Homogeneous Plate Research Articles

Determination of temperature distribution on windings of oil transformer based on the laws of heat transfer

Object of research: development of a technology for determining the temperature of the winding of a power oil transformer, in particular, the analysis of thermal processes in the winding of a power transformer during short-term overloads, taking into account the influence of the environment.
 Investigated problem: temperature distribution in the winding of a power oil transformer taking into account short-term load surges in the problem of assessing the residual life of the insulation of the transformer winding by temperature aging. The calculation of the temperature distribution in the winding was carried out using the passport data and characteristics of the power oil transformer, including the winding, transformer oil, load currents.
 Main scientific results: a mathematical model was calculated, with the help of which the results of temperature distribution in the transformer winding were obtained during short-term load surges or constant work with an increased load. According to the presented model, the analysis of the cooling time of the transformer winding after short-term overloads is carried out. Comparing the results obtained on the simulation model with the known results of experimental studies of the temperature distribution in the winding of a power transformer, the adequacy of the mathematical model is proved. It is shown that the use of the laws of heat transfer in a homogeneous plate to analyze the temperature distribution in the transformer winding is not wrong, but requires clarifications and simplifications.
 The area of practical use of the research results: enterprises of the machine-building industry and energy companies specializing in the production and operation of transformer equipment. Innovative technological product: simulation model of heat distribution in a transformer winding, which can take into account the load of the transformer, the effect of the environment on the insulation of the transformer windings.
 An innovative technological product: a method for diagnosing the duration of the non-failure operation of a transformer, which makes it possible to ensure trouble-free operation and save money for the repair of transformer equipment.
 Scope of application of the innovative technological product: design and development of diagnostic systems for windings of power oil transformers

On semi-analytical Stochastic Boundary Element Method and its application to eigenproblem of thin elastic plate immersed into a fluid

The main objective in this work is to study an application of the B-spline approximations in the Least Squares Method recovery of the structural response for boundary value problems in some linear elastic systems. These responses were approximated before using polynomial bases in the Stochastic perturbation-based Boundary Element Method and now are replaced with second or third order B-spline functions. A majority of such an approach is that the resulting expected values and standard deviations of structural response are obtained using analytical calculus of probability integrals, so that neither statistical nor expansion methods are necessary. Numerical illustration delivered in this paper includes fundamental eigenfrequencies of elastic thin homogeneous and isotropic plate immersed into Newtonian fluid subjected to various boundary conditions at its external edges.

Mechanics of structure genome-based buckling analysis of sandwich structures

Sandwich structures are important structural members in modern lightweight engineering. Accurate and effective buckling predictions are vital to the design and optimization of sandwich structures. This paper extends and validates a homogenization theory namely the mechanics of structure genome (MSG) in predicting eigenvalue buckling of sandwich structures under compressive and bending loads. Global buckling is predicted on a homogeneous plate with effective plate properties computed by MSG. Local buckling is predicted by perturbing the fluctuating function of structure gene under Bloch-periodic boundary conditions. Accuracy of buckling predictions is validated by three-dimensional finite element analysis.

Deformations’ Predictions by Utilizing Load Blast Enhanced against Structural Arbitrary Langrangian Eulerian Methodologies: An LS-DYNA Numerical Simulation Study

Numerical simulation study to predict the transient (maximum) deformation of a rolled homogeneous armor plate which was loaded by the explosion of spherical trinitrotoluene bomb by using the ‘load blast enhanced’ and ‘structured arbitrary langragian eulerian’ methodologies in LS-DYNA is reported in this paper. Three numerical simulation models that utilized the ‘load blast enhanced’ and three numerical simulation models that utilized the ‘structured arbitrary langragian eulerian’ methodologies in LS-DYNA were produced and their results were used to predict and validate the deformations of three blast experimental tests of rolled homogeneous armor plates obtained from a published paper. This study showed that the numerical simulation results from the ‘load blast enhanced’ methodology gave better agreement than the ‘structured arbitrary langragian eulerian’ methodology with an average percentage differences of around 17% for all three cases.

