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1

Mechanics of moving contacts involving functionally graded multiferroics

Toktas S. E., Dag S.

Archives of Mechanics

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2023

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Vol. 75, nr 4

431--468

EN

This article introduces solution procedures for moving contacts involving functionally graded multiferroic coatings. A moving rigid punch of a flat or a triangular profile is assumed to be in contact with a multi-layer medium comprising magneto-electro-elastic coating layers, elastic interlayers, and an elastic substrate, that is modelled as a half-plane. The formulation is based on wave equations of plane elastodynamics and Maxwell’s equations. Applying Fourier and Galilean transformations, a singular integral equation of the second kind is derived for each of the flat and triangular punch problems. An expansion-collocation technique utilizing Jacobi polynomials is developed to numerically solve the integral equations. Proposed procedures are verified through comparisons to the results available in the literature. Parametric analyses carried out considering functionally graded magneto-electro-elastic coatings demonstrate the effects of the property variation profile, punch speed, and coating thickness on contact stresses, electric displacement, and magnetic induction. The methods presented could be of use in analysis and design studies of multiferroic layered systems subjected to moving contacts.

2

Numerical analysis of fracture behavior of functionally graded materials using 3D-XFEM

Benhamena Ali, Fatima Benaoum, Foudil Khelil, Baltach Abdelghani, Chaouch Mohamed Ikhlef

Advances in Materials Science

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2023

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Vol. 23, nr 3(77)

33--46

EN

This paper presents the numerical evaluation of mixed stress intensity factors (SIFs) and non-singular terms of William's series (T-stress) of functionally graded materials (FGMs) using three-dimensional extended finite element method (3D-XFEM). Four-point bending specimen with crack perpendicular to material gradation have been used in this investigation in order to study the effect of some parameters (crack position, crack size, specimen thickness) on the failure of FGMs materials. The fracture parameters (KI KII, phase angle ψ and T-stress) obtained by the present simulation are compared with available experimental and numerical results. An excellent correlation was found of the 3D-XFEM simulations with those available in the literature. From the numerical results, a fitting procedure is performed in order to propose an analytical formulation and subsequently are validated against the 3D-XFEM results.

3

Nonlocal state-space strain gradient approach to the vibration of piezoelectric functionally graded nanobeam

Selvamani Rajendran, Loganathan Rubine, Ebrahimi Farzad

Engineering Transactions

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2022

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Vol. 70, iss. 4

319--338

EN

In this work, the state-space nonlocal strain gradient theory is used for the vibration analysis of piezoelectric functionally graded material (FGM) nanobeam. Power law relations are used to describe the computing analysis of FGM constituent properties. The refined higherorder beam theory and Hamilton’s principle are used to obtain the equations of motion of the piezoelectric nanobeam. Besides, the governing equations of the piezoelectric nanobeam are extracted by the developed nonlocal state-space theory, and the analytical wave dispersion method is used to solve wave propagation problems. The real and imaginary solutions for wave frequency, loss factor and wave number are obtained and presented in graphs.

4

Thermomechanical responses of functionally graded cylinders

Eker Mehmet, Yarımpabuç Durmuş

Journal of Applied Mathematics and Computational Mechanics

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2021

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Vol. 20, nr 4

19--28

EN

In this study, thermal and mechanical stresses in hollow thick-walled functionally graded (FG) cylinders is presented under the convection boundary condition. The convective external condition and constant internal temperature in hollow cylinders are investigated. Inhomogeneous material properties produce irregular and two-point linear boundary value problems that are solved numerically by the pseudospectral Chebyshev method. The displacement and thermal stress distributions are examined for two different material couples under particular boundary conditions that are similar to their real engineering applications.Results have demonstrated that the pseudospectral Chebyshev method has low computation costs, high accuracy and ease of implementation and can be easily customized to such engineering problems.

5

Transient dynamic analysis of functionally graded micro-beams considering small-scale effects

Eshraghi I., Dag S.

Archives of Mechanics

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2021

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Vol. 73, nr 4

303--337

EN

A domain-boundary element method, based on modified couple stress theory, is developed for transient dynamic analysis of functionally graded micro-beams. Incorporating static fundamental solutions as weight functions in weighted residual expressions, governing partial differential equations of motion are converted to a set of coupled integral equations. A system of ordinary differential equations in time is obtained by domain discretization and solved using the Houbolt time marching scheme. Developed procedures are verified through comparisons to the results available in the literature for micro- and macro-scale beams. Numerical results illustrate elastodynamic responses of graded micro-beams subjected to various loading types. It is shown that metal-rich micro-beams and those with a smaller length scale parameter ratio undergo higher displacements and are subjected to larger normal stresses.

