Porous Rectangular Plates Research Articles

Exact solution for thermal vibration of multi-directional functionally graded porous plates submerged in fluid medium

An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study. Mechanical properties of MFG porous plates change according to the length, width, and thickness directions for various materials and the porosity distribution which can be widely applied in many fields of engineering and defence technology. Especially, new porous rules that depend on spatial coordinates and grading indexes are proposed in the present work. Applying Hamilton’s principle and the refined higher-order shear deformation plate theory, the governing equation of motion of an MFG porous rectangular plate in a fluid medium (the fluid-plate system) is obtained. The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to compute the extra mass. The Galerkin-Vlasov solution is used to solve and give natural frequencies of MFG porous plates with various boundary conditions in a fluid medium. The validity and reliability of the suggested method are confirmed by comparing numerical results of the present work with those from available works in the literature. The effects of different parameters on the thermal vibration response of MFG porous rectangular plates are studied in detail. These findings demonstrate that the behavior of the structure within a liquid medium differs significantly from that within a vacuum medium. Thereby, they offer appropriate operational approaches for the structure when employed in various mediums.

Analysis of free vibration characteristics of porous rectangular plates with variable thickness

Analysis of free vibration characteristics of porous rectangular plates with variable thickness

A unified Jacobi–Ritz approach for vibration analysis of functionally graded porous rectangular plate with arbitrary boundary conditions based on a higher-order shear deformation theory

In this paper, based on the higher-order shear deformation theory (HSDT) variational equation, a unified solution for the transient state vibration problem of functionally graded porous (FGP) rectangular plates are proposed using the combination of Jacobi–Ritz method and multi-segment strategy. Using the artificial spring technique makes a FGP rectangular plate can be separated into several segments, which is proved to be helpful to improve the calculation accuracy of natural frequency. Some common boundary conditions are applied to the mode including classical boundary conditions and elastic boundary conditions. Three common types of porous distributions are considered which contain uneven symmetrical, uneven asymmetric and evenly distributions. Through the study of truncated numbers and continuous conditional parameters, it is found that the results have evident convergence. Moreover, the accuracy of this method is proved by comparison. On this premise, the effect of different parameters on the free vibration and pulsating forced vibration of FGP rectangular plates are briefly studied.

Three-Dimensional Buckling Analysis of Functionally Graded Saturated Porous Rectangular Plates under Combined Loading Conditions

The present work studies the buckling behavior of functionally graded (FG) porous rectangular plates subjected to different loading conditions. Three different porosity distributions are assumed throughout the thickness, namely, a nonlinear symmetric, a nonlinear asymmetric and a uniform distribution. A novel approach is proposed here based on a combination of the generalized differential quadrature (GDQ) method and finite elements (FEs), labeled here as the FE-GDQ method, while assuming a Biot’s constitutive law in lieu of the classical elasticity relations. A parametric study is performed systematically to study the sensitivity of the buckling response of porous structures, to different input parameters, such as the aspect ratio, porosity and Skempton coefficients, along with different boundary conditions (BCs) and porosity distributions, with promising and useful conclusions for design purposes of many engineering structural porous members.

Analysis on free vibration and critical buckling load of a FGM porous rectangular plate

The properties of functionally gradient materials (FGM) are closely related to porosity, which has effect on FGM's elastic modulus, Poisson's ratio, density, etc. Based on the classical theory of thin plates and Hamilton principle, the mathematical model of free vibration and buckling of FGM porous rectangular plates with compression on four sides is established. Then the dimensionless form of the governing differential equation is also obtained. The dimensionless governing differential equation and its boundary conditions are transformed by differential transformation method (DTM). After iterative convergence, the dimensionless natural frequencies and critical buckling loads of the FGM porous rectangular plate are obtained. The problem is reduced to the free vibration of FGM rectangular plate with zero porosity and compared with its exact solution. It is found that DTM gives high accuracy result. The validity of the method is verified in solving the free vibration and buckling problems of the porous FGM rectangular plates with compression on four sides. The results show that the elastic modulus of FGM porous rectangular plate decreases with the increase of gradient index and porosity. Furthermore, the effects of gradient index and porosity on dimensionless natural frequencies and critical buckling loads are further analyzed under different boundary conditions with constant aspect ratio, and the effects of aspect ratio and load on dimensionless natural frequencies under different boundary conditions.

