Parameter In Boundary Condition Research Articles

Research on stress field inversion and large deformation level determination of super deep buried soft rock tunnel

Understanding the characteristics and distribution patterns of the initial geo-stress field in tunnels is of great significance for studying the problem of large deformation of tunnels under high geo-stress conditions. This article proposes a ground stress field inversion method and large deformation level determination based on the GS-XGBoost algorithm and the Haba Snow Mountain Tunnel of the Lixiang Railway. Firstly, the hydraulic fracturing method is used to conduct on-site testing of tunnel ground stress and obtain tunnel ground stress data. Then, a three-dimensional model of the Haba Snow Mountain Tunnel will be established, and it will be combined with the GS-XGBoost regression algorithm model to obtain the optimal boundary conditions of the model. Finally, the optimal boundary condition parameters are substituted into the three-dimensional finite-difference calculation model for stress calculation, and the distribution of the in-situ stress field of the entire calculation model is obtained. Finally, the level of large deformation of the Haba Snow Mountain Tunnel will be determined. The results show that the ground stress of the tunnel increases with the increase of burial depth, with the maximum horizontal principal stress of 38.03 MPa and the minimum horizontal principal stress of 26.07 MPa. The Haba Snow Mountain Tunnel has large deformation problems of levels I, II, III, and IV. Level III and IV large deformations are generally accompanied by higher ground stress (above 28 MPa) and smaller surrounding rock strength. The distribution of surrounding rock strength along the tunnel axis shows a clear "W" shape, opposite to the surface elevation "M" shape. It is inferred that the mountain may be affected by geological structures on both sides of the north and south, causing more severe compression of the tunnel surrounding rock at the peak.

INVESTIGATION OF A DISCRETE STURM–LIOUVILLE PROBLEM WITH TWO-POINT NONLOCAL BOUNDARY CONDITION AND NATURAL APPROXIMATION OF A DERIVATIVE IN BOUNDARY CONDITION

The article investigates a discrete Sturm–Liouville problem with one natural boundary condition and another nonlocal two-point boundary condition. We analyze zeroes, poles and critical points of the characteristic function and how the properties of this function depend on parameters in nonlocal boundary condition. Properties of the Spectrum Curves are formulated and illustrated in figures.

A new stacking model method to solve an inverse flow and heat coupling problem for aero-engine turbine blades

The whole temperature distribution of a turbine blade is an important information for heat transfer design for turbine, but it is very difficult and expensive to measure the whole temperature filed, especially for the internal points of a blade. It is necessary to reconstruct the whole temperature distribution by calculating reversely unknown parameters based on sparse temperature values on the blade surface. This paper proposes a new stacking model method for solving inverse heat transfer problems of boundary conditions and it can be applied to cope with multi-input and multi-output regression problems. In order to improve the prediction performance of the stacking model, the Random Forest Regression, the XGBoost Regression and the K-Nearest Neighbors Regression are selected as the base estimators, and the Linear Regression is selected as the meta estimator. An application example for an aero-engine turbine blade is modeled and solved, in which the boundary condition parameters of the exhaust flows are reversely calculated and temperature distributions of a turbine blade surface can be obtained. Numerical experiments have demonstrated that the stacking model outperforms individual base models. This research is of considerable significance to heat transfer design, experimental research and decision support for real-time remote monitoring of aero-engines.

Monotone Positive Solutions for Nonlinear Fractional Differential Equations with a Disturbance Parameter on the Infinite Interval

This paper is concerned with the existence and multiplicity of monotone positive solutions for a class of nonlinear fractional differential equation with a disturbance parameter in the integral boundary conditions on the infinite interval. By using Guo–Krasnosel’skii fixed-point theorem and the analytic technique, we divide the range of parameter for the existence of at least two, one and no positive solutions for the problem. In the end, an example is given to illustrate our main results.