Determination of the dispersion relation in cross-laminated timber plates: Benchmarking of time- and frequency-domain methods

The availability of a reliable estimate of the dispersion relation of plates is of great importance for acoustic modelling. Several experimental methods for the extraction of wavenumber and wave velocity information are discussed in the literature. They differ, among other factors, by the sensitivity to noise and multiple reflections, frequency range of application and implementation of the processing algorithm. While for homogeneous thick or thin plates well-established analytical solutions are available, non homogeneous materials would benefit from experimental characterisation. In this framework, our attention is focused on cross-laminated timber (CLT) elements, load-bearing orthotropic layered wood plates that revolutionised the sector of timber construction. The anisotropic and non homogeneous nature of wood suggested testing methods that, though converging for homogeneous materials, could bring different results in their application to CLT elements. The aim of this paper is therefore to benchmark methods for the extraction of wavenumber information on CLT plates, from which the effective elastic properties to model CLT structures as an equivalent homogeneous plate can be derived. This is achieved through a numerical and experimental benchmark of well-established methods for the evaluation of the real component of the propagating wavenumber in CLT elements. Five relevant methods were selected through a literature review, implemented and analyzed: three in the time domain, namely maximum peak, cross-correlation and kurtosis, and two in the frequency domain: phase difference and wave correlation. First, the five methods were benchmarked by numerical simulation on a homogeneous material. In this ideal case, results showed to be consistent for all methods. Then, wavenumber measurements were performed on a cross-laminated timber plate. The results show that the maximum peak, cross-correlation and the wave correlation method provide the lowest dispersion of the data. Considering the time required by the installation of the setup, the wave correlation method seems to be the best alternative among the proposed ones.

Modelling and evaluation of thermoelastic damping of FGM micro plates based on the Levinson plate theory

Thermoelastic damping (TED) in a simply supported functionally graded material (FGM) micro rectangular plate is investigated analytically based on the higher-order shear deformation plate theory. The equations of motion for the thermo-elastic coupled transverse free vibration and the heat conduction equation coupled are derived based on the Levinson plate theory and the one-way coupled heat conduction theory. A semi-analytical solution of the heat conduction equation with variable coefficients is obtained by using a layer-wise homogenization approach. The complex frequency of the micro plate including TED is determined in terms of the frequency of the corresponding isothermal homogenous Kirchhoff plate by using the mathematical similarity between the eigenvalue problems for the two types of plates. The effects of the shear deformation, the material gradient and the geometry on the TED are examined in detail for the FGM micro plate made of ceramic–metal constituents with the power-law gradient profile. The numerical results show that the TED evaluated by the Levinson plate theory is smaller than that by the Kirchhoff plate theory. Therefore, for a thick or moderately thick micro plate the Levinson plate theory can provide a more accurate prediction of the TED than the Kirchhoff plate theory.

Calculating the centre of mass of circular sector plates using series and limits

Series and limits were used to calculate the centre of mass of homogeneous circular sector plates. The method presented can be used to teach students about discrete and continuous systems.

Stochastic Fracture Analysis Using Scaled Boundary Finite Element Methods Accelerated by Proper Orthogonal Decomposition and Radial Basis Functions

This paper presents a stochastic analysis method for linear elastic fracture mechanics using the Monte Carlo simulations (MCs) and the scaled boundary finite element method (SBFEM) based on proper orthogonal decomposition (POD) and radial basis functions (RBF). The semianalytical solutions obtained by the SBFEM enable us to capture the stress intensity factors (SIFs) easily and accurately. The adoption of POD and RBF significantly reduces the model order and increases computation efficiency, while maintaining the versatility and accuracy of MCs. Numerical examples of cracks in homogeneous and bimaterial plates are provided to demonstrate the effectiveness and reliability of the proposed method, where the crack inclination angles are set as uncertain variables. It is also found that the larger the scale of the problem, the more advantageous the proposed method is.

