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1

Research on the Performance Optimization of Turbulent Self-Noise Suppression and Sound Transmission of Acoustic Windows Made from Functionally Graded Material

Li Bing, Zhou Fu-Lin, Fan Jun, Wang Bin, Tan Liwen

Archives of Acoustics

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2023

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Vol. 48, No. 4

475--495

EN

For a simplified sonar dome model, an optimization method for internal gradients of functionally graded material (FGM) acoustic windows is proposed in this paper. This method can be used to design optimized FGM acoustic windows with better turbulent self-noise suppression and sound transmission performances. A theoretical model of FGM acoustic windows to evaluate the reduction of self-noise caused by the turbulent boundary layer (TBL) pulsating pressure and the sound transmission loss (STL) is derived through the double Fourier transform and the wavenumber frequency spectrum analysis, respectively, based on the transfer matrix idea and the classical elastic theory. The accuracy of the theory is verified by the finite element results of COMSOL Multiphysics. Utilizing the genetic algorithm (GA) and taking the monotonic gradient as the constraint condition, the internal gradient optimization method of FGM acoustic windows obtains the optimization variables in the Bernstein polynomial when the optimization objective is minimized by iterating the optimization variables in the deviation function represented by the Bernstein polynomial that is introduced in the gradient function. The STL, the turbulent self-noise reduction or a weighting function of the STL and turbulent self-noise reduction of FGM acoustic windows is chosen as the optimization objective. The optimization calculation of the sound transmission or turbulent self-noise suppression performances is carried out for the FRP-rubber FGM (FGM with fiber reinforced plastic (FRP) as the substrate material and rubber as the top material) acoustic window. The optimized results show that both the sound transmission and turbulent self-noise suppression performance are effectively improved, which verifies the effectiveness of the optimization method. Finally, the mechanism of the sound transmission and self-noise suppression characteristics before and after optimization are explained and analyzed based on the equivalent model of graded materials. The research results of this paper provide a reference value for the future design of FGM acoustic windows for sonar domes.

2

Free vibration analysis of porous functionally graded piezoelectric microplates resting on an elastic medium subjected to electric voltages

Wu C.-P., Lin E.-L.

Archives of Mechanics

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2022

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Vol. 74, nr 6

463--511

EN

Basing on the consistent couple stress theory (CCST), we develop a unified size-dependent shear deformation theory to analyze the free vibration characteristics of simply supported, porous functionally graded (FG) piezoelectric microplates which resting on the Winkler-Pasternak foundation are subjected to electric voltages. Various CCST-based shear deformation theories can be reproduced by incorporating their corresponding shape functions, which characterize the through-thickness distributions of the shear deformations, into the unified size-dependent theory. The reproduced CCST-based plate theories include the classical plate theory (CPT), the first-order shear deformation plate theory (SDPT), Reddy’s refined SDPT, the sinusoidal SDPT, the exponential SDPT, and the hyperbolic SDPT. The unified size-dependent theory is subsequently used to determine the natural frequencies of simply supported, porous FG piezoelectric microplates and their corresponding vibration mode shapes. The effects of the material length scale parameter, the length-to-thickness ratio, the material-property gradient index, different values of the applied voltages, the porosity parameter, different porosity distribution patterns, the Winkler spring coefficient, and the shear modulus of the surrounding medium on the natural frequencies of the porous FG piezoelectric microplates are examined and appear to be significant.

3

Design and analysis of cementless hip-joint system using functionally graded material

Asiri Saeed

Archive of Mechanical Engineering

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2022

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LXIX, nr 1

129--146

EN

Functionally Graded Materials (FGM) are extensively employed for hip plant component material due to their certain properties in a specific design to achieve the requirements of the hip-joint system. Nevertheless, if there are similar properties, it doesn’t necessarily indicate that the knee plant is efficiently and effectively working. Therefore, it is important to develop an ideal design of functionally graded material femoral components that can be used for a long period. A new ideal design of femoral prosthesis can be introduced using functionally graded fiber polymer (FGFP) which will reduce the stress shielding and the corresponding stresses present over the interface. Herein, modal analysis of the complete hip plant part is carried out, which is the main factor and to date, very few research studies have been found on it. Moreover, this enhances the life of hip replacement, and the modal, harmonic, and fatigue analysis determines the pre-loading failure phenomena due to the vibrational response of the hip. This study deals with the cementless hip plant applying the finite element analysis (FEA) model in which geometry is studied, and the femoral bone model is based in a 3D scan.

