Sandwich Disk Research Articles

2D-GDQM and adaptively tuned deep neural network for frequency analysis of the sandwich disk with honeycomb resting on elastic foundation

The 2D-GDQM (Two-Dimensional Generalized Differential Quadrature Method) and adaptively tuned deep neural network are two computational methods that have been proposed for the frequency analysis of sandwich disks with honeycomb cores. Sandwich disks are commonly used in aerospace and automotive industries due to their lightweight and high strength properties. However, accurately predicting their natural frequencies is crucial for ensuring their structural integrity. The 2D-GDQM is a numerical method that discretizes the equations of motion of the sandwich disk using a grid-based approach. The method has been used to obtain accurate and efficient frequency solutions for various types of sandwich structures. In this study, the 2D-GDQM was applied to analyze the frequency response of the sandwich disk with honeycomb core with first and higher-order deformation theories to model displacement field. Additionally, an adaptively tuned deep neural network was used to predict the natural frequencies of the sandwich disk. This method involves training a deep neural network with a dataset of frequency solutions obtained from the 2D-GDQM simulations. The neural network is then optimized to provide accurate predictions for new cases. The results of this study showed that both the 2D-GDQM and the adaptively tuned deep neural network can provide accurate predictions of the natural frequencies of the sandwich disk with honeycomb core. The 2D-GDQM was found to be more computationally efficient, while the neural network approach can be more flexible and adaptable to new geometries or material properties.

On the vibrations of the Electrorheological sandwich disk with composite face sheets considering pre and post-yield regions

Electrorheological (ER) is a type of material that can change its state from liquid to solid by being under an electrical field, bringing much attention from researchers. So, in this article, the vibration of a three-layered disk made of an ER core and two graphene nanoplatelets reinforced composite (GPLRC) face sheets is carried out. The shear strain and stress of ER layer were obtained in the pre- and post-yield state. First- and third-order shear deformation theories (FSDT and TSDT) are utilized to model the face sheets and core of the structure. By using HDQM – hyperbolic differential quadrature method – the results are acquired. By employing other published studies, the validation investigation is carried out. Lastly, the influence of such parameters as graphene nanoplatelets (GPLs) distribution, foundation parameters, open-angle of the disk, the thickness of different layers, inner in addition to the outer radius of the disk, and GPLs’ weight fraction on the vibrational behavior of the system is investigated.

Computer simulation for stability analysis of the viscoelastic annular plate with reinforced concrete face sheets

This article deals with the frequency analysis of viscoelastic sandwich disk with graphene nano-platelets (GPLs) reinforced viscoelastic concrete (GPLRVC) face sheets and honeycomb core. The honeycomb core is made of aluminum due to its low weight and high stiffness. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the concrete. By employing Hamilton's principle, the governing equations of the structure are derived and solved with the aid of the Generalize Differential Quadrature Method (GDQM). In this paper, viscoelastic properties are modeled according to Kelvin-Voigt viscoelasticity. The deflection as the function of time can be solved by the fourth-order Runge-Kutta numerical method. Afterward, a parametric study is carried out to investigate the effects of the outer to inner radius ratio, hexagonal core angle, thickness to length ratio of the concrete, the weight fraction of GPLs into concrete, and the thickness of honeycomb core to inner radius ratio on the frequency of the viscoelastic sandwich disk with honeycomb core and FGGPLRVC face sheet.

Nonlinear frequency and chaotic motion of the honeycomb higher-order disk with graphene nanoplatelets face sheets subjected to harmonic excitation via two-dimensional analysis

Honeycomb structures are one type of structure that has the geometry of a honeycomb to allow the minimization of the amount of used material to reach minimal material cost and minimal weight. For this issue, in the current analysis, an attempt is made to develop the nonlinear mathematical model for the chaotic and large-amplitude motions of a sandwich disk with graphene nanoplatelet face sheets honeycomb core and subjected to external excitation. Using Hamilton’s principle, higher-order shear deformation theory (HSDT), and the Von-Karman nonlinear theory, the nonlinear governing equation is derived. The generalized differential quadrature method (GDQM) and perturbation approach (PA) are eventually used to develop a precise solution approach. This article’s fundamental and golden results are that for clamped–clamped boundary conditions, the softening of the system in zone 2 is less than zone 1, whereas the instable responses in zone 2 are more than zone 1. Also, for the sandwich disk with clamped–clamped boundary conditions, the system’s dynamic behavior tends to be more harmonious and less chaotic as the fiber’s angle increases. Therefore, increasing the fiber angle reduces the system’s chaos with clamped edges, which is very important for future works.