Broadband diffuse field sound insulation of double layer metamaterial plates lined with porous material

We propose a composite acoustic metamaterial consisting of double layer metamaterial plates (DLMPs) lined with porous material (PM). Numerical results show that DLMPs lined with PM can produce a very high diffuse field sound transmission loss (STL) beyond the mass law over an ultra-wide low-frequency range. The unusual behavior is interpreted by explicit formulas. For validation, a large-scale specimen is fabricated using light surface mass density (5.72 kg/m2) and small thickness (5 cm). Measured data show that the specimen possesses an excellent diffuse field STL deeply breaking the mass law at broadband low frequencies (248–1624 Hz), and simultaneously, it has an improved diffuse field STL within a wide low-frequency band (208–850 Hz) compared with the conventional double layer homogeneous plates lined with PM. Owing to the simple construction, light weight, and thinness, the proposed composite metamaterial has promising applications in noise control engineering.

Impact sound prediction of finite floor structures with the modal transfer matrix method

The transfer matrix method (TMM) is commonly employed for wave propagation analysis in layered media of fluid, elastic and porous nature. Up to now it has been used extensively to analyze airborne sound transmission and sound absorption. Its use for impact sound transmission has been investigated to a limited extent, i.e. for thick homogeneous elastic plates of infinite extent and for specific receiver points. This contribution aims to broaden the scope such that the global impact sound, radiated by finite floor structures containing elastic, fluid and/or porous layers, can be analyzed in a more robust way than previously available in literature. A disadvantage of the conventional TMM is that only floors of infinite extent can be implemented. It is possible to remove this drawback using a spatial windowing technique. Furthermore, the modal behavior of the floor is approximately taken into account by projecting the impact force onto the mode shapes and only allowing for the propagation of those waves, corresponding to modal wavenumbers, in the structure. Predictions of the radiated sound power are made for various bare floors and floating floor systems of both infinite and finite extent.

Construction of piezoelectric and flexoelectric models of composites by asymptotic homogenization and application to laminates

The effective piezoelectric and flexoelectric properties of heterogeneous solid bodies with constituents obeying a piezoelectric behavior are evaluated in full generality, based on the asymptotic expansion method. The successive situations of materials obeying a piezoelectric and flexoelectric behavior at the macroscale is envisaged in the present work. Closed-form expressions for the effective flexoelectric properties are obtained for stratified materials. A general theory for laminated piezoelectric plates is formulated on the basis of the formulated asymptotic models, and the response of the homogeneous substitution plate is evaluated for a loading consisting of a pure bending moment, triggering electric fields and strain and electric fields gradients within the plate thickness. The local mechanical and electric fields at the microscopic level within the initial heterogeneous stratified domain are evaluated by solving unit cell boundary value problems for the localization operators. An effective flexoelectric plate model for a stratified composite is constructed, showing the generation of the gradient of an electric field under application of a pure bending moment.

Low-frequency vibroacoustic performance of an acoustic metamaterial plate with periodical single-stage multi-degree-of-freedom resonators attachment

This paper demonstrates low-frequency vibration suppression and sound radiation of an acoustic metamaterial plate which is composed of periodical single-stage multi-degree-of-freedom (MDOF) resonators and a homogeneous plate. Dispersion relation for a unit cell and vibroacoustic performance for a simply supported metamaterial plate has been derived. Multiple band gaps can be obtained for the metamaterial plate, within which large vibration suppression and sound reduction can be achieved for the finite simply supported metamaterial plate. Analysis of the infinite and finite meta-plate implies a validation between these two theoretical methods. Low-frequency vibration suppression and sound reduction within band gaps can be attributed to the translational and rotational resonance from the attached resonators which generate inertia to counterbalance the shear force in the plate induced by the flexural wave. Study in this work shows potential in the practical application for requirements of small room installation and multiple band gaps.

Solid Truss to Shell Numerical Homogenization of Prefabricated Composite Slabs.