4

Finite element formulation and free vibration analyses of rotating functionally graded blades

Karahan Elif Demirsoy, Özdemir Özge

Journal of Theoretical and Applied Mechanics

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2021

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Vol. 59 nr 1

3--15

EN

In this study, free vibration characteristics of functionally graded (FG) blades whose material properties change through the blade thickness are inspected. Finite Element Method (FEM) is used to create blade models and to calculate natural frequencies. The blade formulations are derived for both Euler-Bernoulli and Timoshenko beams to inspect the effect of different parameters on vibration characteristics. For each beam, stiffness and mass matrices are derived from energy expressions. In the solution part, effects of several parameters, i.e. rotational speed, material properties, power law index parameter, different boundary conditions and slenderness ratio are investigated. The calculated results are compared with those in open literature and a very good agreement between them is confirmed, which reveals the correctness and accuracy of the finite element formulation developed in this study. Formulations are carried out in great detail and additionally, the results are displayed in several figures and tables, which can be a significant source of information for authors working in this area.

5

Design of Functionally Graded Composites through Friction Stir Processing

Sai B. V. Hima Sekhar

Journal of Mechanical and Energy Engineering

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2021

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Vol. 5, No 2

95--101

EN

An Investigation was conducted to produce Aluminium based Functionally graded material (FGM) composites by Friction stir processing (FSP). A reinforcement strategy featuring the use of Alumina and TiC reinforcements was investigated, where holes were drilled in an Aluminium plate, filled with reinforcements and stirred using FSP. A mathematical model was formulated for the positioning of holes in such a manner that the composition of the reinforcements varies from maximum to minimum over a given length. Samples were subjected to various numbers of FSP passes from one to three with a 100% overlap and its influence on particle distribution and homogeneity was studied using Scanning electron microscopy (SEM) at cross sections parallel to the tool traverse direction. A progressive gradient in hardness values was observed for the surface composites at all the passes.

6

Thermoelastic analysis of pressurized hollow spherical vessels with arbitrary radial non-homogeneity

Rani Pooja, Singh Kuldip

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 4

192--205

EN

In this study, a general analysis of one dimensional steady-state thermal stresses of a functionally graded hollow spherical vessel with spherical isotropy and spherically transversely isotropy is presented with material properties of arbitrary radial non-homogeneity. The material properties may arbitrarily vary as continuous or piecewise functions. The boundary value problem associated with a thermo-elastic problem is converted to an integral equation. Radial and tangential thermal stress components distribution can be determined numerically by solving the resulting equation. The influence of the gradient variation of the material properties on the thermal stresses is investigated and the numerical results are presented graphically.

7

Thermal stresses due to non-uniform internal heat generation in functionally graded hollow cylinder

Rani P., Singh K., Muwal R.

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 2

186--200

EN

Thermal stresses of a functionally graded hollow thick cylinder due to non-uniform internal heat generation are studied in this paper. Analytical solutions are obtained with radially varying properties by using the theory of elasticity. Thermal stresses distribution for different values of the powers of the module of elasticity and varying power law index of heat generation are studied. The results have been computed numerically and illustrated graphically.

8

Three-dimensional analysis of laminated plates with functionally graded layers by two-dimensional numerical model

Pluciński Piotr, Jaśkowiec Jan

Engineering Transactions

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2020

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Vol. 68, iss. 1

21--45

EN

This work presents a three-dimensional (3D) numerical analysis of multi-layered laminated plates in which selected layers may be made of functionally graded material (FGM), in which the Young’s modulus may change along the thickness as a consequence of a continuous and graded mixture of two materials. For the analysis, the method, known as FEM23, is applied, which uses a two-dimensional (2D) mesh, yet enables obtaining full 3D results for the layered structure. In FEM23, the layered structure may be a combination of thin and thick layers made of materials with significantly different properties. This paper presents two examples comparing the results to other numerical or analytical solutions. The examples confirm the correctness and flexibility of FEM23 for laminated plates with functionally graded layers.

