Uneven Porosity Distributions Research Articles

Vibration analysis of sandwich functionally graded material plate with cut-outs using artificial neural network technique

In the present article, the effect of geometric discontinuities on the vibrational response of porous sandwich functionally graded material (SFGM) plates with double FGM facesheets has been investigated using the artificial neural network (ANN) technique. Generalized governing equations for the SFGM plate have been derived based on nonpolynomial based higher-order shear deformation theory (HSDT). Geometric discontinuities have been incorporated in terms of cut-outs in the SFGM plates. The FGM layers integrate a porosity model, while the core layer is considered a ceramic layer within the SFGM plate structure. Further, a C° continuous isoparametric finite element formulation with a four-noded, isoparametric quadrilateral element with seven degrees of freedom (DOFs) per node has been employed to accomplish the results. The accuracy of the present results has been demonstrated through convergence and validation studies. A comprehensive study has been carried out to investigate the influence of volume fraction index, even and uneven porosity distribution and cut-outs on the frequency parameter of SFGM plates. However, the finite element method (FEM) is computationally challenging. Therefore, the motivation behind adopting ANN technique to develop a predictive model for reasonable accuracy with less computational time. The ANN technique is proposed to predict the NDFP of the SFGM plate using cut-outs under various conditions using numerical simulation datasets. An optimised ANN model has been developed with an architecture of (6–5–10–5–1), exhibits best performance based on mean error value, which accurately predicts the Non-Dimensional Frequency Parameter (NDFP) of the SFGM plate.

Peridynamic differential operator for stress analysis of imperfect functionally graded porous sandwich beams based on refined zigzag theory

This study focuses on the stress analysis of imperfect functionally graded porous (FGP) sandwich beams using the Peridynamic Differential Operator (PDDO) and Refined Zigzag Theory (RZT). Functionally graded materials (FGMs) can be found in diverse engineering applications since they offer smooth transitions in the mechanical properties of distinct materials, unlike traditional composite materials. Micro-voids and porosities may appear inside the FGMs due to technical challenges during the manufacturing process of such materials. Therefore, understanding the stress variations of the FG sandwich beams with porosities/micro-voids, which are called imperfect FGMs, under loads is of vital importance. In order to achieve the porous configuration in the FG structures, the modified rule of mixtures is applied to calculate the effective material properties of FGMs. The RZT is very suitable for stress analysis of laminated composites, especially for thick and moderately thick beams. It contains only four kinematic variables and eliminates the use of the shear correction factors. In this study, the equilibrium equations of the RZT are solved by means of the PDDO for the stress analysis of imperfect FG sandwich beams having uniform and non-uniform porosity distributions. The PDDO transforms the differential equations into their nonlocal form, namely integral form, providing highly accurate approximations of the derivatives. A comprehensive PDDO analysis is performed for the investigation of the influence of the material variation, and even and uneven porosity distributions on the stress variations of the imperfect FG sandwich beams. It is noted that when the FG core exhibits soft material distributions, the effect of porosity is evident. The even type porosity distribution pattern is more influential on the axial displacement and stress variations in comparison with those of the uneven type porosity distribution pattern.

Active vibration control of rotating smart bidirectional FGPTC subjected to internal mechanical shock

This study considers the active vibration control of a sandwich truncated cone, whose intermediate layer is made of bidirectional functionally graded (FG) porous material bonded with integrated piezoelectric actuator and sensor layers on its outer and inner surfaces. The material properties of the bidirectional functionally graded porous truncated cone (FGPTC), with even and uneven porosity distributions along the length and thickness directions, are changed using a power law function. The governing motion equations utilize the two-dimensional (2D) axisymmetric theory of elasticity rather than simple shell theories. The solving of the governing motion equations is accomplished through the utilization of graded finite element and Newmark methods. The study investigates the impact of dimensions, parameters, and porosity types on transient response behavior, including the semi-vertex angle and the ratio of truncated cone length to outer radius. Furthermore, the effects of power index, porosity volume fractions, rotational velocities, and boundary conditions are examined. Active vibration control (AVC) of the piezoelectric FGPTC is achieved by employing a closed-loop control algorithm based on velocity feedback. Several numerical simulations are conducted to evaluate the effectiveness of the proposed active vibration control system in reducing structural vibrations. The results demonstrate significant reductions in vibration amplitudes and improved structural stability achieved through the active control approach.

