sheets with embedded pre‐strained shape memory alloy (SMA) wires. Brinson's model is applied in this research to estimate the recovery stress produced by SMAs. A comparative study is performed to show the ability of the proposed model to offer high solution accuracy at low computational costs. Specifically, the results of the present research exhibit less than a 2% difference from those obtained from the mixed LW/ESL models in the framework of Carrera's unified formulation (CUF). As the second goal, the influences of some parameters such as the pre‐strain of SMAs, the volume fraction of SMAs, and core thickness on the fundamental frequencies of SMA‐reinforced sandwich plates are examined. The results reveal that depending on the geometric parameters and operating temperature, SMAs may have constructive or destructive effects on the free vibration of sandwich plates.

A five-variable model and experiments for dynamic analysis of sandwich plates with holes

Due to their simplification and efficiency, five-variable higher-order models have been widely developed for static and dynamic analysis of multilayered composite and sandwich plates. Nevertheless, the existing five-variable higher-order models will encounter difficulty to produce accurately natural frequencies of sandwich plates. Thereby, this paper proposes a five-variable sine-type higher-order model, which can predict reasonably natural frequencies of sandwich plates. To broaden the scope of application, the finite element formulation in the light of the proposed model is presented. In order to verify the reliability of the proposed model, experiments including two groups of samples have been carried out to test natural frequencies of sandwich plates with diverse holes. After the proposed model is evaluated by experiments, natural frequencies of sandwich plates with different boundary conditions and cutout shapes have been investigated in detail by utilizing the proposed model, which will be further assessed by employing the three-dimensional finite element method (3D-FEM). In addition, the typical five-variable higher-order models published from 1980s to 2020s have been also selected to assess the proposed model. Numerical results show that the proposed model can yield more accurate results than the previous five-variable models. Furthermore, variation of natural frequencies of sandwich plates is also explored by changing the material properties of face sheets, which can provide a consultation for design of dynamic characteristics of sandwich plates.

Impact of blast and mechanical loads on the shear deformable stiffened sandwich plate with an auxetic core layer in thermal environment

By using the first order shear deformation theory (FSTD), this paper presents the results of the nonlinear dynamic behavior and natural frequencies of sandwich plate supported by elastic foundations in thermal environment and subjected to mechanical load and blast loading. This work takes advantage of the sandwich plate configuration with three layers: graphene platelet –reinforced composite (GPL) layer – auxetic layer – FGM layer, to analyze the dynamic and vibration problem, in which the auxetic core layer has a negative Poisson's ratios and the FGM layer is reinforced by stiffeners made of full metal or full ceramic depending on a situation of stiffeners at the metal-rich or ceramic-rich side of the plate respectively. Corresponding to the combination of material layers, the mechanical quantities of the problem are processed and calculated to suit the structure and reinforcement conditions. Numerical results are provided to explore the influences of geometrical parameters, elastic foundation parameters, GPL volume fraction, blast and mechanical loads on the nonlinear dynamic behavior and vibration of sandwich plate resting on elastic foundation and in thermal environment. In addition, the study is not only assumed that the material properties depend on environment temperature variation, but also considered the thermal stresses in the stiffeners, as well as considered the effect of imperfections in the original shape of the structure.

WITHDRAWN: Optimization design of vibration characterizations for functionally graded porous metal sandwich plate structure

In this study, numerical analysis is developed to optimize natural frequencies of sandwich plate functionally graded plate with porosity demonstrated by formulating several MOGA methods (Multi-Objective Genetic Algorithm) design optimization parameters. First, we proposed a new analytical model and analyzed the resultant effects for different parameters. The second results have been validated by comparison to results from detailed finite element (FE) models. Finally, a design of experiments (DOE) based response surface optimization method combined with ANSYS software 2020 R2 is used to maximize fundamental frequencies while minimizing the mass and cost of the FG sandwich plate. Constraints of the maximum natural frequency are imposed. ANSYS DesignXplorer Add-in for Excel in combination with dxrom software used to approximate solutions. A 3D model of the FG system was constructed and meshed with 8-node SOLID186 elements using the default grid. The input parameters are the face sheet thickness, core height, porosity ratio, and power-law index. By considering 100 design points, the first six natural frequencies of a functionally graded sandwich plate are obtained and analyzed. A numerical analysis is performed on the sandwich plate's examples with various boundary conditions, power-law index, FG core thickness, porosity parameter, and slenderness ratios. The calculated results are compared with those solved analytically to show the current approach's accuracy and effectiveness, and the optimized natural frequencies of sandwich plates are also investigated. A predicted error for each parameter can also be recorded. An accepted agreement can be observed between analytical and numerical results with a maximum percentage discrepancy of 5%.