Transverse free vibration analysis of thin sectorial plates by the weak form quadrature element method

The weak form quadrature element method is applied to free vibration analysis of thin sectorial plates with arbitrary vertex angles and boundary conditions. To tackle the strong stress singularity around the vertex, analytical displacement descriptions are introduced into the inner sectorial subdomain, while the outer annular subdomain is modeled by a single weak form quadrature thin plate element. The continuity on the interface between the two subdomains is enforced afterwards. Eventually, a generalized eigenvalue formulation is established after introducing Hamilton’s principle. The first six non-dimensional frequency parameters for various vertex angles and boundary conditions are obtained and compared with available results. Several typical free vibration modes are plotted. The accuracy, convergence rate, and computational cost of the present formulation are discussed at length.

Probing of operation economy for coal-fired unit under low loads with two fixed boundary conditions

Coal-fired power plants are forced to participate in deep peak shaving of power grid. As load of peak shaving unit further decreases to 30 % or less, operation economy of coal-fired unit at ultra low load has become one of the main focuses of concern after unit flexibility. Excessive air coefficient, as an important technical parameter affecting economic operation of unit, can be enhanced to maintain combustion stability at low loads under stationary fuel boundary condition (SFBC) and stationary steam parameters boundary condition (SSBC). To obtain energy consumption characteristics of 660 MW supercritical unit during steady-state processes of SFBC and SSBC, the model of influence of excess air coefficient on overall performance and main parameters of unit is further developed. Subsequently, quantitative evaluation and analysis of unit performance on variable excess air coefficient is executed under modes of SFBC and SSBC. Influence mechanism of excess air coefficient on operation parameters and energy consumption characteristics of unit is revealed and clarified. Pre-eminently, evolution mechanism for heat rate and relative internal efficiency of steam turbine, steam temperature and coal consumption rate is given quantitatively and firstly.Results demonstrates that, SSBC mode is more economical for unit running with excess air coefficient lower than 1.3. With excess air coefficient higher than 1.4, economic difference between two operation modes is small. However, load as low as 30 % boiler maximum continuous rating (BMCR), SFBC mode shows its advantages, which is more suitable for peak shaving of ultra low load. Maximum difference in coal consumption under two operation modes is up to 0.5 g/kWh corresponding optimal operating range of excess air coefficient at 30 % BMCR. This study is expected to provide a detailed reference for upgrading operation economy of coal-fired power plants during low load peak shaving.

A Data-Driven Variance Reduction Technique for Efficiently Modelling Astronaut Radiation Doses in Spacecraft in High-Energy Isotropic Radiation Fields.

The ionizing radiation exposure to crew on current and future space missions can significantly increase their health risks for cancers, degenerative diseases, and other acute and late effects. A common approach for estimating risk to crew is by completing stochastic (e.g., Monte Carlo) or deterministic particle transport simulations. Within the simulated environment, a small fraction of the particle histories tracked will interact with the astronaut or detector, particularly for larger spacecraft such as the International Space Station, Tiangong Space Station or Lunar Gateway. These simulations can be computationally intensive as they require a very large number of particle histories to achieve a low statistical uncertainty. Variance reduction techniques are applied to simulations to reduce the computational time of the simulation while maintaining the same (or less) statistical uncertainty. The variance reduction technique developed herein involves applying a directional source bias to an isotropic radiation field, such as galactic cosmic rays, to reduce the quantity of particles that have a low probability of interacting with the astronaut or detector. A custom application has been developed utilizing the Geant4 Toolkit that computes the trajectories and energies of particles in three dimensions in the International Space Station using the Monte Carlo method. The results demonstrate the impact of our variance reduction technique on effective dose equivalence depending on: primary and secondary particle type (proton, neutron, photon, heavy ion, etc.), geometric volumes and spacecraft materials. Our variance reduction technique can be tuned by the user to optimize the simulation time depending on their objectives and enables rapid testing of different shield configurations and materials. This variance reduction technique is implemented easily using several input parameters for boundary conditions. Recommended values are presented for rapid implementation in simulations.

