Discrete Singular Convolution Research Articles

Vibration analysis of a sandwich Timoshenko beam reinforced by GOAM/CNT with various boundary conditions using VIM

In the present study, a sandwich beam reinforced by carbon nanotubes (CNTs)/graphene origami auxetic metamaterials (GOAM) and porous cores is studied. Various distributions of CNTs in facesheets and porosity in the core are stated in terms of thickness. The equations of motion for a sandwich beam are derived and solved under various boundary conditions using variational iteration method (VIM), in which, it is a powerful technique with higher convergence with the computational method that gives analytical response to a linear problem. The effect of the types of CNT distributions, porosity coefficient, types of porous cores, porosity parameter, weight fraction and folding degree of GOAM, different geometric dimensions and different B.C.’s on the natural frequency is investigated. The obtained results are compared with the other literature, that there is a good agreement between them. On the other hands, the maximum error percentage of the present work (VIM) with Civalek and Kiracioglu [66] (Discrete singular convolution method) for the first five frequencies is equal to 0.3% according to Table 2, while in Table 3, the maximum error percentage of the present work (VIM) with Yas and Samadi [67] (differential quadrature method) for the first frequency with various boundary conditions and nanocomposite material is equal to 0.22%. In this regard, the present study can be a suitable platform to find the natural frequency and prevent the phenomenon of resonance and increase the life of the structure. Moreover, it is seen that with enhancing of weight fraction of GOAM, frequency increases because increasing the stiffness of structures. The importance of this research is to extract the formulation of sandwich beam structure for GOAM under different boundary conditions and compare the results between them by repeating the changes.

Application of the optimized deep networks in the prediction of the coupled thermoelasticity response of the axially graded composite system subjected to thermal shock loading

This research is done to examine the coupled thermoelastic response of composite axially graded beams. Thermal shock is applied axially to the beam. Three-dimensional elasticity theory is used to generate the governing equations of motion. While the Fourier heat conduction relationship and the Lord–Shulman heat transfer theorem are used to construct the time-varying heat conduction connection. Using the discrete singular convolution approach and the Laplace transform, the time-varying equations of motion are solved at design locations. A modified version of the Dubner and Abate method is used to translate the system response from the Laplace domain to the time domain. The Whale Optimization Algorithm and the optimized deep neural network are employed as a prediction mechanism to estimate the system reaction under various scenarios in the final stage. By comparing the outcomes of the procedures utilized with those found in published resources, the correctness of the approaches was confirmed. Results on the doubly thermoelastic response of axially graded composite beams exposed to thermal shock loading are important and are presented in this work. As applicable results for related industries can be observed that by changing the boundary conditions from SS to CC, the location of maximum normal strain tends to be at the center of the axially graded beam

Mathematical Investigation of the Infection Dynamics of COVID-19 Using the Fractional Differential Quadrature Method

In recent times, the global community has been faced with the unprecedented challenge of the coronavirus disease (COVID-19) pandemic, which has had a profound and enduring impact on both global health and the global economy. The utilization of mathematical modeling has become an essential instrument in the characterization and understanding of the dynamics associated with infectious illnesses. In this study, the utilization of the differential quadrature method (DQM) was employed in order to anticipate the characterization of the dynamics of COVID-19 through a fractional mathematical model. Uniform and non-uniform polynomial differential quadrature methods (PDQMs) and a discrete singular convolution method (DSCDQM) were employed in the examination of the dynamics of COVID-19 in vulnerable, exposed, deceased, asymptomatic, and recovered persons. An analysis was conducted to compare the methodologies used in this study, as well as the modified Euler method, in order to highlight the superior efficiency of the DQM approach in terms of code-execution times. The results demonstrated that the fractional order significantly influenced the outcomes. As the fractional order tended towards unity, the anticipated numbers of vulnerable, exposed, deceased, asymptomatic, and recovered individuals increased. During the initial week of the inquiry, there was a substantial rise in the number of individuals who contracted COVID-19, which was primarily attributed to the disease’s high transmission rate. As a result, there was an increase in the number of individuals who recovered, in tandem with the rise in the number of infected individuals. These results highlight the importance of the fractional order in influencing the dynamics of COVID-19. The utilization of the DQM approach, characterized by its proficient code-execution durations, provided significant insights into the dynamics of COVID-19 among diverse population cohorts and enhanced our comprehension of the evolution of the pandemic. The proposed method was efficient in dealing with ordinary differential equations (ODEs), partial differential equations (PDEs), and fractional differential equations (FDEs), in either linear or nonlinear forms. In addition, the stability of the DQM and its validity were verified during the present study. Moreover, the error analysis showed that DQM has better error percentages in many applications than other relevant techniques.