An advanced five-unknown higher-order theory for free vibration of composite and sandwich plates

Accurate prediction of dynamic characteristics is quite critical to understand the strength of layered structures. Nevertheless, the existing five-unknown higher-order theories encounter difficulties to forecast accurately the dynamic response of sandwich structures. Therefore, a new five-unknown higher-order theory is developed for free vibration analysis of composite and sandwich plates, which possesses the same degree of freedom as those of other five-unknown higher-order theories. The developed model can meet beforehand interlaminar continuity conditions and the free-surface conditions of transverse shear stresses. To assess capability of the proposed model, analytical solution for such composite structures with simply-supported conditions has been presented by employing Hamilton’s principle, which is utilized for analysis of mechanical behaviors of composite and sandwich plates. Compared with the three-dimensional (3D) elasticity solutions, 3D finite element results and the results obtained from the chosen five-unknown higher-order models, the proposed model can yield accurately natural frequencies of composite and sandwich plates. Even for the thick plates, the higher-order frequencies calculated from the proposed model are in good agreement with the 3D finite element results. By studying effect of the thickness/length ratios on natural frequencies, it is found that the proposed model is adaptable to predicting natural frequencies of the sandwich plates with the thickness/length ratios between 1/4 and 1/100. In addition, some factors influencing accuracy of five-unknown higher-order models have been investigated in detail. Finally, by means of numerical analysis and discussion, some conclusions have been drawn as well, which can serve as a reference for other investigators.

Parametric uncertainty quantification in natural frequency of sandwich plates using polynomial neural network

In this paper, uncertainty quantification in natural frequencies for laminated soft core sandwich plates is presented by employing finite element (FE) coupled polynomial neural network (PNN) approach. The computational efficiency and accuracy is achieved by using PNN as surrogate model. Latin hypercube sampling method is employed for training of data in PNN model. The stochastic first three natural frequencies of sandwich plates are studied for individual variation in input parameters. The stochasticity in individual input parameters are considered in order to assess their influence on global response of the structure. The algorithm discussed in this article is observed to be converging with the previously published literature (for deterministic case) and validated with full scale Monte Carlo simulation (MCS) i.e. original finite element approach (for stochastic case). The computational time and cost reduced significantly by employing the present surrogate based FE approach compared to that of conventional Monte Carlo simulation approach.

Three-Dimensional Vibration Analysis of a Functionally Graded Sandwich Rectangular Plate Resting on an Elastic Foundation Using a Semi-Analytical Method.

The three-dimensional vibration of a functionally graded sandwich rectangular plate on an elastic foundation with normal boundary conditions was analyzed using a semi-analytical method based on three-dimensional elasticity theory. The material properties of the sandwich plate varied with thickness according to the power law distribution. Two types of functionally graded material (FGM) sandwich plates were investigated in this paper: one with a homogeneous core and FGM facesheets, and another with homogeneous panels and an FGM core. Various displacements of the plates were created using an improved Fourier series consisting of a standard Fourier cosine series along with a certain number of closed-form auxiliary functions satisfying the essential boundary conditions. The vibration behavior of the FGM sandwich plate, including the natural frequencies and mode shapes, was obtained using the Ritz method. The effectiveness and accuracy of the suggested technique were fully verified by comparing the natural frequencies of sandwich plates with results from investigations of other functionally graded sandwich rectangular plates in the literature. A parametric study, including elastic parameters, foundation parameters, power law exponents, and layer thickness ratios, was performed, and some new results are presented.

Free Vibrations of Sandwich Plates with Damaged Soft-Core and Non-Uniform Mechanical Properties: Modeling and Finite Element Analysis.

The paper aims to investigate the natural frequencies of sandwich plates by means of a Finite Element (FE) formulation based on the Reissner-Mindlin Zig-zag (RMZ) theory. The structures are made of a damaged isotropic soft-core and two external stiffer orthotropic face-sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. A non-uniform distribution of the reinforcing fibers is assumed along the thickness of the skin and is modeled analytically by means of peculiar expressions given as a function of the thickness coordinate. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution of the straight fibers, stacking sequence, and mass fraction of the constituents. Some final remarks are presented to provide useful observations and design criteria.