The need for quick and easy deflection calculations of various prefabricated slabs causes simplified procedures and numerical tools to be used more often. Modelling of full 3D finite element (FE) geometry of such plates is not only uneconomical but often requires the use of complex software and advanced numerical knowledge. Therefore, numerical homogenization is an excellent tool, which can be easily employed to simplify a model, especially when accurate modelling is not necessary. Homogenization allows for simplifying a computational model and replacing a complicated composite structure with a homogeneous plate. Here, a numerical homogenization method based on strain energy equivalence is derived. Based on the method proposed, the structure of the prefabricated concrete slabs reinforced with steel spatial trusses is homogenized to a single plate element with an effective stiffness. There is a complete equivalence between the full 3D FE model built with solid elements combined with truss structural elements and the simplified homogenized plate FE model. The method allows for the correct homogenization of any complex composite structures made of both solid and structural elements, without the need to perform advanced numerical analyses. The only requirement is a correctly formulated stiffness matrix of a representative volume element (RVE) and appropriate formulation of the transformation between kinematic constrains on the RVE boundary and generalized strains.

Precise and target-oriented control of the low-frequency Lamb wave bandgaps

Precise and target-oriented control of acoustic/elastic wave bandgaps in phononic crystals or acoustic metamaterials according to particular requirements is of both theoretical and practical importance. A very challenging and also interesting task is to tune the widths and the overall positions of the bandgaps of interest independently and arbitrarily. This work presents a simple and smart acoustic metamaterial structure, which can achieve the above mentioned goal by considering the symmetric Lamb waves. The proposed acoustic metamaterial structure consists of a homogenous piezoelectric plate which is connected to the LC circuits through an array of periodic surface electrodes. The control of the resonance bandgaps (RBGs), which are generated by the coupled resonance of the piezoelectric plate with the external LC circuits, is the focus of this study. To solve the problem at hand, we develop a two-dimensional (2D) spectral element method (SEM) considering the full electro-mechanical coupling, and the high tunability of the RBGs is demonstrated numerically in the low-frequency range. Especially, we find that the upper/lower boundary of a RGB can be intentionally fixed at any specified frequency while changing its’ bandwidth. To explore the corresponding physical phenomena and reveal the regulation mechanism, a simplified theory is developed based on the assumption of thin piezoelectric plates. Several simple analytical formulas are established, which are essential to the precise control of the RBGs for both the thin and thick piezoelectric plates. A numerical example is given to demonstrate the detailed procedure of precisely tuning a RBG in a targeted frequency range, which is also verified by the transmission spectrum for the corresponding finite piezoelectric acoustic metamaterial plate.

The Influence of a Heterogeneous Surface on the Free Volume Oscillations of an Oblate Gas Bubble

The natural oscillations of a cylindrical gas bubble surrounded by an incompressible fluid with free interface are considered. The bubble has an equilibrium cylindrical shape and is bounded axially by two parallel solid surfaces. Dynamics of contact lines is taken into account by an effective boundary condition: velocity of the contact line is assumed to be proportional to contact angle deviation from the equilibrium value. The equilibrium contact angle is right. Different Hocking parameters determine individual damping rates, but dissipation in the integral system is determined by their total contribution. The frequency of the volume (breathing) harmonic of free oscillations can vanish in a certain interval of the values of the Hocking parameter for homogeneous plate surface. However, Surface inhomogeneity destroys this monotonic damping effect.

Application of EN 16615 (4-Field Test) for the Evaluation of the Antimicrobial Activity of the Selected Commercial and Self-Made Disinfectant Wipes.