6

Free vibration analysis of imperfect functionally graded sandwich plates: analytical and experimental investigation

Njim E.K., Bakhy S.H., Al-Waily M.

Archives of Materials Science and Engineering

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2021

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Vol. 111, nr 2

49--65

EN

Purpose: This paper develops a new analytical solution to conduct the free vibration analysis of porous functionally graded (FG) sandwich plates based on classical plate theory (CPT). The sandwich plate made of the FGM core consists of one porous metal that had not previously been taken into account in vibration analysis and two homogenous skins. Design/methodology/approach: The analytical formulations were generated based on the classical plate theory (CPT). According to the power law, the material properties of FG plates are expected to vary along the thickness direction of the constituents. Findings: The results show that the porosity parameter and the power gradient parameter significantly influence vibration characteristics. It is found that there is an acceptable error between the analytical and numerical solutions with a maximum discrepancy of 0.576 % at a slenderness ratio (a/h =100), while the maximum error percentage between the analytical and experimental results was found not exceeding 15%. Research limitations/implications: The accuracy of analytical solutions is verified by the adaptive finite elements method (FEM) with commercial ANSYS 2020 R2 software. Practical implications: Free vibration experiments on 3D-printed FGM plates bonded with two thin solid face sheets at the top and bottom surfaces were conducted. Originality/value: The novel sandwich plate consists of one porous polymer core and two homogenous skins which can be widely applied in various fields of aircraft structures, biomedical engineering, and defense technology. This paper presents an analytical and experimental study to investigate the free vibration problem of a functionally graded simply supported rectangular sandwich plate with porosities. The objective of the current work is to examine the effects of some key parameters, such as porous ratio, power-law index, and slenderness ratio, on the natural frequencies and damping characteristics.

7

Thermal buckling and free vibration of Euler–Bernoulli FG nanobeams based on the higher-order nonlocal strain gradient theory

Janevski G., Despenić N., Pavlović I.

Archives of Mechanics

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2020

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Vol. 72, nr 2

139--168

EN

A size-dependent Euler–Bernoulli beam model is derived within the framework of the higher-order nonlocal strain gradient theory. Nonlocal equations of motion are derived by applying Hamilton’s principle and solved with an analytical solution. The solution is obtained using the Navier solution procedure. In the case of simply supported boundary conditions, the analytical solutions of natural frequencies and critical buckling temperature for free vibration problems are obtained. The paper investigates the thermal effects on buckling and free vibrational characteristics of functionally graded size-dependent nanobeams subjected to various types of thermal loading. The influence of higher-order and lower-order nonlocal parameters and strain gradient scale on buckling and vibration are investigated for various thermal conditions. The obtained results are compared with previous research.

8

An analytical study on the nonlinear forced vibration of functionally graded carbon nanotube-reinforced composite beams on nonlinear viscoelastic foundation

Shafiei H., Setoodeh A. R.

Archives of Mechanics

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2020

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Vol. 72, nr 2

81--107

EN

This paper deals with the nonlinear forced vibration of nanocomposite beams resting on a nonlinear viscoelastic foundation and subjected to a transverse periodic excitation. It is considered that the functionally graded carbon nanotubereinforced composite (FG-CNTRC) beam is made of an isotropic matrix reinforced by either aligned- or randomly oriented-straight single-walled carbon nanotubes (SWCNTs) with four types of distributions through the thickness direction of the beam. Both the Eshelby–Mori–Tanaka approach and extended rule of mixtures are used to predict the effective material properties of the FG-CNTRC beams. The mathematical model of the beam is developed based on the Euler–Bernoulli beam theory together with von Kármán assumptions. Subsequently, the accurate analytical solutions of the governing equation are obtained through applying the variational iteration method (VIM). Several examples are verified to have higher accuracy than those available in the literature. In addition, a comprehensive investigation into the effect of carbon nanotubes (CNTs) distribution, CNTs volume fraction, end supports, vibration amplitude, and foundation coefficients on the vibrational characteristics of the nanocomposite beam is performed and some new results are presented.