9

Stationary heat conduction in a solid with functionally graded thermal properties

Bagdasaryan Vazgen, Szołucha Jan

Przegląd Naukowy Inżynieria i Kształtowanie Środowiska

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2019

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Vol. 28, No. 4

539--546

EN

In the paper the solutions for stationary heat conduction in a two dimensional composite with functionally graded heat properties were obtained. Numerical solutions for the taken boundary conditions are shown for several types of changes of composite’s thermal conductivity. The solutions were obtained with the use of the finite-difference method.

10

Stress and deformation analysis of clamped functionally graded rotating disks with variable thickness

Thawait Amit K., Sondhi Lakshman, Sanyal Shubhashis, Bhowmick Shubhankar

Mechanics and Mechanical Engineering

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2019

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Vol. 23, nr 1

202--211

EN

The present study reports the linear elastic analysis of variable thickness functionally graded rotating disks. Disk material is graded radially by varying the volume fraction ratios of the constituent components. Three types of distribution laws, namely power law, exponential law and Mori-Tanaka scheme are considered on a concave thickness profile rotating disk, and the resulting deformation and stresses are evaluated for clamped-free boundary condition. The investigation is carried out using element based grading of material properties on the discretized elements. The effect of grading on deformation and stresses is investigated for each type of material distribution law. Further, a comparison is made between different types of distributions. The results obtained show that in a rotating disk, the deformation and stress fields can be controlled by the distribution law and grading parameter n of the volume fraction ratio.

11

Thermal buckling of temperature-dependent functionally graded Timoshenko beams

Chen Wei-Ren, Chen Chun-Sheng, Chang Heng

Archive of Mechanical Engineering

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2019

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Vol. LXVI, nr 4

393--415

EN

Thermal buckling behavior of a functionally graded material (FGM) Timoshenko beam is studied based on the transformed-section method. The material and thermal properties of the FGM beam are assumed to vary across the beam thickness according to a power-law function, a sigmoid function and an exponential function. The results of buckling temperature for the FGM beams with respective temperature-dependent and temperature-independent properties under uniform and non-linear temperature rises are presented. Some results are compared with those in the published literature to verify the accuracy of the present work. The effects of the material distributions, temperature fields, temperature-dependent properties and slenderness ratios on the thermal buckling behaviors of FGM beams are discussed. It is believed that the present model provides engineers with a simple and effective method to study the effects of various parameters of the FGM beam on its thermal buckling behavior.

12

Frictionless contact between a rigid indentor and a transversely isotropic functionally graded layer

Patra R., Barik S. P., Chaudhuri P. K.

International Journal of Applied Mechanics and Engineering

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2018

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Vol. 23, no. 3

655--671

EN

This article is concerned with the study of frictionless contact between a rigid punch and a transversely isotropic functionally graded layer. The rigid punch is assumed to be axially symmetric and is supposed to be pressing the layer by an applied concentrated load. The layer is resting on a rigid base and is assumed to be sufficiently thick in comparison with the amount of indentation by the rigid punch. The graded layer is modeled as a non-homogeneous medium. The relationship between the applied load P and the contact area is obtained by solving the mathematically formulated problem through using the Hankel transform of different order. Numerical results have been presented to assess the effects of functional grading of the medium and the applied load on the stress distribution in the layer as well as on the relationship between the applied load and the area of contact.

13

Fabrication of Al2O3-Ni graded composites by centrifugal casting in an ultracentrifuge

Zygmuntowicz J., Zielant D., Suchecki P., Konopka K., Kaszuwara W.

Composites Theory and Practice

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2018

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R. 18, nr 3

174--179

EN

The work explored the possibility of producing Al2O3-Ni gradient composites using non-absorbent molds in a high-speed centrifuge. As a result of the centrifugal force, the mass was compacted and the solvent was separated from the solid part. The influence of rotational speed and the change in the solid phase content in the slurry on the obtained microstructure of the composites was investigated. The produced composites were characterized on the basis of macroscopic observations of the obtained samples immediately after the casting process (green body) and after the sintering process. To determine the gradient of the metallic phase, the observations were made on cross sections of the samples. Densification of the sinters was determined by the Archimedes method. The obtained results showed that using an appropriate correlation of technological parameters, i.e. rotational speed and solid phase content in the slurry, enables the fabrication of Al2O3-Ni composites with a microstructure gradient by the centrifugal casting method using non-absorbent forms. It was found that with an increase in the solid phase content in the mass, a clear boundary is formed which separates the area containing only ceramic (Al2O3) and metallic (Ni) particles.