Effect of thermal gradient load on thermo-elastic vibrational behavior of sandwich plates reinforced by carbon nanotube agglomerations

In this study, we investigated the effect of thermal gradient load on natural frequencies of sandwich plates with polymer-based nanocomposite face sheets reinforced by functionally graded (FG) single-walled carbon nanotubes (SWCNTs) agglomerations. Volume fractions and agglomerations of CNTs change across the thickness of each nanocomposite face sheet and temperature-dependent properties of polymer/CNT composite can be estimated with the Eshelby-Mori-Tanaka method. First-order shear deformation theory and a moving least square (MLS) shape function based mesh-free method have also been developed for free vibration and steady state thermal analysis on sandwich plates on two-parameter elastic foundations. We investigated the effects of orientation, aggregation, volume fraction and distribution of CNT. We also studied the effects of essential boundary conditions, sandwich dimensions, and elastic foundation coefficients on frequency behavior of sandwich plates.

Vibration response of viscoelastic sandwich plate with magnetorheological fluid core and functionally graded-piezoelectric nanocomposite face sheets

In this research, vibration analysis of a viscoelastic sandwich plate rested on a visco-Pasternak foundation is investigated. Sandwich plate consists of a magnetorheological (MR) fluid core and viscoelastic nanocomposite face sheets which include piezoelectric matrix and functionally graded carbon nanotubes (FG-CNTs) fiber. Core and face sheets are affected by applying magnetic and electric fields, respectively. The elastic medium is simulated by a visco-Pasternak model which is considered in terms of the effects of springiness, shear and damping of foundation. At first, the constitutive equations of sandwich plate are expressed by employing the geometric continuity conditions. Then, the equations of motion are derived by applying the energy method and Hamilton’s principle and an appropriate analytical approach is proposed to solve them. This approach can be considered as the different boundary conditions. Finally, the influences of various parameters such as the type of MR material, core to face sheets thickness ratio, volume fractions and symmetric distributions of CNTs in face sheets, magnetic and electric fields, viscoelastic constant of face sheets and elastic medium on the dimensionless natural frequencies of sandwich plate are studied. The results show that increasing core-to-face sheet thickness ratio leads to a decrease in the natural frequencies because the MR fluid core is softer than nanocomposite face sheets. Thus, the MR fluid core acts like a damper. Also, the loss factor of the MR fluid core decreases with increasing magnetic field intensity, and consequently, the natural frequency grows. In addition, increasing the volume fraction of CNTs causes the stiffness of the structure to increase. The results of this research can be utilized to realize applicable semi-active devices with controllable stiffness.

Parametric study on nonlinear vibration of composite truss core sandwich plate with internal resonance

Nonlinear vibrations of carbon fiber reinforced composite sandwich plate with pyramidal truss core are investigated. The governing equation of motion for the sandwich plate is derived by using a Zig-Zag theory under consideration of geometrically nonlinear. The natural frequencies of sandwich plates with different dimensions are calculated and compared with those obtained from the classic laminated plate theory and Reddy’s third-order shear deformation plate theory. The frequency responses and waveforms of the sandwich plate when 1:3 internal resonance occurs are obtained, and the characteristics of the internal resonance are discussed. The influences of layer number of face sheet, strut radius, core height and inclination angle on the nonlinear responses of the sandwich plate are analyzed. The results demonstrate that the strut radius and inclination angle mainly affect the resonance frequency band of the sandwich plate, and the layer number and core height not only influence the resonance frequency band but also significantly affect the response amplitude.

Free vibration analysis of corrugated-face sheet composite sandwich plates

Free vibrational characteristics of corrugated sandwich plates consisting of two corrugated composite face sheets and a foam filling core were investigated. Natural frequencies of sandwich plates with sinusoidal and trapezoidal corrugation shapes are obtained and compared with that of flat sandwich plates. Three-dimensional (3D) finite element method (FEM) is employed to compare and contrast the natural frequencies. FEM models of the proposed sandwich plates are constructed using ANSYS 12.0 code. The core of the sandwich plates is assumed to be a soft isotropic material which is adhesively bonded to two stiff laminated composite face sheets. The effects of significant parameters such as corrugation shape, boundary conditions, composite layup and thickness ratio of the structure on the natural frequencies and mode shapes of the corrugated sandwich structures are assessed. Comparison of the obtained numerical results with those values available in the literatures demonstrates the accuracy of the proposed models. The numerical results indicate that employing corrugated composite face sheets increase the natural frequencies of sandwich plates, significantly.