RETRACTED ARTICLE: Dynamic simulation of moderately thick annular system coupled with shape memory alloy and multi-phase nanocomposite face sheets

The current research work analyzes dynamics of a sandwich disk which is gently thick. The mentioned sandwich structure has honeycomb core, a couple of middle layers having fibers of shape memory alloy (SMA), and a couple of external layers of multi-scaled hybrid nanocomposite (MHC) considering in-plane force. The core in the shape of honeycomb is manufactured of aluminum due to its high stiffness and less density compared with other materials. Applying energy methods called the principle of Hamilton, we obtained governing motion equations of the mentioned structure and solved them using First-order shear-deformation-theory (FSDT), as well as generalized-differential-quadrature-method (GDQM), respectively. To layers’ joint, the compatibility equations have been taken into account. Then, a parametric mathematical manipulation has been conducted to analyze the impacts of fibers of SMA, boundary conditions (BCs), internal loads, honeycomb network angle, ratio of external to internal radiuses, ratio of thickness to length of the honeycomb, weight fraction of CNTs, angle of fibers, ratio of honeycomb to face-sheet thickness on the frequency of the multi-phase sandwich disk. The outcomes derived reveal that for any amount of internal pressure and each BCs, the relation of the honeycomb’s thickness ratios to MHC layer ( $${h}_{H}/{h}_{t}$$ ) and sandwich structure’s frequency is similar to quadratic function. Further results show that the effects of the fibers’ angle on the frequency can be ignored for larger $${h}_{H}/{h}_{t}$$ amounts.

Computer simulation for high-order stability analysis of a multi-layer disk with honeycomb core under residual stress

Structures in honeycomb shapes have the configuration of a honeycomb to minimize material usage and to reach minimal cost of material and optimized weight. Thereby, this paper investigates the vibrations of sandwich disk which has imperfect honeycomb core with face sheets of graphene nano-platelets reinforced composite (GPLRC). The core of honeycomb is manufactured of aluminum based on to its high stiffness and low density. In order to have an efficient material constant for the layers of composite, this paper considers the modified Halpin–Tsai theory and the mixture rule. The structure’s governing equations of motion are extracted and solved using the Hamilton’s principle and generalized differential quadrature method (GDQM), respectively. Then, in order to present the impacts of the patterns of FG, the GPLs’ weight fraction, thickness ratio of FG face sheet, GPLs’ thickness to length ratio, external to internal radius ratio, the honeycomb core’s thickness to internal radius ratio, the compressive and tensile external load on the sandwich disk’s frequency with FG-GPLRC face sheet and honeycomb core under a uniform pressure, a parametric research study has been carried out. The results show that the lowest and highest frequency is for FG-O and FG-X patterns, respectively. Another consequence is that the when GPLs are wider, the frequency is much higher, particularly at the initial lGPL /tGPL

Frequency simulation of viscoelastic multi-phase reinforced fully symmetric systems

Honeycomb structures have the geometry of the lattice network to allow the minimization of the amount of used material to reach minimal material cost and minimal weight. In this regard, this article deals with the frequency analysis of imperfect honeycomb core sandwich disk with multiscale hybrid nanocomposite (MHC) face sheets rested on an elastic foundation. The honeycomb core is made of aluminum due to its low weight and high stiffness. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite layers. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of the generalized differential quadrature method (GDQM). Afterward, a parametric study is done to present the effects of the orientation of fibers ( $$\theta_{{\text{f}}} /\pi$$ ) in the epoxy matrix, Winkler–Pasternak constants ( $$K_{{\text{w}}}$$ and $$K_{{\text{p}}}$$ ), thickness to length ratio of the honeycomb network ( $$t_{{\text{h}}} /l_{{\text{h}}}$$ ), the weight fraction of CNTs, value fraction of carbon fibers, angle of honeycomb networks, and inner to outer radius ratio on the frequency of the sandwich disk. The results show that it is true that the roles of $$K_{{\text{w}}}$$ and $$K_{{\text{p}}}$$ are the same as an enhancement, but the impact of $$K_{{\text{w}}}$$ could be much more considerable than the effect of $$K_{{\text{p}}}$$ on the stability of the structure. Additionally, when the angle of the fibers is close to the horizon, the frequency of the system improves.