Buckling analysis of multi-span non-uniform beams with functionally graded graphene-reinforced foams

This paper conducts the buckling analysis of multi-span functionally graded (FG) beams reinforced by three-dimensional graphene foams (3D-GFs) restrained by elastic supports. The graphene foams are considered as graded variation in the thickness direction according to four different porosity distributions. The width and height of the non-uniform beams vary in the longitudinal direction in accordance with the power-law principle, and the multi-span beams consist of two types of optional beams. The governing equations of buckling behavior are derived based on the Timoshenko beam theory and the principle of virtual displacements, and solved by the discrete singular convolution (DSC) method. The purpose of this paper is to obtain the critical buckling load of FG 3D-GFs reinforced beams under the consideration of variable cross-section and multi-span beams with 2–4 spans. The effect of porosity coefficients, slenderness ratio, and spring constants on the buckling characteristic also are studied. The results suggest that the taper ratio of beams and the configuration of multi-span beams lead to remarkable changes in the critical buckling load of beams.

On the supersonic vibrations of the advanced composite quasi-3D hyperbolic refined high-order sector annular/circular structure in thermal environment

Functionally graded materials (FGMs) have been used in many high-tech engineering fields because they could improve material properties. Some well-known applications of these materials are over different geometrical shapes like shells and plates. Multi-directional FGMs have the main role in the improvement of multi-functional materials by introducing modern materials. A detailed study of sector annular/circular disks with different thickness directions has been carried out. In practice, the material properties need to be categorized in other directions as well. Sector annular/circular disks made of multi-dimensional FGM (MD-FGM) are vulnerable to high-temperature gradients and enormous deflections. Using the discrete singular convolution method (DSCM), we investigated asymmetric deformations of MD-FG sector annular/circular disk tolerating thermo-aerodynamics loads. What makes this research unique is using thickness classification for the material properties of the disk while radial and circumferential directions follow an exponential trend. In practical conditions, this assumption would result in a more accurate simulation. Having developed equations based on quasi-3D new refined theory (Q3D-NRT) considering the effect of thickness stretching, we solved the equations based on our conditions. With the aid of COMSOL multi-physics finite element simulation, the results are verified and new recommendations for improving the stability of presented MD-FG sector disks are reported. This research might be helpful for scientists working in the field of thermoelastic theory of disks. Since it is very important to have small and uniform thermal stresses in every direction of the materials, the study’s results could be used as a trustworthy database to determine a material property function.

Dynamic characteristics of non-uniform multi-span functionally graded 3D graphene foams reinforced beams with elastic restraints

This paper investigates the dynamic characteristics of non-uniform multi-span functionally graded (FG) 3D graphene foams (3D-GFs) reinforced beams with elastic boundary conditions. It is assumed that the foams are distributed according to four porosity distributions along the thickness direction and the beams sections varies in height and width along the length with the power-law distribution. Based on Timoshenko beam theory and Hamilton’s principle, the equations of motion for multi-span beams are derived and the discrete singular convolution (DSC) method is adopted to solve them numerically. The present analysis is rigorously validated through direct comparisons against the results by those available in open literatures. A comprehensive parametric study is conducted to study the effects of porosity distribution, slenderness ratio, taper ratio and different combination types of multi-span beams with non-uniform sections. This study provides a new conception of multi-span beam composition, providing designers with choices of beam forms under vibration response.