Frequency analysis of sandwich plate with active SMA hybrid composite face-sheets and temperature dependent flexible core

In this research, a new finite element model is presented for frequency analysis of a sandwich plate with composite face sheets embedded with pre-strained SMA wires under thermal condition. Mechanical properties of a flexible core are considered temperature dependent. The mixed LW/ESL models in the framework of Carrera’s Unified Formulation are employed in this study in order to increase the accuracy of the results with low computational cost. In this regard, the nonlinear strains are used for obtaining the thermal effects and also the effect of recovery stresses in the SMA wires. The constitutive equation proposed by Brinson is used for modeling the recovery stresses in the SMA wires. In this research, the total stiffness of the structure is categorized to essential and acquired stiffness types and results are more discussed. Results show that as the temperature increases, the natural frequencies of the classic sandwich plate decreases due to the degradation of the core’s properties, while, by using the active SMA wires, the stiffness of the sandwich plate can be improved and therefore has a positive effect on the natural frequencies of the sandwich plate.

Free vibration of functionally graded sandwich plates in thermal environment using a layerwise theory

Abstract In this work, a layerwise finite element formulation is presented for the first time for dynamic analysis of two types of functionally graded material (FGM) sandwich plates with nonlinear temperature variation along the thickness and the FGM having temperature dependent material properties. Natural frequencies of sandwich plates made of FGM in thermal environment are presented using a layerwise theory. Two configurations of sandwich plate, one with homogenous facesheets and functionally graded core and the second with functionally graded facesheets and homogenous core are considered. The material properties of both types of FGM sandwich plates are varied according to Mori–Tanaka (MT) scheme and the rule of mixture (ROM). The layerwise theory used in this work is based on the assumption of the first order shear deformation theory in each layer and the displacement continuity is satisfied at each layer interface. In the present investigation, it is seen that the natural frequencies converge with lesser number of elements and the results are found to be accurate. Natural frequencies are presented for FGM sandwich plates with different geometric and elastic properties, thermal load and boundary conditions.

Natural frequencies of sandwich plate with functionally graded face and homogeneous core

In the present paper, meshless global collocation method based on the thin plate spline radial basis function and nth-order shear deformation theory are used to analyze the free vibration of sandwich plate with functionally graded face and homogeneous core. Meshless global collocation method approximates the solution of governing differential equations using the all nodes in the problem domain. The third-order theory of Reddy can be considered as a special case of the present nth-order theory. Natural frequencies of the sandwich plates with various side-to-thickness ratios, thickness ratio of each layer, boundary conditions and material properties are calculated by the present nth-order theory and meshless global collocation method. The results are compared with the three dimensional Ritz solutions.

Natural frequencies of sandwich plates with FGM core via variable-kinematic 2-D Ritz models

This paper deals with the formulation of advanced two-dimensional Ritz-based models for accurate prediction of natural frequencies of thin and thick sandwich plates with core made of functionally graded material (FGM). The formulation is rather general due to its invariant properties with respect to the underlying plate kinematic theory and the admissible set of Ritz functions. Convergence and accuracy of the method are investigated in this work using an entire family of higher-order layerwise and equivalent single-layer theories, whose corresponding displacement variables are approximated by series of Chebyshev polynomials multiplied by appropriate boundary functions. Results are presented for rectangular sandwich FGM plates with various thickness-to-length ratios and combinations of clamped, free and simply-supported edges.

An accurate higher-order theory and C0 finite element for free vibration analysis of laminated composite and sandwich plates

Abstract At present, it is difficult to accurately predict natural frequencies of sandwich plates with soft core by using the C 0 plate bending elements. Thus, the C 1 plate bending elements have to be employed to predict accurately dynamic response of such structures. This paper proposes an accurate higher-order C 0 theory which is very different from other published higher-order theory satisfying the interlaminar stress continuity, as the first derivative of transverse displacement has been taken out from the in-plane displacement fields of the present theory. Therefore, the C 0 interpolation functions is only required during its finite element implementation. Based on the Hamilton’s principle and Navier’s technique, analytical solutions to the natural frequency analysis of simply-supported laminated plates have been presented. To further extend the ranges of application of the proposed theory, an eight-node C 0 continuous isoparametric element is used to model the proposed theory. Numerical results show the present C 0 finite element can accurately predict the natural frequencies of sandwich plate with soft core, whereas other global higher-order theories are unsuitable for free vibration analysis of such soft-core structures.