On the vibrations of the imperfect sandwich higher-order disk with a lactic core using generalize differential quadrature method

This article presents the frequency responses of a sandwich disk with a lactic core (honeycomb), two middle layers containing SMA fiber, and two outer layers (multi-scale hybrid nanocomposite (MHC)). The honeycomb core is made of aluminum due to its low weight and high stiffness. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite layers. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of the generalized differential quadrature method (GDQM). Compatibility equations are considered for modeling the interface between the layers of the sandwich disk. Afterward, a parametric study is done to present the effects of SMA fiber, boundary conditions, outer to inner radius ratio, honeycomb network angle, thickness to length ratio of the honeycomb, fibers angle, weight fraction of CNTs, honeycomb to face sheet thickness ratio on the frequency of the multi-phase sandwich disk. The results show that employing the honeycomb network as the core of the structure improves the dynamic response of the structure, impressively. Another consequence is that if there are C-C, C-S boundary conditions, by ever-increase in the θh/π, the dynamic response tends to decline.

Influence of in-plane loading on the vibrations of the fully symmetric mechanical systems via dynamic simulation and generalized differential quadrature framework

Honeycomb structures are one type of structure that has the geometry of a honeycomb to allow the minimization of the amount of used material to reach minimal material cost and minimal weight. In this regard, this article deals with the frequency analysis of imperfect honeycomb core sandwich disk with multi-scale hybrid nanocomposite (MHC) face sheets. The honeycomb core is made of aluminum due to its low weight and high stiffness. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite layers. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of the generalized differential quadrature method. Afterward, a parametric study is carried out to investigate the effects of the thickness to length ratio of the honeycomb core, honeycomb core thickness to inner radius ratio, value fraction of carbon fibers, radius ration of the disk, the angle of honeycomb network, the weight fraction of CNTs, and tensile and compressive in-plane force on the frequency of the sandwich disk with honeycomb core and MHC. The results show that the critical fiber angle is $$\theta_{{\text{f}}} /\pi =$$ 0.5 for C–C and C–S boundary conditions. Another consequence is that when the structure is fixed with S–S boundary conditions, for $$p =$$ 500 and $$p = 1000$$ , as well as the critical dimensionless angle for fibers is 0.5, there are two more range for critical fiber angle in which they are $$0.275 \le \theta_{{\text{f}}} /\pi \le 0.375$$ and $$0.23 \le \theta_{{\text{f}}} /\pi \le 0.39$$ , respectively. Additionally, the range of the critical dimensionless angle for fibers increases by increasing the applied load. Some new results related to dynamic behavior of an MHC are also presented, which can serve as benchmark solutions for future investigations.

Analytical solution for magneto-thermo-elastic responses of an annular functionally graded sandwich disk by considering internal heat generation and convective boundary condition

In this paper, an exact solution for stress distribution of a rotating sandwich disk subjected to magnetic, thermal fields, and convection heat transfer with the consideration of internal heat generation is presented. The sandwich disk is composed of three different layers in which the central layer is made of functionally graded material, whereas the inner and outer layers are made from pure metal and ceramic materials, respectively. All mechanical and thermal properties of the central layer are assumed to obey a power-law form in the radial direction with different non-homogeneity constants. Axisymmetric temperature distributions in each layer are obtained by solving Fourier heat conduction equation. By substituting the constitutive equations in equilibrium equation, a second-order differential equation in terms of radial displacement for each layer is derived by considering centrifugal force and Lorentz magnetic force obtained from Maxwell’s relations. Thereafter, the governing equations are analytically solved and radial displacement, radial and circumferential stresses for the current disk are obtained. Numerical simulations reveal the effects of internal heat generation, convection heat transfer, magnetic field, material properties, and angular velocity on the magneto-thermo-elastic response of the functionally graded sandwich disk. Also, a comparison study between metal, functionally graded, ceramic, and functionally graded sandwich disks is performed.

On the magneto-thermo-elastic responses of FG annular sandwich disks

In this article, the magneto-thermo-elastic response of a functionally graded annular sandwich disk is investigated. The present sandwich disk is subjected to non-uniform steady-state thermal load and placed in a magnetic field. The core is made from a metal-ceramic functionally graded material while the inner and outer faces are made from metal and ceramic materials, respectively. The magnetic, thermal and mechanical properties of the functionally graded material are assumed to be temperature independent and continuously vary in the radial direction of the disk. The variation of Young’s modulus, thermal expansion and conductivity coefficients are represented by a novel exponential law distribution through the radial direction of the disk. The governing differential equations are exactly satisfied at every point of the disk. Analytical solutions for the temperature, radial displacement and stresses are derived. Numerical results are presented due to the magneto-thermal bending. The distributions of these results during the radial direction of the sandwich disk are presented graphically. Finally, the significance of gradation of the metal–ceramic components and the geometry of the disk in the magneto-thermo-elastic responses of annular disks is investigated.