On exact wave propagation analysis in a beach volleyball ball

Wave propagation and vibration state in the sports balls have important effects on the stability in movement and accuracy of hits. In some sports, similar to football and volleyball, the balls are subjected to continuous strong hits from players. In the current study, the wave propagation in a beach volleyball ball under the effect of temperature change, different material characteristics, different thicknesses, and the total mass is investigated. In this regard, the ball is modeled using a spherical shell structure and a higher-order displacement field is considered. The classical theory of elasticity is employed along with Hamilton’s principle for the spherical shell. The outcome equations with different boundary conditions are solved by engaging the discrete singular convolution method (DSCM). In addition, the finite element method is used to obtain the modal shape and natural frequency. The formulations and solution method are utilized in different steps of convergence examination, validation, and parametric study to acquire a comprehensive insight into the behavior of beach volleyball balls under the effect of the dynamic loading conditions. In specific, we are more interested in the phase velocity of the ball. The results are presented for different temperature changes and geometrical and material properties.

Numerical assessment of the nanocomposite sector annular plates with the aim of promoting their mixed-form thermal shock response

As practical research, this study assesses the resistance of the radially-graded graphene-platelets reinforced (RG-GPLR) nanocomposite annular sector plates against thermal shock. Three-dimensional declaration of the elasticity theory is the base for defining the governing equations of the system. Discrete singular convolution technique (DSCT) is applied as an efficient solution to determine the stress and defection variation of the clamped plate against the instantaneous thermal shock. For the first time, this study considers the effect of thermal shock induced by the radical temperature gradient, heat flux, and the mixed form. Laplace transform combined with the extended Dubner and Abate's technique to find the time history of the system's thermomechanical behavior. The accuracy of the solution is inspected through a comparative analysis between the present and published studies’ results. As a valuable outcome, it is revealed that the fluctuations of the system's response around their ultimate constant values would be damped faster when the applied heat flux is higher.

Efficient discrete singular convolution differential quadrature algorithm for solitary wave solutions for higher dimensions in shallow water waves

In this research, discrete singular convolution, that depends on Regularized Shannon kernel, is used to look for the efficient solution of (4 + 1) dimensional nonlinear Fokas equation. The governing system of nonlinear five-dimensional Fokas equation is transformed into a system of nonlinear ordinary differential equations via discrete singular convolution quadrature technique. Consequently, the 4th order Runge–Kutta technique is employed to solve this system. The validity of this approach is achieved by comparing the obtained numerical solution with the exact solution, where the error is ≤ 1 × 10−5. Moreover, a parametric analysis is presented to examine the influence of the used approach on solitary wave solution. The computed solutions display strength, reliability and efficiency of the implemented techniques that can be effectively work for nonlinear equations in a like manner to linear models. Our treatment in this work works to solve higher dimensional nonlinear problems of physical and numerical features.

Modeling and Solution of Reaction-Diffusion Equations by Using the Quadrature and Singular Convolution Methods.

In the present work, polynomial, discrete singular convolution and sinc quadrature techniques are employed as the new techniques to derive accurate and efficient numerical solutions for the reaction–diffusion equations. Three models, Fitzhugh-Nagumo, Newell–Whitehead–Segel, and tumor growth models, were presented. The equations of three models are reduced to nonlinear ordinary differential equations by using different quadrature schemes. Then, Runge–Kutta fourth-order method is employed to solve nonlinear ordinary differential equations. In addition, the MATLAB program is used to solve these problems. Comparisons between the new methods and the existing ones are included, demonstrating the ease of implementation and efficiency. Also, the calculated results are supported by four various statistical errors. It is found that the rate of error reaches ≤ 10–6 in discrete singular convolution depending on regularized Shannon kernel which is better than others. Further, a parametric analysis is presented to discuss the influence of diffusion and reaction parameters on the solution.