Nonlinear vibrations analysis of two-directional functionally graded porous cylindrical shells resting on elastic substrates in a thermal environment based on Donnell nonlinear shell theory

The primary objective of this study is to investigate the nonlinear free vibrational characteristics of temperature-dependent two-directional functionally graded porous (TDFGP) cylindrical shells resting on elastic substrates in a thermal environment. To accomplish this, the thermomechanical equations are derived based on the Donnell nonlinear shell theory framework in conjunction with the von Kármán assumption. Two-directional functionally graded porous cylindrical shell models have mechanical properties that can change smoothly and continuously across the length and thickness of the shell. Additionally, it is assumed that the internal porosities in the matrix materials can be dispersed into two independent patterns, either even or uneven porosity distribution. The nonlinearity in free vibration assessed via the nonlinear-to-linear frequency ratio concerning the central deflection amplitude can be gained employing the Galerkin discretization approach and modified Poincare–Lindstedt (P-L) method. The accuracy and effectiveness of the present analytical model are indicated through comparison with existing solutions. Finally, some comprehensive parametric investigations are carried out to gain insight into the impacts of several factors on the nonlinear free vibration characteristics of structures under different conditions. The results of this article demonstrate that parameters such as gradient indices, volume fraction, distribution pattern of porosity, geometric parameters, and ambient temperature rise significantly influence the structure’s nonlinear frequency and free vibration response.

Effect of porosity on the nonlinear free vibrational behavior of two-directional functionally graded porous cone-shaped shells resting on elastic substrates

The present article describes an analytical approach to investigate the nonlinear free vibrational behavior of a two-directional functionally graded porous (TDFGP) cone-shaped shell resting on elastic substrates. A mixture model with the power-law distribution functions is utilized to obtain the TDFGP shell’s mechanical properties. In addition, it is assumed that the internal porosities in the matrix materials can be dispersed into two independent patterns, either even or uneven porosity distribution. The field displacement in the TDFGP shell is approximated using first-order shear deformation theory. Hamilton’s principle and von Karman’s large deformation assumptions give a dynamic model for the TDFGP shell. The Galerkin decomposition method is employed to discretize the governing partial differential equations into time-dependent ordinary differential equations. The harmonic balance method is used to analytically solve the final time-dependent equations and acquire the nonlinear frequency response of the TDFGP shell. Research has been conducted on porosity, gradient indexes, elastic substrates, boundary conditions, and geometric ratios through parametric studies to investigate the outcomes and their applicability to real-world issues.

Finite element based dynamic analysis of a porous exponentially graded shaft system subjected to thermal gradients

Abstract In modern applications, demand for the rotor shafts made of FGM has increased in aerospace, gas turbine and turbo jet engines due to its improved dynamic characteristics at elevated temperatures. The dynamic vibration response of a functionally graded Jeffcott rotor-bearing system with induced porosities has been studied for non-uniform porosity distributions. The functionally graded (FG) shaft’s radial direction exhibits continuous variation in the material qualities. The FG rotor’s cross-sectional material properties have been graded using the exponential law. The temperature gradients have been considered to be varied across the cross-section based on exponential temperature distribution. For the first time, using the FE method, it has been possible to study the impact of induced porosities on the free vibration frequencies and steady-state vibration responses of the functionally graded rotor-bearing system. This has led to the development of a two-node porous functionally graded rotor element with uneven porosity distributions using the Timoshenko beam theory. It has been observed that the free vibration frequencies and the FG rotor-bearing system critical speeds are affected by increased porosity and thermal gradients. The frequency responses demonstrate that as temperature gradient and volume fraction of porosity rise, the FG rotor-bearing system’s critical speeds shift to the left.