Exact rate of accelerated propagation in the Fisher-KPP equation with nonlocal diffusion and free boundaries

Accelerated propagation is a new phenomenon associated with nonlocal diffusion problems. In this paper, we determine the exact rate of accelerated propagation in the Fisher-KPP equation with nonlocal diffusion and free boundaries, where the nonlocal diffusion operator is given by ∫RJ(x-y)u(t,y)dy-u(t,x)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\displaystyle \\int _{\\mathbb {R}}J(x-y)u(t,y)dy-u(t,x)$$\\end{document}, and the kernel function J(x) behaves like a power function near infinity, namely lim|x|→∞J(x)|x|α=λ>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lim _{|x|\\rightarrow \\infty } J(x)|x|^{\\alpha }=\\lambda >0$$\\end{document} for some α∈(1,2]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\in (1,2]$$\\end{document}. This is the precise range of α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} where accelerated spreading can happen for such kernels. By constructing subtle upper and lower solutions, we prove that the location of the free boundaries x=h(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x=h(t)$$\\end{document} and x=g(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x=g(t)$$\\end{document} goes to infinity at exactly the following rates: limt→∞h(t)tlnt=limt→∞-g(t)tlnt=μλ,whenα=2,limt→∞h(t)t1/(α-1)=limt→∞-g(t)t1/(α-1)=22-α2-αμλ,whenα∈(1,2).\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} {\\left\\{ \\begin{array}{ll} \\displaystyle \\lim _{t\\rightarrow \\infty }\\frac{h(t)}{t\\ln t}=\\lim _{t\\rightarrow \\infty }\\frac{-g (t)}{t\\ln t}=\\mu \\lambda ,&{} \\hbox { when } \\alpha =2,\\\\ \\displaystyle \\lim _{t\\rightarrow \\infty }\\frac{h(t)}{ t^{1/(\\alpha -1)}}= \\lim _{t\\rightarrow \\infty }\\frac{-g (t)}{ t^{1/(\\alpha -1)}}=\\frac{2^{2-\\alpha }}{2-\\alpha }\\mu \\lambda , &{} \\hbox { when } \\alpha \\in (1,2). \\end{array}\\right. } \\end{aligned}$$\\end{document}Here μ>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu >0$$\\end{document} is a given parameter in the free boundary condition. Accelerated propagation can also happen when lim|x|→∞J(x)|x|(ln|x|)β=λ>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lim _{|x|\\rightarrow \\infty }J(x)|x|(\\ln |x|)^\\beta =\\lambda >0$$\\end{document} for some β>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta >1$$\\end{document}. For this case, we prove that -g(t),h(t)=exp{[(2βμλβ-1)1/β+o(1)]t1/β}ast→∞.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} -g (t), h(t)=\\exp \\Big \\{\\Big [\\Big (\\frac{2\\beta \\mu \\lambda }{\\beta -1}\\Big )^{1/\\beta }+o(1)\\Big ]t^{1/\\beta }\\Big \\} \\hbox { as } t\\rightarrow \\infty . \\end{aligned}$$\\end{document}These results considerably sharpen the corresponding ones in [20], and the techniques developed here open the door for obtaining similar precise results for other problems. A crucial technical point is that such precise conclusions on the propagation are achievable by finding the correct improvements on the form of the lower solutions used in [20], even though the precise long-time profile of the density function u(t, x) is still lacking.

Analisis Modifikasi Desain pada Lokomotif CC-201 Tipe GE U18C dengan Metode Simulasi CFD

The CC-201-type U18C locomotives are widely used for public transportation in Indonesia. Like other modes of transportation or vehicles, the body's design is an important factor to consider because it influences the aerodynamic capabilities of the vehicle. The study aims to analyze the effect of variations in the design angle of the CC-201 type U18C locomotive body on the coefficient of drag and aerodynamics. The method used in this research is CFD simulation using CAE-based engineering software, Ansys Fluent R2 2022. CFD simulations were performed on locomotive body designs with angle variations of 90°, 135°, and 150° using the same boundary condition parameters. The results show that the locomotive body design with the 60° variation has the smallest drag coefficient value of 0.51076379. The study conclusion explains that changing the angle of 150 degrees at the top of the GE U18C-type locomotive body has a significant effect on lowering the value of the drag coefficient by up to 29%.