Innovative statistical approach on graphical optimization and closed-form dynamic response of the poroelastic nanocomposite sandwich structure

Present research with the aid of multivariate analysis of variance explores the closed-form dynamics of the poroelastic nanocomposite sandwich plate. Additionally, graphical optimization of the system’s vibration by proper adjusting the involved parameters is provided by employing response surface methodology. p-value and F-value tests are executed to determine the contribution percentage of each parameter on the dynamics of the structure. The nanocomposite face-sheets are made of graphene-platelets reinforced polymer. The main relations governing the dynamics of the initially stressed sandwich system are defined in the background of theory known as linear poroelasticity. Bidirectional format of discrete singular convolution approach (2D-DSCA) is employed in order to determine the design-points’ dynamic performance. Validity of the applied solution procedure is tested through comparison with the outcomes of the first-rate articles. In this research, it is revealed that the graphical optimization is a reliable way to determine the proper adjustment of the parameters for achieving the optimum vibration performance. Moreover, it is observed that the aspect ratio of the plate is the most decisive factor in the free oscillation response of the sandwich plate compared with other factors whose influence are examined in the present article including GPL’s weight-fraction, GPL’s dispersion patterns, in-plane initial stresses, and the poroelasticity coefficient.

RETRACTED: Nonlocal strain/stress gradient vibration of the high-order 2D-FG concrete beam via physics-informed deep neural network

This research introduces physics of neural networks which are able to be trained for the purpose of solving supervised learning duties with considering any provided physics laws explained by the dynamic problem. In this research, we report developments in the concept of solving two key types of problems: data-driven discovery and solution of vibrations. Using the method of variation, the governing equations pertaining two-directional functionally graded nanobeams have been obtained by utilizing the discrete singular convolution integrated method (DSC-IM). A nonlocal strain/stress gradient theory (NS/SGT) is initiated in this study, which is a sized dependent theory. Made of concrete material the material is varied in both transverse and axial directions. The role of FG power index in both directions, length/width ratio, and size-dependent factor, then, has been investigated on the frequency of studied nanobeams by performing a parametric study. Comparing the results with already reported findings elsewhere, validation of the present approach is verified. The findings of the present study would be helpful for the design of nanostructures made of concretes in Standard texts or handbooks.

Simulation of multi – field coupling damping characteristics of magnetorheological damper in ring system by artificial intelligence method

A new kind of smart material called Magnetorheological (MR) has attracted a lot of attention among designers due to its mechanical properties that can alter in a controlled fashion by an external magnetic field. Regarding this issue, in the current work, for the first attempt, the dynamic stability of a sandwich shell made of MR core and graphene nanoplatelets reinforced composite (GPLRC) face sheets is presented. Using the role of the mixture and modified Halpin–Tsai model, the effective material properties of GPLRC face sheets are presented. Via Hamilton’s principle and linear viscoelastic theory, the governing equations of the current sandwich structure are developed. Also, compatibility equations for accurate modeling of the sandwich structure are presented. The discrete singular convolution integration method (DSC-IM) for prediction of nth-order derivatives of a sufficiently smooth function via weighted linear sum function of the amounts at each separated point in the throughout allowable input range is presented. For more verification, a deep neural network as an artificial intelligence method is presented. Finally, the results show that GPL’s weight fraction, viscoelastic foundation, the geometry of GPLs, and geometry of the structure have an important role in dynamic stability and modal loss factor parameter of sandwich shells.

On the dynamics of the axisymmetric circular system via an exact continuum elasticity theory and discrete singular convolution method

The vibration for the circular sector plates made of reinforced composite with carbon nanotubes based on a 3D-poroflexibility theory is presented in this research. A discrete singular convolution integration method (DSC-IM) is used. By using the renowned rule of mixtures, the effective mechanical properties are related to reinforced composites. The present results, formulations, and solution procedures are verified. The novelty of this work considers the effects of 3D- elasticity theory’s initial radial and environmental stresses and various boundary conditions via DSC-IM. Consequently, the outcomes demonstrate that in-plane boundary conditions, CNT’s volume fraction, Biot’s coefficient, and radial and circumferential initial stresses greatly impact the vibration frequency of the circular sector plates. Also, the effect of initial circumferential stress is more prominent than radial ones in determining the vibration frequency. Also, in higher open-angle, the impact of volume fraction related to CNTs on the vibrational frequency of the system is more apparent.