The purpose of disinfectants is to reduce microorganisms on a contaminated surface and to prevent the spread of microorganisms. The relatively new EN 16615 simulates disinfection by wiping and allows for assessing the recovery of microorganisms from the surface and, importantly, the degree of spread of microorganisms when the surface is disinfected by wiping. For the first time, using this standard, the tested products in the form of commercial disinfectant wipes were compared with self-made wipes soaked in respective disinfectant liquids. The disinfected surfaces were simulated by homogeneous polyvinyl chloride plates. The studies were carried out not only with the standard, but also with clinical multidrug-resistant microbial strains. Based on the research, it can be concluded that the most effective products in the disinfection process (log10 reduction of ≥5) with the shortest contact time (1 min) were products containing ethanol, propanol, and quaternary ammonium compounds (self-made wipes) and propanol (commercial wipes). The least effective products (log10 reduction of <5) in terms of the contact time declared by the manufacturer were products containing ethanol and sodium hypochlorite (commercial wipes). Much better antimicrobial activity of self-made wipes was observed in comparison to the activity of the commercial wipes.

Numerical Optimization of Stress Concentration in Composite Structures for Different Material Arrangement.

Complex machine parts are characterized by different shapes, material characteristics and working loads. The simultaneous theoretical optimization of shape and material properties is difficult because the single objective functional with a unique physical interpretation is unknown for these two features. The optimization is the multi-criteria procedure or the functional is a weighted average of partial criteria with the assumed weight values. Therefore, the structure and material characteristics are optimized numerically. The main goal of the article was to model and optimize the stress distribution inside the composite plates subjected to complex load. The advanced material composition was made of four different materials: steel, ductile iron, E-glass fibers and carbon fibers. The stress distributions were optimized for the homogeneous plate, the sandwich composite made of metal and textile layers, and the plate with additional stiffening elements (ribs and another plate along the neck portion). Based on the numerical simulations, the optimal structural shapes and material arrangements were determined.

Experimental realization of a pillared metasurface for flexural wave focusing

A metasurface is an array of subwavelength units with modulated wave responses that show great potential for the control of refractive/reflective properties in compact functional devices. In this work, we propose an elastic metasurface consisting of a line of pillars with gradient heights, erected on a homogeneous plate. The change in the resonant frequencies associated with the height gradient allows us to achieve transmitted phase response covering a range of 2π, while the amplitude response remains at a relatively high level. We employ the pillared units to design a focusing metasurface and compare the properties of the focal spots through simulation and experiment. The subwavelength transverse and lateral full width at half maximum of the focusing intensity profiles are observed in both simulation and experiment, with the underlying mechanism being the interference and diffraction of the scattered waves from the resonant pillars as well as the boundaries (especially for experiment). The good correspondence between the experimental and simulated relative focal lengths shows the robustness of the focusing pillared metasurfaces with respect to fabrication imperfections. This proposed compact, simple, and robust metasurface with unaffected mechanical properties provides a new platform for elastic wave manipulation for energy harvesting, wave communication, sensing, and non-destructive testing among others.

Preparation methods and performance of new tungsten-based ceramic alloy

In this study, a new tungsten-based ceramic alloy (TCA) is obtained using liquid-phase sintering during the preparation of traditional 95 W alloys. In this process, sintered Al2O3 ceramic microspheres with a purity of 99%, a mass fraction of 1% ~ 5%, and the particle size of 60 ~ 120 μm are added. This new material's microstructure, mechanical properties, fracture mechanism, and high-speed penetration performance are studied. Results show that the TCA's tensile strength, ductility, and impact toughness decrease with the addition of Al2O3 ceramic. However, when 3 wt% Al2O3 ceramic is added, the TCA spherical fragment exhibits the best high-speed impact property against the 616 rolled homogeneous armor plate (22SiMn2TiB) of 15 mm thick. Therefore, TCA can be used as the material of the kinetic energy damage element to improve its high-speed penetration ability.

DYNAMIC BIAXIAL STRESS ANALYSIS OF FLAT LAYERED CERAMIC COMPOSITES

We study theoretically the biaxial bending of symmetric, flat layered ceramic composites (laminates) due to external loading. We focus on three-layered alumina/zirconia laminates. We compare the principal stresses in the samples in the case of static and harmonic dynamic loading. The dynamic equation within the Kirchhoff theory for thin homogeneous plates is first generalized to the case of multilayered plates. It is solved numerically with the relaxation method, which we have developed for this purpose.