Analysis of Stability and Oscillations of Porous Power and Sigmoid Functionally Graded Sandwich Plates by the R-Function Method

In this paper, the R-function method is used for the first time to study the stability and oscillations of porous functionally graded (FG) sandwich plates with a complex geometric shape. It is assumed that the outer layers of the plate are made of functionally graded materials (FGM), and the filler is isotropic, namely ceramic. The differential equations of motion were obtained using the usual first-order shear deformation theory with a given shear coefficient (FSDT). Two models of porosity distribution according to the power (P-law) and sigmoid (S-law) laws were studied. Analytical expressions for calculating the effective mechanical characteristics of FG materials with even and uneven porosity distribution were obtained. The proposed approach takes into account the fact that the subcritical state of the plate can be heterogeneous, and therefore, first of all, the stresses in the middle plane of the plate are determined, and then the eigenvalue problem is solved in order to find the critical load. To determine the critical load and plate frequencies, the Ritz method was used along with the R-function method. The developed algorithms and software are tested on test examples and compared with known results obtained using other methods. A number of problems of stability and oscillations of the FG of porous sandwich plates with a complex geometric shape for various layer stacking schemes, various boundary conditions and laws of porosity distribution have been solved.

Hydraulic Analysis of a Passive Wedge Wire Water Intake Screen for Ichthyofauna Protection

A passive wedge screen, thanks to its many functional and environmental advantages, has recently become a popular type of surface water intake for municipal and industrial purposes. The design solutions proposed in this paper for a passive wedge wire screen intake model and two different deflectors have been experimentally tested under conditions that can be considered as no-flow conditions at the hydraulic flume. There was only a slight flow associated with the operation of the screen, while there was almost no flow in the hydraulic channel itself, such that it would be considered a watercourse. A hydraulic analysis was carried out, including velocity distribution around the screen as well as the determination of head losses with or without deflectors installed inside the screen. Lower inlet and inflow velocities to the surface of the water intake reduce the risk of injury or death to small fish and fry as well as attracting pollutants understood as sediments, debris, and plant remains floating in the river. In order to achieve the lowest possible maximum inlet and inflow velocities at the highest possible intake capacity, it was necessary to equalize the approach velocity distributions. It was shown that by using the proposed deflectors, the approach velocity distributions were equalized and the maximum values of inflow and inlet velocities were reduced. A water intake screen with a deflector with an uneven porosity distribution equalized the approach velocities better than a deflector with equal openings, but the differences were small. Installing the wedge screen model reduced the maximum inlet velocity from exceeding 2 m/s to a value of 0.08 m/s, and after installing deflectors with equal and unequal openings to values of 0.06 m/s and 0.05 m/s, respectively. In addition to laboratory tests, the paper describes the numerical simulations performed in ANSYS Fluent software. The results of the simulations made it possible to obtain a broader study, as well as to compare the velocity values obtained at the measuring points during the laboratory tests.

Analytical modelling of a multifunctional heterogeneous beam-bending analysis

Pores have a crucial role in shaping the features of functionally graded materials. If the distribution of pores is permitted to gradually rise from the outside inwards towards the center, many more features can be incorporated. A shear shape function is used to analyze the bending response of a two-directional functionally graded porous beam (FGPB), which can be considered a multifunctional heterogeneous material while accounting for both even as well as uneven porosity distributions. The power law is adapted to modify the material properties of FGPB through out the length and thickness dimensions. The notion of virtual displacements is applied when establishing equilibrium equations in FGPB. The Navier method is applied to clamped-clamped, clamped-free boundary conditions and simply supported boundary conditions to offer solutions to FGPB. The proposed methodology is supported by the numerical results of functionally graded beams from earlier studies. The dimensionless deflections and stresses under study are affected by gradient exponents, porosities, and aspect ratios.

Free vibration response of rotating pretwisted porous exponential and sigmoid functionally graded conical shells in thermal environment

A finite element method is used to analyze the free vibration of rotating functionally graded (FG) porous conical shell in thermal environment. Exponential and sigmoid laws are used for grading the FG conical shell in the presence of even and uneven porosity distributions. The one-dimensional Fourier heat conduction equation is used to calculate the nonlinear temperature distribution across the thickness of the shell. The parametric studies reveal that the porosity volume fraction has a significant impact on natural frequency. Centrifugal stiffening, which manifests as a geometrical stiffness matrix, causes rotational speed to enhance the natural frequency of the FG shell.