An Optimal Fourth-Order Finite Difference Scheme for the Helmholtz Equation Based on the Technique of Matched Interface Boundary

In this paper, a new optimal fourth-order 21-point finite difference scheme is proposed to solve the 2D Helmholtz equation numerically, with the technique of matched interface boundary (MIB) utilized to treat boundary problems. For the approximation of Laplacian, two sets of fourth-order difference schemes are derived firstly based on the Taylor formula, with a total of 21 grid points involved. Then, a weighted combination of the two schemes is employed in order to reduce the numerical dispersion, and the weights are determined by minimizing the dispersion. Similarly, for the discretization of the zeroth-order derivative term, a weighted average of all the 21 points is implemented to obtain the fourth-order accuracy. The new scheme is noncompact; hence, it encounters great difficulties in dealing with the boundary conditions, which is crucial to the order of convergence. To tackle this issue, the matched interface boundary (MIB) method is employed and developed, which is originally used to accommodate free edges in the discrete singular convolution analysis. Convergence analysis and dispersion analysis are performed. Numerical examples are given for various boundary conditions, which show that new scheme delivers a fourth order of accuracy and is efficient in reducing the numerical dispersion as well.

A computational three-dimensional elasticity theory for bending and frequency analysis of the axisymmetric circular/annular plates via machine learning and discrete singular convolution integration methods

The present study deals with the frequency and bending behavior of annular/circular nanocomposite plates. The nanocomposite is made of three-phase materials of graphene oxide (nanoscale) and carbon fibers (microscale), and epoxy matrix (macro-scale) in multiple layers of different orientations. The governing equation extracted to investigate the multiscale hybrid laminated nanocomposite reinforced (MHLNR) is a three-dimensional elasticity theory. Furthermore, the whole structure is on the elastic substrate, which takes into account the horizontal forces in the calculations. The displacement compatibility and equilibrium condition are considered in the interlayers of the three, five, and seven layers of the composite structure. The bulk material properties at each layer are evaluated utilizing fiber micromechanics and Halpin–Tsai equations. The discrete singular convolution method is employed to transform the equations and solve equations. The obtained results are further verified using several references in this field. In addition, an adaptively tuned deep neural network model is designed based on the data of the current study to predict the results. Finally, a comprehensive parametric study is carried out to demonstrate the influences of different parameters on the internal stress field and frequency responses of the current sandwich structure.

Computer simulation as an aid to predict fundamental frequency of a sandwich system via discrete singular convolution method

Present article is the first attempt to analyze the vibration behavior of the composite sandwich cylindrical panels based on the integration of a statistical approaches with numerical solver of differential equations. The motion equations of the structure with functionally graded graphene-platelets reinforced composite (FG-GPLRC) face-sheets imbedded in linear and torsional spring-simulated elastic substrate and subjected to multi-orientational initial stresses are formulated based upon three-dimensional poroelasticity theory. Bi-directional discrete singular convolution method (DSCM) is implemented to find the natural frequency of the mentioned system at design-points. Then, the response surface method is utilized to acquire the closed form of the natural frequency and predict the vibration response of the system according to the reduced third-order polynomial functions. The modified format of Halpin-Tsai micromechanics is employed in order to approximate the elastic properties of the structure. The veracity of the solving procedure is verified by comparing its outcomes with those recorded by the high-quality literature. The results reveal that the span-angle of the panel plays the most important role in the free vibration response of the system compared with the other parameters whose effects are studied in this article. Additionally, it is concluded that reinforcing the face-layers of the sandwich panel by graphene-platelets (GPL) is the more effective way to increase the stiffness of the sandwich structure compared with the case of reinforcing the core section.