PL

W ramach pracy zbadano możliwość wytwarzania kompozytów gradientowych Al2O3-Ni z zastosowaniem form nienasiąkliwych. W tym celu zastosowano wirówkę wysokoobrotową. W wyniku działania siły odśrodkowej nastąpiło zagęszczenie masy poprzez odseparowanie rozpuszczalnika od części stałej. Zbadano wpływ prędkości obrotowej oraz zmianę zawartości fazy stałej w masie lejnej na uzyskaną mikrostrukturę kompozytów. Wytworzone kompozyty scharakteryzowano na podstawie obserwacji makroskopowych uzyskanych próbek bezpośrednio po procesie odlewania, jak również po procesie spiekania. Przeprowadzono obserwacje wzdłuż przekroju poprzecznego próbek w celu określenia gradientu rozmieszczenia fazy metalicznej. Zagęszczenie spieków oceniono poprzez pomiar gęstości metodą Archimedesa. Uzyskane rezultaty pokazały, że zastosowanie odpowiedniej kombinacji parametrów technologicznych, tj. szybkości obrotowej oraz zawartości fazy stałej w masie lejnej, umożliwia wytworzenie metodą odlewania odśrodkowego, przy użyciu form nienasiąkliwych, kompozytów Al2O3-Ni z gradientem mikrostruktury. Stwierdzono, że wraz ze wzrostem zawartości fazy stałej w masie lejnej powstaje wyraźna granica rozdzielająca obszar zawierający cząstki ceramiczne (Al2O3) oraz metaliczne (Ni).

14

Plane receding contact problem for a functionally graded layer supported by two quarter-planes

Çömez İ., Kahya V., Erdöl R.

Archives of Mechanics

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2018

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Vol. 70, nr 6

485--504

EN

In this study, the plane receding contact problem for a functionally graded (FG) layer resting on two quarter-planes is considered by using the theory of linear elasticity. The layer is indented by a rigid cylindrical punch that applies a concentrated force in the normal direction. While the Poisson’s ratio is kept constant, the shear modulus is assumed to vary exponentially through-the-thickness of the layer. It is assumed that the contact at the layer-punch interface and the layer-substrate interface is frictionless, and only the normal tractions can be transmitted along the contact regions. Applying the Fourier integral transform, the plane elasticity equations are converted to a system of two singular integral equations, in which the contact stresses and the contact widths are unknowns. The singular integral equations are solved numerically by Gauss–Jacobi integration formula. Effects of the material inhomogeneity, the distance between quarter-planes and the punch radius on the contact stresses, the contact widths, and the stress intensity factors at the sharp edges are shown. Although the theoretical analysis is formulated with respect to elastic quarter planes, the numerical studies are carried out only for rigid ones.

15

Compressive study of functionally graded plates resting on Winkler–Pasternak foundations under various boundary conditions using hyperbolic shear deformation theory

Zenkour A. M., Radwan A. F.

Archives of Civil and Mechanical Engineering

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2018

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Vol. 18, no. 2

645--658

EN

Equilibrium equations of a functionally graded plate resting on two-parameter elastic foundations are derived using hyperbolic shear deformation theory. This theory takes into account the hyperbolic distribution of transverse shear deformation and satisfies that the corresponding shear stresses equal to zero on upper and lower surfaces of the plate without requiring any shear correction factors. Eight different types of boundary conditions are considered. Governing equations are obtained including the plate-foundation interaction. The present results are compared well with the corresponding available in the literature. Effects of boundary conditions, linear (Winkler) modulus and shear foundation (Pasternak) modulus, gradient index, plate aspect ratio, side-to-thickness ratio on the stresses and deflections are all discussed. It is established that the present model is more accurate than some theories developed previously.