Nonlinear free vibration of bi-directional functionally graded porous plates

Understanding the nonlinear behavior of advanced engineering structures is of great importance in supporting the analysis, design, and manufacturing processes. The primary objective of this paper, therefore, is to focus on exploring the nonlinear free vibrational characteristics of bi-directional functionally graded (FG) plates considering internal pores under various conditions. To accomplish this, we present an approximate numerical model derived based on the framework of NURBS-based isogeometric analysis (IGA), in conjunction with four-variable refined plate theory (RPT) and the von Kármán assumption, to reckon the displacement field. The mechanical properties of bi-directional FG plate models can smoothly and continuously vary along two in-plane directions according to a power law. Additionally, it is assumed that internal porosities in the matrix materials can be dispersed into two independent patterns, either the even or uneven porosity distributions. The nonlinearity in free vibration, assessed by means of the nonlinear-to-linear frequency ratio related to the central deflection amplitude, can be obtained using an iterative scheme with a displacement control strategy. The accuracy and effectiveness of the current numerical model are demonstrated through a comparison with existing solutions. Comprehensive parametric investigations are subsequently carried out to provide insight into the impact of various factors on the nonlinear free vibration characteristics of plate structures under different conditions. The new insights obtained from this research could serve as valuable benchmark outcomes as well as contribute to a more comprehensive understanding of the nonlinear responses in future analysis and design processes.

Mechanical Behavior of 2D FGP Beam with Uneven Porosity Distribution

This study gives the mechanical behavior of 2D functionally graded porous (FGP) beams using the finite element method. The Matlab code with simple Timoshenko beam elements is written to solve 2D FGP beam problems under distributed load. The transverse deflections are plotted along the length to provide mechanical views about this structure in reality.

An improved MITC3 element for vibration response analysis of piezoelectric functionally graded porous plates

The main goal of this paper is to improve the mixed interpolation of tensorial components triangular (MITC3) by using the edge-based smoothed finite element method (ES-FEM), so-called ES-MITC3, for analyzing the vibration of piezoelectric functionally graded porous (p-FGP) plates subjected to dynamic loading. The material properties of the FGP core vary through thickness with uneven porosity distribution. Besides, the linear relationship between the electric potential and the thickness of the piezoelectric sublayer is taken into account. A closed-loop control algorithm is employed to actively control the vibration of p-FGP plates, through feedback from displacement and velocity. The performance of the proposed method is verified through comparative examples. Finally, the authors hope that the present method can be effectively applied to many smart material models in a multiphysics environment and contribute to understanding texture control by piezoelectric materials through numerical results.

Vibration Analysis of Bidirectional Functionally Graded Porous Plates Using MITC3+

The article presents the vibration behavior of bidirectional functionally graded (BDFG) porous plates using the new triangular 3-node element (a cubic bubble function for the interpolation of the rotations to enrich the bending displacements) which is called the MITC3+ element. The BDFG porous plates have material properties varying in two directions with even and uneven porosity distribution. Based on Hamilton’s principle, the motion equations for BDFG plates are derived. Then, some examples are performed to verify the accuracy and reliability of the proposed method. Finally, the new numerical results on the free vibration response of BDFG porous plates are provided.

Nonlinear static analysis of functionally graded porous sandwich plates resting on Kerr foundation

The main purpose of this work is to explore the nonlinear static bending analysis of functionally graded porous sandwich plates with a ceramic core (FSCC) subjected to a transverse uniform load resting on Kerr foundation (KF) using the mixed interpolation of tensorial components for the four-node rectangular element (called MITC4). Porosity appearing in two skin layers is assumed according to the uneven porosity distribution with a porosity factor The advantage of this element is fast convergence, high accuracy and cancels the shear-locking phenomenon. The present study considers the geometrical nonlinearity resulting from mid-plane stretching based on the von Kármán geometrical nonlinearity. The first-order shear deformation theory (FSDT) is employed to approximate the displacement field of the plate due to its simplicity and efficiency. The current formulation’s authenticity is evaluated by comparing it with previously published works. For the first time, the nonlinear bending of FSCC subjected to a transverse uniform load resting on the Kerr foundation is investigated. Furthermore, the influence of input parameters on the nonlinear bending behavior of FSCC is fully provided.

Deflection of FGM sandwich conoidal shell with porous core

The maximum deflection of functionally graded sandwich conoidal (FGSC) shell with porous core is studied in this paper. Even and uneven porosity distribution is considered to investigate the effect of porosity in the core of the FGSC shell. The inclusion of porosity (even or uneven) in the core makes the sandwich shell lighter. The modified power law is used to account the porosity distribution. The governing equations are developed based on improved mathematical model. An isoparametric finite element (FE) having 9 nodes and 63 degrees of freedom have been used. The improved mathematical model is executed in the present FE code. The numerical results in terms of maximum deflections are compared with available results in the literature. A broad parametric study is carried out to check the effect of porosity, volume fraction index and material properties on the maximum deflection of FGSC shell with porous core.