Sinc and discrete singular convolution for analysis of three‐layer composite of perovskite solar cell

This work studies the performance of composite solar cell model consisting of perovskite absorber layer (CH3NH3PbI3), electron transport layer (TiO2 or PCBM), and hole transport layer (Spiro-OMeTAD or CuI) via sinc and discrete singular convolution quadrature techniques. The governing equations for hole transport layer, electron transport layer, and absorber layer (perovskite) are derived depending on the equations of continuity and Poisson. Different quadrature and block-marching techniques convert these equations to the nonlinear algebraic system. Then, we apply the iterative method to solve the problem of nonlinearity. For each scheme, a programmed code is designed to get a numerical solution for composite perovskite solar cells by MATLAB. To ensure the efficiency and convergence of these schemes, the obtained results match with previous experiments and other numerical schemes. From these comparisons, the discrete singular convolution quadrature technique gives high accuracy, speed of convergence, and more reliability than other methods with error up to 10−8. Consequently, the effects of different thicknesses, mobilities, band gaps, temperatures, absorption factors, wavelengths, and doping concentrations on current density, open-circuit voltage, and efficiency of solar cells are investigated in a full parametric study. Hence, the obtained effects of the current schemes increase the efficiency of perovskite solar cells. Novelty Statement Sinc and discrete singular convolution quadrature techniques are applied to reach high performance for perovskite absorber layer sandwiched between electron transport layer (ETL) and hole transport layer (HTL). The study demonstrates that the discrete singular convolution quadrature method gives high efficiency and accurate results at different parameters. It is obtained that the power conversion efficiency is approximately 35% at specific parameters.

Discrete singular convolution method for modelling of waveguide interaction of beam-type structures with impedance boundaries

Discrete Singular Convolution (DSC) is an accurate local/global mathematical method for the vibration and acoustic analysis of individual continuous structures. In recent years, successful applications of the DSC method for handling connected structures have been performed. However, the studies are very limited and applicable only for common basic boundary conditions such as the pinned, clamped or free boundaries. This study extends the applicability of the DSC method to waveguide interactions of connected structures with the mechanical impedance boundaries. For this purpose, vibration analyses of structures composed of beams forming I-, L- and T-type structures are performed via the DSC. Taylor series expansion is utilized to implement the mechanical impedance boundary conditions. The structural models support the longitudinal and bending waveguides and related interactions. Natural frequencies and vibration displacement responses to a point force excitation are predicted via the proposed methodology. The results are validated by finite element and/or analytical solutions. It has been shown that the DSC method can be reliably applied for structures exhibiting waveguide interactions with impedance boundaries.

Bending analysis of FG-GPLRC axisymmetric circular/annular sector plates by considering elastic foundation and horizontal friction force using 3D-poroelasticity theory

Composite structures encounter different types of imperfections and defects during the installation, working environment, and fabrication process. In the present research, a 3D-poroflexibility theory has been presented to study the bending responses of the functionally graded graphene nanoplatelets reinforced composite (FG-GPLRC) axisymmetric circular/annular sector plates on the elastic substrate. For modeling elastic substrate, horizontal friction force and the elastic foundation with five elastic parameters have been formulated. For obtaining the exact displacement and stress/strain responses of the current structure, a discrete singular convolution integration method (DSC-IM) has been utilized. Also, the outputs of the current research have been verified with the results of COMSOL Multi-physics software. Consequently, the outcomes demonstrate that GPL’s weight fraction, in-plane boundary condition, radial and circumferential initially stresses, and Biot's coefficient have a remarkable impact on the bending responses of the circular/annular sector plates. Also, when the normal compressive stress increases, the negative effect from normal tensile stress on the bending characteristics of the structures is more remarkable than the positive effect from normal compressive stress. Also, the effect of GPL’s weight fraction on the stress and displacement fields is more considerable at the higher value of the opening angle of the current composite structure.