Large deflection analysis of functionally graded saturated porous rectangular plates on nonlinear elastic foundation via GDQM

In the current study, large deflection analysis of a functionally graded saturated porous (FGSP) rectangular plate subjected to transverse loading which is located on a nonlinear three-parameter elastic foundation is provided. The constitutive law for the porous materials is written based on Biot's model which considers the effect of fluids within the pores. The mechanical properties of the plate are changed through its thickness according to different functions which are called porosity distributions. The shear deformation effects are taken into account, accordingly, the first-order shear deformation theory (FSDT) is used to describe the displacement components of the plate. Employing the Minimum total potential energy principle and calculus of variation, the governing equations, and associated boundary conditions are extracted. A generalized differential quadrature method (GDQM) is used to solve them for various boundary conditions. The results for the simpler state are validated with the previously published works and then the effects of different parameters on the deflection of the plate are investigated. It is seen increasing the porosity and Skempton coefficient, enhances and reduces the deflection of the structure, respectively. The results of this study may help to design and manufacture more reliable engineering structures that are exposed to loads.

Dynamic response analysis of fluid-saturated porous rectangular plates

Abstract Based on Biot’s model for saturated porous media, the governing equation of fluid-saturated porous rectangular plates is presented, in which the compressibility of solid particles and fluid and the viscosity of pore fluid is taken into account. A series solution is given for simply-supported fluid-saturated porous plates. The accuracy of the solution is validated by degenerating the fluid-saturated porous rectangular plates into single-phase solid rectangular plates. As a numerical example, the free vibration characteristic and the dynamic response under harmonic loads are analysed. The influence of surface infiltration conditions, porosity, pore fluid permeability coefficient and loading frequency on the free vibration frequency is discussed.

Shear deformation theories for elastic buckling of fluid-infiltrated porous plates: An analytical approach

In this paper, Reddy’s higher-order and Mindlin’s first-order plate theories are used for buckling analysis of porous rectangular plates subjected to various types of mechanical loading. The condition of the internal pores is considered to be either free of or saturated by fluid. Biot’s theory of poroelasticity is thereby employed to model the behaviour of fluid. Distribution of pores is assumed to vary through the thickness according to an asymmetric distribution. For each displacement field considered, five highly coupled partial differential equations are derived by means of variational principle. These systems of equations are first decoupled through an efficient method, and then solved analytically for Levy-type boundary conditions. Accuracy of the approach is examined by comparing the obtained results with those available in literature. Eventually, comprehensive parametric studies are provided to investigate the effects of geometrical parameters, boundary conditions, loading conditions, porosity coefficient and pore fluid compressibility on the buckling response of the system. The results suggest that a structure with higher equivalent rigidity is met, when its corresponding internal pores are saturated by fluid. The results of the current work can be considered as a benchmark for future studies.

Vibration analysis of FG porous rectangular plates reinforced by graphene platelets

The aim of this study is to investigate free vibration of functionally graded porous nanocomposite rectangular plates where the internal pores and graphene platelets (GPLs) are distributed in the matrix either uniformly or non-uniformly according to three different patterns. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. The GPL-reinforced plate is modeled using a semi-analytic approach composed of generalized differential quadrature method (GDQM) and series solution adopted to solve the equations of motion. The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and those reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. New results reveal the importance of porosity coefficient, porosity distribution, graphene platelets (GPLs) distribution, geometrical and boundary conditions on vibration behavior of porous nanocomposite plates. It is observed that the maximum vibration frequency obtained in the case of symmetric porosity and GPL distribution, while the minimum vibration frequency is obtained using uniform porosity distribution.