Free vibration analysis of the structural integrity on the porous functionally graded plates using a novel Quasi-3D hyperbolic high order shear deformation theory

In this study, a novel quasi-three dimensional hyperbolic high-order shear deformation theory (quasi-3D HHSDT) is developed for free vibration analysis of porous functionally graded plates (FGPs). There are six unknowns in the current displacement field, and no shear correction factor is required. The mechanical properties are varied continuously through the thickness of porous FG plates using a modified power law function while considering the effect of porosities on the plate’s structural integrity. Two distinct porosity distribution models are considered, including even and uneven porosity distributions. The Navier technique is employed to obtain the closed-form solutions of motion's equations. An exhaustive parametric study is presented to show the influence of the different parameters on the fundamental frequencies.

Hygro-thermo-mechanical vibration analysis of functionally graded porous curved nanobeams resting on elastic foundations

This paper presents an analytical solution using Chebyshev polynomials based on Rayleigh–Ritz method and Navier's solution to analyze the free vibration response of functionally graded porous (FGP) curved nanobeams embedded resting on an elastic medium under hygro-thermo-mechanical load. Applying Hamilton's principle based on the quasi-3D higher-order shear deformation beam theory and the nonlocal elasticity theory, the governing equation of FGP curved nanobeam is derived. Material properties of nanobeam continuously change through the thickness via a power-law distribution and porosity distribution is described by two laws including even porosity distribution and uneven porosity distribution, respectively. The impact of thermal and moisture on structures are assumed to cause tension load in the plane and do not change the material properties. The elastic foundation used in this work is the Winkler–Pasternak type. The accuracy of the proposed method is verified by comparing the obtained numerical results with those of the published works in the literature. In addition, the influence of curvature radius, nonlocal coefficient, porosity coefficient, stiffness of foundation, and boundary conditions on the free vibration of the nanobeam are examined in detail.

Effect of uniform and nonuniform temperature distributions on sound transmission loss of double-walled porous functionally graded magneto-electro-elastic sandwich plates with subsonic external flow

Using the third-order shear deformation theory (TSDT), this research investigates the loss in sound transmission through air-filled rectangular double-walled sandwich smart magneto-electro-elastic (MEE) plates with a porous functionally graded material (PFGM) core layer, in the presence of external mean airflow and subjected to uniform and non-uniform temperature distributions. Multiple temperature profiles are evaluated in order to correctly capture the impact of the temperature rises over the thickness. Based on the power-law model, three different types of uneven porosity distributions are considered for the PFGM core layer. These distributions should change along the in-plane and thickness directions. Hamilton's concept is used to achieve the derivation of vibroacoustic equations as coupled relations. The sound transmission loss (STL) equation is obtained by using a double Fourier series in combination with an analytical method, i.e., the second velocity potential. The produced solution is evaluated in terms of accuracy and precision by comparing it to other accessible data from a previous study. The effects of the initial electric and magnetic potentials, porosity distributions, incidence angles, acoustic cavity depth, and changes in temperature profile on STL are shown by parameter investigations.

Dynamic response of functionally graded porous-core sandwich plates subjected to blast load using ES-MITC3 element

The main objective of this paper is to use the combination of the edge-based smoothed finite element method (ES-FEM) and mixed interpolation of tensorial components triangular (MITC3) element. As a result, the so-called ES-MITC3 element is proposed for the dynamic analysis of sandwich plates with a functionally graded porous (FGP) core subjected to blast load. Sandwich plates include a bottom layer made of homogeneous metal, an all-ceramic top layer and a FGP core layer with uneven porosity distribution. The ES-MITC3 element is created to enhance the accuracy and convergence of the MITC3 element as well as the traditional triangular element. Employing Hamilton’s principle, governing equations of sandwich plates are inferred. Then, solving linear differential equations is conducted by using the Newmark-beta approach. A few studies are conducted to confirm the performance of the current method. Finally, the new numerical results on the vibration characteristic of sandwich plates are provided.