Thermoelastic Analysis of an Annular Sandwich Disk with Metal/Ceramic Faces and Functionally Graded Core

Thermoelastic analysis of a functionally graded annular sandwich disk subjected to nonuniform steady-state thermal load is carried out in this paper. The inner and outer faces of the present disk are made from metal and ceramic materials, respectively. While the core is made from a metal-ceramic functionally graded material. Thermal and mechanical properties of the functionally graded material are assumed to be temperature independent and continuously vary in the radial direction of the disk. The variation of Young's modulus, thermal expansion and conductivity coefficients are represented by a novel exponential law distribution through the radial direction of the disk, but Poission's ratio is kept constant. The governing differential equations are exactly satisfied at every point of the disk. Closed form solutions for the temperature and stress fields are derived in terms of an exponential integral and Whittaker's functions. Some results for stress, strain, and displacement components are presented due to the thermal bending. The distribution of these results during the radial direction of the disk are graphically presented and remarking conclusion is made.

Interfacial Fracture Toughness of Synthetic Bone-Cement Interface

Conventionally, the bonding strength of bone-cement interface is obtained by mechanical strength testing which tends to produce large variability between specimens and test methods. In this work, interfacial fracture toughness of synthetic bone-cement interface has been determined using sandwiched Brazilian disk specimens. Experiments were carried out under selected loading angles from 0 to 25 degrees to achieve full loading conditions from mode I to mode II. Solutions for complex stress intensity factors as well as strain energy release rates were obtained for a sandwich disk with a finite interlayer using the finite element method. Phase angles were obtained at a fixed distance to the crack tip. The fracture loads were obtained from the load displacement curves and the values of interfacial fracture toughness were calculated from the fracture loads and the finite element J-integral solutions. The implication of this information on the assessment of fixation in acetabular replacements was discussed in the light of in-vitro fatigue testing of implanted acetabula.

A Method to Measure the Proton Conductivity of LiNaSO4 under Fuel Cell Conditions

A method has been developed for measurement of proton conductivity of hydrogen-reducible ionic conductors under protonic fuel cell conditions in which the reducible electrolyte is sandwiched between layers of a nonreducible proton-conducting electrolyte in a disk. The proton conductivity of under the fuel-cell condition was determined with Y-doped (BCY) as the nonreducible sandwich layers, using conventional methods under hydrogen at high temperature, under which conditions would otherwise be chemically unstable. and BCY had good chemical and mechanical compatibility in the sandwich disk. The major portion of the ionic conductivity of at is due to and ion transport, and proton conductivity ( at to at ) accounts for only 5–10% of total ion conductivity ( at to at ). These data explain the poor performance of hydrocarbon conversion fuel cells using as the electrolyte.

Fracture testing of Brazilian disk sandwich specimens

The reliability of a joint subjected to mechanical and thermal loads during processing and service constitutes a major technical problem. Joints contain flaws. The observed strength of a joint depends upon the location and size of the flaws, as well as the crack path through the joint. The aim of this investigation is to measure the fracture toughness of a crack in an adhesive joint, as well as to observe its path through the bond. Sandwich Brazilian disk specimens made of two aluminum adherends joined by a thin layer of epoxy are employed in the testing. A thin paraffin notch is located within the adhesive layer. Numerical analyses are carried out to calibrate the specimens. It is seen that asymptotic expressions for the energy release rate and phase angle of a sandwich specimen with a thin layer are inappropriate in this investigation. A wide range of mixed modes is attained with this specimen. Values of the critical energy release rate Gc are obtained as a function of the phase angle ψ. A fracture criterion is compared to the results. During testing, all cracks divert from within the layer and grow toward and into the interface. Comparison of crack path direction is made to two theories.

A Study of Viscoelastic Damped Sandwich Disk Vibration.

Vibration analysis of the viscoelastic damped sandwich disk is studied. Analytical results are as follows. (1) Analytical method of natural frequency coupled with loss factor for the sandwich disk is presented. (2) Loss factor of the sandwich disk is the function of parameters which arc elasticity, damping and thickness of the viscoelastic layer. And, maximum loss factor is obtained using suitable value of these parameters. (3) Natural frequencies coupled with loss factor are higher than the case of without loss factor. Especially, this tendency is remarkable at maximum loss factor.