9

Computation of SIFs for cracked FGMs under mechanical and thermal loadings

Ait Ferhat Yazid, Boulenouar Abdelkader

Archives of Mechanical Technology and Materials

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2020

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Vol. 40

12--19

EN

The objective of this study is to present a numerical modeling of mixed-mode fracture in isotropic functionally graded materials (FGMs), under mechanical and thermal loading conditions. In this paper, a modified displacement extrapolation technique (DET) was proposed to calculate the stress intensity factor (SIFs) for isotropic FGMs. Using the Ansys Parametric Design Language APDL, the continuous variations of the material properties are incorporated by specified parameters at the centroid of each element. Three numerical examples are presented to evaluate the accuracy of SIFs calculated by the proposed method. Comparisons have been made between the SIFs predicted by the DET and the available reference solutions in the current literature. A good agreement is obtained between the results of the DET and the reference solutions.

10

On size-dependent large-amplitude free oscillations of FGPM nanoshells incorporating vibrational mode interactions

Yi Hongwei, Sahmani Saeid, Safaei Babak

Archives of Civil and Mechanical Engineering

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2020

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Vol. 20, no. 2

257--279

EN

At nanoscale, surface free energies of the atoms located on the free surfaces of structures significantly affect their mechanical characteristics. In this study, nonlinear large-amplitude free vibration response of nanoshells prepared from functionally graded porous materials (FGPM) is investigated by taking into account surface stress size effects and vibrational mode interactions. Non-classical shell model is constructed on the basis of the Gurtin–Murdoch type of the surface theory of elasticity having the capability of capturing surface stress size dependency. The accuracy of nonlinear vibration analysis is improved by incorporating the interaction of the main vibration mode and the first, third and fifth symmetric oscillation modes. Moreover, the closed-cell Gaussian-Random field scheme is put to use to extract the mechanical characteristics of FGPM nanoshell. Multiple timescales technique is then applied to achieve surface stress elastic-based nonlinear frequency of FGPM nanoshell analytically for different interactions between vibrational modes. It is revealed that by incorporating the interactions of the main vibration mode and higher symmetric oscillation modes, the behavior of the backbone curves belongs to the nonlinear free oscillation response of FGPM nanoshells changes from hardening to softening schema. It is found that when only the main vibration mode is taken into account, surface elasticity effects makes an enhancement in the significance of the hardening schema. However, by considering the interactions of higher symmetric oscillation modes, surface elasticity effects makes a reduction in the significance of the softening schema.

11

Impact of vibro-compaction on microstructure and properties of aluminium matrix composite with SiC particles

Godzierz Marcin, Olszówka-Myalska Anita, Dudzińska Karolina, Urbiczek Mateusz

Inżynieria Materiałowa

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2019

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Vol. 40, nr 6

140--145

EN

In the paper, the effect of vibro-compaction in processing of sintered SiCp – aluminium matrix composite was presented. The composite with 15% vol. of SiCp, obtained with three stages: vibro-compaction with use of different amplitude (0.75 mm, 1.125 mm and 1.5 mm), cold pressing and pressure less sintering. The obtained composites were characterized by porosity measurements, microhardness, quantitative metallography analysis and dry sliding tests. It was proved that the application of chosen compaction method, for powder mixture consisting of powders with different density (Al and SiC), allows to obtain graded structure composite. An increase of SiC particles volume fraction as well as microhardness increase was observed towards the bottom of the sample. The most beneficial effect, in SiCp distribution and microhardness values, was noted for the sample were the amplitude of vibro-compaction was 1.5 mm. Moreover, the tribological examinations showed differences in friction coefficients and mass losses for opposite surfaces of composite samples, due to different SiCp volume fraction across the sample. The vibro-compacted material revealed lower porosity, higher mean value of friction coefficient and lower mass loss comparing to the reference composite.