Free vibrations of functionally graded porous rectangular plate with uniform elastic boundary conditions

In this paper, the free vibrations of functionally graded porous (FGP) rectangular plate with uniform elastic boundary conditions is investigated by means of an improved Fourier series method (IFSM). It is assumed that the distributions of porosity are uniform or non-uniformly along a certain direction and three types of the porosity distribution are considered, among which material property of two non-uniform porous distributions was expressed as the simple cosine. The size of the pore in a rectangular plate is determined by the porosity coefficients. Using the first-order shear deformation theory(FSDT), the energy expression of FGP rectangular plate is created. In order to obtain the admissible function of displacement for functionally graded porous rectangular plate, the IFSM is employed. Then, the Rayleigh-Ritz method is used to solve coefficients in the Fourier series which determine natural frequencies and modal shapes. Convergence and comparative research are performed to prove the convergence, reliability and accuracy of the current method. On this foundation, some new results covering the influence of the geometrical parameters subject to classical and elastic boundary condition are presented, and the parametric studies are also investigated in detail, which can provide a reference for future research by other researchers.

Three-dimensional exact solution for vibration analysis of thick functionally graded porous (FGP) rectangular plates with arbitrary boundary conditions

In this paper, a novel three-dimensional exact solution is performed for vibration analysis of thick functionally graded porous rectangular plates subject to arbitrary boundary conditions. The theoretical model is based on the three-dimensional elastic theory. Three kinds of porosity distributions including even, uneven and the logarithmic-uneven are performed. Non consideration boundary conditions, all displacements of the rectangular plate are unified expanded as a improve Fourier series, which consists of standard three-dimensional (3-D) Fourier cosine series supplemented with closed-form auxiliary functions introduced to eliminate all the relevant discontinuities with the displacements and its derivatives at the edges. As the displacement field is sufficiently smooth in the entire solution domain, the exact solution of the energy function of the plate is obtained through the Rayleigh Ritz process. The numerical examples are given to verify the accuracy and reliability of the present method, in which both the present results and those reported in the literature are provided. Besides, several numerous new results for thick FGP plates with elastic boundary conditions are also presented.

Size-dependent vibration analysis of a three-layered porous rectangular nano plate with piezo-electromagnetic face sheets subjected to pre loads based on SSDT

ABSTRACTIn the present research vibration of a porous rectangular plate which is located between two piezo-electromagnetic layers based on two variables sinusoidal shear deformation plate theory and according to nonlocal theory is investigated. The plate is resting on Winkler–Pasternak foundation and was subjected to pre loads. The motion equations have been obtained using Hamilton principle and are solved using analytical Navier's solution method. The effects of porosity coefficient, pores distribution, nonlocal parameter, pre load values, foundation constants and geometric size of the plate have been discussed in details. The results can be used to design more efficient sensors and actuators.

Combined effect of viscosity variation on rough porous rectangular plates with magneto hydrodynamic effect

The squeezing action between rough porous parallel rectangular plates under the effect of magneto hydrodynamic force and viscosity variation effect is considered in this paper. The modified Reynolds equation is derived . The load carrying capacity of the plate thus derived is found to increase with increase in the magnetic, roughness and viscosity variation parameter.

On the effect of coupled solid-fluid deformation on natural frequencies of fluid saturated porous plates

Abstract This paper is concerned with the effect of deformation coupling between solid and fluid on the free vibration characteristics of isotropic rigid porous rectangular plates under undrained condition. Mindlin plate theory is employed to model the moderately thick porous plate. The problem addressed is formulated by using Hamilton's principle, which leads to a set of partial differential equations dealing with frequency response of the plate. The governing equations of motion are solved analytically for Levy-type porous plates by introducing some auxiliary functions. The fluid viscosity is assumed to be very low so that it cannot cause energy dissipation in system. Numerical results are obtained in non-dimensional form. The accuracy of the solution is confirmed by making some comparisons of the obtained frequencies with those available in literature. It is found that the effect of coupled solid-fluid deformation cannot be neglected when the Biot-Willis constants are considerable compared to mechanical properties of solid skeleton of the plate. It is also observed that the plate's effective stiffness increases as fluid is trapped in pore network of the porous medium.

Rectangular ZnO porous nano-plate assembly with excellent acetone sensing performance and catalytic activity

An assembled porous rectangular single crystalline ZnO plate with superior acetone sensing performance and catalytic activity is presented.