16

Preparation with modeling and theoretical predictions of mechanical properties of functionally graded polyethylene/clay nanocomposites

Yas M. H., Khorramabadi M. K.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 2

583—593

EN

This paper presents preparation with modeling and theoretical predictions of mechanical properties of compatibilized functionally graded and uniform distribution polyethylene/modified montmorillonite nanocomposites manufactured by solution and melt mixing techniques. The morphology is studied by Scanning Electron Microscopy (SEM) and comparisons are made between two techniques. Young’s modulus of nanocomposites for functionally graded and uniform distributions is calculated using a genetic algorithm and is then compared with the results of other theoretical prediction models mentioned in the literature as well as experimental results. It is found that the melt mixing technique is the preferred preparation method, and the results obtained from the theoretical predictions of genetic algorithm procedure are in good agreement with the experimental ones.

17

Boundary element method modyfications for use in some impedance and optical tomography applications

Pańczyk M., Sikora J.

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2017

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T. 7, nr 1

154--160

EN

The article presents two elements associated with the practice of application of the boundary element method. The first is associated with BEM ability to analyze an open boundary objects and application of infinite boundary elements in the area of mammography. The second element is associated with the damped wall investigations. Wall humidity and moisture represents heterogeneous environment (Functionally Graded Materials) which has to be treated in a special way.

PL

Artykuł prezentuje dwa elementy związane z praktyką stosowania metody elementów brzegowych w zagadnieniach mammografii i środowisk niejednorodnych. Pierwszy związany możliwością analizy obszarów nieograniczonych i zastosowaniem tym celu elementów brzegowych nieskończonych w zagadnieniach mammograficznych. Drugi związany jest z badaniami zawilgoceń murów stanowiących z punktu widzenia obliczeń środowisko niejednorodne.

18

Double contact analysis of multilayered elastic structures involving functionally graded materials

Yan J., Mi C.

Archives of Mechanics

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2017

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Vol. 69, nr 3

199--221

EN

This paper analyzes the frictionless double contact problem of a two-layer laminate pressed against a homogeneous half-plane substrate by a rigid punch. The laminate is composed of a homogeneous elastic strip and a functionally graded layer, perfectly bonded along their interface. The mechanical properties of the graded layer are modeled by an exponentially varying shear modulus and constant Poisson’s ratio. Both the governing equations and the boundary conditions of the double contact problem are converted into a pair of singular integral equations by Fourier integral transforms, which are numerically integrated by Chebyshev–Gauss quadrature. The contact pressure and the contact size at both the advancing and the receding contact interface are eventually obtained by an iterative algorithm, developed from the method of steepest descent. Extensive parametric studies suggest that it is possible to control contact stress and contact size by introducing functionally graded materials into multilayered elastic structures.

19

Boundary element method application in wall dampness tomography

Pańczyk M., Sikora J.

Przegląd Elektrotechniczny

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2016

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R. 92, nr 3

96--98

EN

The boundary element method implementation used to find tomographic image of damped wall humidity distribution is presented. Damped wall represents non-homogeneous media where humidity has a spatial distribution that varies with two co-ordinates. Real measurements were taken and function coefficients where found using boundary element method, verified again by finite element method.

PL

Artykuł prezentuje opis matematyczny implementacji środowisk niejednorodnych w metodzie elementów brzegowych zastosowanej do poszukiwania rozkładu zawilgocenia wnętrza muru. Wyniki obliczeń porównane są z realnymi pomiarami zawilgocenia zbudowanego w warunkach laboratoryjnych muru, wykonanymi z użyciem 26 elektrodowego tomografu impedancyjnego.

20

Three-dimensional thermal buckling analysis of functionally graded cylindrical panels using differential quadrature method (DQM)

Ahmadi S. A., Pourshahsavari H.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 1

135--147

EN

Thermal buckling analysis of functionally graded cylindrical panels subjected to various conditions is discussed in this paper. Buckling governing equations are solved using the differential quadrature method. It is assumed that the mechanical properties of the panel are graded through thickness according to a power function of the thickness variable. The panel is assumed to be under the action of three types of thermal loading including uniform temperature rise and variable temperature rise in the axial and radial direction. In the present study, the effects of power law index, panel angle, different thermal load conditions and geometric parameters on the buckling behavior of functionally graded curved panels are studied. The results obtained through the present method are compared to the finite element solutions and the reported results in the literature. A desirable compatibility is concluded.