PL

Głównym obszarem zastosowania kompozytów na osnowie aluminium zbrojonych cząstkami ceramicznymi są skojarzenia ślizgowe i cierne, takie jak grupa tłokowo-cylindrowa maszyn tłokowych i łożyska ślizgowe, a w przemyśle samochodowym klocki hamulcowe, sprzęgła, przekładnie pasowe czy bloki silnika. W wielu elementach nie są wymagane takie same właściwości tribologiczne materiału na całym przekroju lub nie jest technologicznie możliwe uzyskanie ekstremalnie wysokich parametrów użytkowych związanych z dużą zawartością cząstek w całej objętości. W takich przypadkach rozwiązaniem mogą być materiały charakteryzujące się gradientowym rozmieszczeniem cząstek ceramicznych i istnieje wiele koncepcji technologicznych pozwalających uzyskać ten typ mikrostruktury. W pracy przedstawiono możliwość uzyskania metodą metalurgii proszków struktury gradientowej w kompozycie Al–SiCp, dla udziału zbrojenia w mieszaninie wyjściowej 15% obj. Założono, że gradientowe zróżnicowane rozmieszczenie zbrojenia w osnowie powstanie dzięki różnicy gęstości komponentów (Al 2,7 g/cm3, SiC 3,21 g/cm3), podczas zgęszczania wibracyjnego, dzięki bardziej intensywnemu w porównaniu z proszkiem aluminium przemieszczaniu się cząstek SiC w dół formy.

12

Torsion of functionally graded anisotropic linearly elastic circular cylinder

Baksa A., Ecsedi I.

Engineering Transactions

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2018

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Vol. 66, iss. 4

413--426

EN

The object of this paper is Saint-Venant torsion of functionally graded anisotropic linearly elastic circular cylinder. The class of anisotropy considered has at least one plane of elastic symmetry normal to the axis of the circular cylinder. The elastic coefficients have radial dependence only. Here, we give the solution of Saint-Venant torsion problem for circular cylinder made of functionally graded anisotropic linearly elastic materials.

13

Synthesis and Characterization of Functionally Graded Al-6Cr-Y2O3 Composites

Satish Kumar T., Krishna Kumar K., Shalini S., Subramanian R.

Archives of Metallurgy and Materials

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2018

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Vol. 63, iss. 4

1649--1655

EN

The present investigation aims at fabricating a functionally graded Al-6Cr-Y2O3 composite and its microstructural and property characterization. Al-6Cr-alloys with varying percentage of Y2O3 (5-10 vol. %) have been used to fabricate FGM by powder metallurgy route. The samples were subsequently subjected to solution treatment at 610°C for 4h followed by artificially aged at 310°C for 4h. The microstructure, hardness and wear behavior of these FGM have been evaluated. FGM exhibited superior hardness (360 ± 5 VHN) as compared to the unprocessed composites (220 ± 5 VHN) due to the uniform dispersion of Y2O3 particles. Wear resistance of Al-6Cr-10Y2O3 FGM were compared that of with pure Al-6Cr alloy by dry abrasive wear test. Al-6Cr-10Y2O3 FGM composites were found to exhibit higher wear resistance with the minimum wear rate of 0.009 mm3/m compared to the Al-6Cr alloy wear rate 0.02 mm3/m.

14

Free vibration analysis of functionally graded rectangular nanoplates considering spatial variation of the nonlocal parameter

Alipour Ghassabi A., Dag S., Cigeroglu E.

Archives of Mechanics

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2017

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Vol. 69, nr 2

105--130

EN

We present a new nonlocal elasticity-based analysis method for free vibrations of functionally graded rectangular nanoplates. The introduced method allows taking into account spatial variation of the nonlocal parameter. Governing partial differential equations and associated boundary conditions are derived by employing the variational approach and applying Hamilton’s principle. Displacement field is expressed in a unified way to be able to produce numerical results pertaining to three different plate theories, namely Kirchhoff, Mindlin, and third-order shear deformation theories. The equations are solved numerically by means of the generalized differentia quadrature method. Numerical results are generated by considering simply-supported and cantilever nanoplates undergoing free vibrations. These findings demonstrate the influences of factors such as dimensionless plate length, plate theory, power-law index, and nonlocal parameter ratio upon vibration behavior.

15

Elastic and Viscoelastic Stresses of Nonlinear Rotating Functionally Graded Solid and Annular Disks with Gradually Varying Thickness

Allam M. N. M., Tantawy R., Yousof A., Zenkour A. M.

Archive of Mechanical Engineering

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2017

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Vol. LXIV, nr 4

423--440

EN

Analytical and numerical nonlinear solutions for rotating variable-thickness functionally graded solid and annular disks with viscoelastic orthotropic material properties are presented by using the method of successive approximations.Variable material properties such as Young’s moduli, density and thickness of the disk, are first introduced to obtain the governing equation. As a second step, the method of successive approximations is proposed to get the nonlinear solution of the problem. In the third step, the method of effective moduli is deduced to reduce the problem to the corresponding one of a homogeneous but anisotropic material. The results of viscoelastic stresses and radial displacement are obtained for annular and solid disks of different profiles and graphically illustrated. The calculated results are compared and the effects due to many parameters are discussed.