Magnetohydrodynamic (MHD) squeeze film characteristics between finite porous parallel rectangular plates with surface roughness

Purpose – The purpose of this paper is to consider magnetohydrodynamic (MHD) squeeze film characteristics between finite porous parallel rectangular plates with surface roughness. Design/methodology/approach – Based upon the MHD theory, this paper analyzes the surface roughness effect squeeze film characteristics between finite porous parallel rectangular plates lubricated with an electrically conducting fluid in the presence of a transverse magnetic field. Findings – It is found that the magnetic field effects characterized by the Hartmann number produce an increased value of the load carrying capacity and the response time as compared to the classical Newtonian lubricant case. The modified averaged stochastic Reynolds equation governing the squeeze film pressure is derived. Research limitations/implications – The present study has considered both Newtonian fluids and non-Newtonian liquids. Practical implications – The work represents a very useful source of information for researchers on the subject of MHD squeeze film with finite porous parallel rectangular plates lubricated with an electrically conducting fluid. Originality/value – This paper is relatively original and illustrates the squeeze film characteristics between finite porous parallel rectangular plates with MHD effects.

A Study on the Performance of Hydromagnetic Squeeze Film between Anisotropic Porous Rectangular Plates with Couplestress Fluids

A Study on the Performance of Hydromagnetic Squeeze Film between Anisotropic Porous Rectangular Plates with Couplestress Fluids

Numerical Simulation of Drying of a Saturated Deformable Porous Media by the Lattice Boltzmann Method

A numerical study is reported here to investigate the drying of saturated deformable porous rectangular plate based on the Darcy–Brinkman extended model. All walls of the plate are maintained to a convective heat flux as well as the top and bottom faces are also subjected to a mass flux. The model for the energy transport is based on the local thermodynamic equilibrium between the fluid and the solid phases. The lattice Boltzmann method is used for solving the governing differential equations system. A comprehensive analysis of the influence of the Poisson’s coefficient, the Young’s modulus and the permeability on macroscopic fields is investigated throughout this work.

Numerical Solution of the MHD Reynolds Equation for Squeeze-Film Lubrication between Porous and Rough Rectangular Plates

The present theoretical study investigates the effects of surface roughness and couple-stress fluid between two rectangular plates, of which an upper rough plate has a roughness structure and the lower plate has a porous material in the presence of transverse magnetic field. The lubricant in the gap is taken to be a viscous, incompressible, and electrically conducting couple-stress fluid. This gap is separated by a film thickness H which is made up of nominal smooth part and rough part. The modified Reynolds equation in the film region is derived for one-dimensional longitudinal roughness structure and solved numerically using multigrid method. The numerical results for various physical parameters are discussed in terms of pressure distribution, load capacity, and squeeze film time of the bearing surfaces. Our results show that, the pressure distribution, load capacity and squeeze film time are predominant for larger values of Hartman number and roughness parameter, and for smaller values of couple-stress parameters when compared to their corresponding classical cases.

Numerical Study of Surface Roughness and Magnetic Field between Rough and Porous Rectangular Plates

This paper theoretically examines the combined effects of surface roughness and magnetic field between two rectangular parallel plates of which the upper plate has roughness structure and the lower plate has porous material in the presence of transverse magnetic field. The lubricating fluid in the film region is assumed to be Newtonian fluid (linearly viscous and incompressible fluid). This model consists of mathematical formulation of the problem with appropriate boundary conditions and solution numerically by finite difference based multigrid method. The generalized average modified Reynolds equation is derived for longitudinal roughness using Christensen’s stochastic theory which assumes that the height of the roughness asperity is of the same order as the mean separation between the plates. We obtain the bearing characteristics such as pressure distribution and load carrying capacity for various values of roughness, Hartmann number, and permeability parameters. It is observed that the pressure distribution and load carrying capacity were found to be more pronounced for increasing values of roughness parameter and Hartmann number; whereas these are found to be decreasing for increasing permeability compared to their corresponding classical cases. The physical reasons for these characters are discussed in detail.