16

Calculation of Stress Intensity Factor for an Internal Circumferential Crack in a Rotating Functionally Graded Thick-Walled Hollow Circular Cylinder under Thermal Shock

Ghafoor E. M. R., Rokhi M. M.

Archive of Mechanical Engineering

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2017

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Vol. LXIV, nr 4

455--479

EN

In this article, the fracture behavior of functionally graded thick-walled cylinder under thermo-mechanical shock is investigated. For this purpose, classical coupled thermoelastic equations are used in calculations. First, these equations are discretized with extended finite element method (XFEM) in the space domain and then they are solved by the Newmark method in the time domain. The most general form of interaction integral is extracted for axially symmetric circumferential crack in a cylinder under thermal and mechanical loads in functionally graded materials and is used to calculate dynamic stress intensity factors (SIFs). The problem solution has been implemented in MATLAB software.

17

Characterization of the starting materials for functionally graded thermoelectric materials for pseudobinary system of Bi2Te3-Sb2Te3

Januszko K., Chetty R., Mashimo T., Wojciechowski K.T.

Mechanik

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2016

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R. 89, nr 5-6

522--523

EN

Samples of Bi-Sb-Te system were prepared by solid state synthesis from pure elements, microstructure and thermoelectric properties were characterized. From obtained powders segmented samples were construct-ed in order to confirm change of the thermoelectric properties with composition. Segmented element is expected to have better efficiency.

PL

Próbki otrzymane w wyniku syntezy z czystych pier-wiastków zostały scharakteryzowane pod względem mikrostruktury i właściwości termoelektrycznych. Z otrzymanych proszków skonstruowano element seg-mentowy i potwierdzono zmianę właściwości termoelektrycznych ze zmianą składu chemicznego. Przewiduje się podwyższoną sprawność takiego elementu.

18

Metal-ceramic functionally graded materials – manufacturing, characterization, application

Chmielewski M., Pietrzak K.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2016

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Vol. 64, nr 1

151--160

EN

Functionally graded materials (FGMs) belong to a new, continuously developing group of materials, finding application in various branches of industry. The idea of freely designing their construction profile, restricted only by the available manufacturing techniques, enables obtaining materials with composition and structure gradients having unprecedented properties. In this paper, selected results of works carried out by the authors and relating to the application of the developed metal-ceramic composites were presented in order to manufacture functionally graded materials for target purposes. Gradient structures with various construction profiles that can play different roles were produced on the basis on the following material pairs: Cr-Al2O3, NiAl-Al2O3 and Cu-AlN. Manufacturing conditions, microstructure characteristics and selected properties, crucial from the point of view of future applications, were presented.

19

Tin-Copper-Lead Alloy Produced by Horizontal Centrifugal Casting

Vahdat S. E.

Archives of Foundry Engineering

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2016

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Vol. 16, iss. 1

131--137

EN

Horizontal centrifugal casting is an effective method for the production of hollow metal with good mechanical properties, low defect, cast to size and relatively cheap. The ability of a metal to satisfy the above requirements highly depends on its microstructure. In this study, the relationship between microstructural parameters such as grain size and the amount of phases with bulk hardness of SnCu4Pb3 is concerned in three areas of the product. Consequently, to achieve the desired hardness of the product in a particular area, the interaction of two factors of the microstructure including, grain size and particles amount of the hard intermetallic compositions (Cu6Sn5) should be noted.

20

Zastosowanie metody elementów brzegowych dla środowisk niejednorodnych na przykładzie badania zawilgocenia murów

Pańczyk M., Sikora J.

Zeszyty Naukowe. Elektryka / Politechnika Łódzka

|

2015

|

z. 126

117--124

PL

Artykuł prezentuje opis matematyczny implementacji środowisk niejednorodnych w metodzie elementów brzegowych. Wyniki obliczeń porównane są z realnymi pomiarami zawilgocenia zbudowanego w warunkach laboratoryjnych muru, wykonanymi z użyciem 26 elektrodowego tomografu impedancyjnego i klasycznej metody suszarkowo-wagowej.

EN

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