Hairy black holes in AdS with Robin boundary conditions

We study hairy black holes in Einstein-Maxwell-complex scalar theory in four-dimensional asymptotically global anti-de Sitter (AdS) spacetime when the Robin boundary conditions are imposed on the scalar field. This setup is dual to the double trace deformation of strongly interacting field theory on R × S2 by charged scalar operators. We identify the instability of the Reissner-Nordström-AdS (RNAdS) black holes under the Robin boundary conditions and construct backreacted geometries branching at the onset of the instability. Also considering associated horizonless geometries called boson stars, we obtain phase diagrams with fairly rich structure in the grand canonical ensemble depending on the boundary condition parameter or the deformation parameter, where phase transition occurs between thermal AdS, RNAdS, charged boson stars, and hairy black holes.

Bayesian approach to micromechanical parameter identification using Integrated Digital Image Correlation

Micromechanical parameters are essential in understanding the behavior of materials with a heterogeneous structure, which helps to predict complex physical processes such as delamination, cracks, and plasticity. However, identifying these parameters is challenging due to micro-macro length scale differences, required high resolution, and ambiguity in boundary conditions, among others. The Integrated Digital Image Correlation (IDIC) method, a state-of-the-art full-field deterministic approach to parameter identification, is widely used but suffers from high sensitivity to boundary data errors and is limited to identification of parameters within well-posed problems. This article employs Bayesian approach to estimate micromechanical shear and bulk moduli of fiber-reinforced composite samples under plane strain assumption, and to improve handling of boundary noise. The main purpose of this article is to quantify the effect of uncertainty in the boundary conditions in the stochastic setting. To this end, the Metropolis–Hastings Algorithm (MHA) is employed to estimate probability distributions of bulk and shear moduli and boundary condition parameters using IDIC, considering a fiber-reinforced composite sample under plane strain assumption. The performance and robustness of the MHA are compared to two versions of deterministic IDIC method, under artificially introduced random and systematic errors in kinematic boundary conditions. Although MHA is shown to be computationally more expensive and in certain cases less accurate than the recently introduced Boundary-Enriched IDIC, it offers significant advantages, in particular being able to optimize a large number of parameters while obtaining statistical characterization as well as insights into individual parameter relationships. The paper furthermore highlights the benefits of the non-normalized approach to parameter identification with MHA (leading, within deterministic IDIC, to an ill-posed formulation), which significantly improves the robustness in handling the boundary noise.

A Vector Fitting Approach for the Automated Estimation of Lumped Boundary Conditions of 1D Circulation Models.

The choice of appropriate boundary conditions is a crucial step in the development of cardiovascular models for blood flow simulations. The three-element Windkessel model is usually employed as a lumped boundary condition, providing a reduced order representation of the peripheral circulation. However, the systematic estimation of the Windkessel parameters remains an open problem. Moreover, the Windkessel model is not always adequate to model blood flow dynamics, which often require more elaborate boundary conditions. In this study, we propose a method for the estimation of the parameters of high order boundary conditions, including the Windkessel model, from pressure and flow rate waveforms at the truncation point. Moreover, we investigate the effect of adopting higher order boundary conditions, corresponding to equivalent circuits with more than one storage element, on the accuracy of the model. The proposed technique is based on Time-Domain Vector Fitting, a modeling algorithm that, given samples of the input and output of a system, such as pressure and flow waveforms, can derive a differential equation approximating their relation. The capabilities of the proposed method are tested on a 1D circulation model consisting of the 55 largest human systemic arteries, to demonstrate its accuracy and its usefulness to estimate boundary conditions with order higher than the traditional Windkessel models. The proposed method is compared to other common estimation techniques, and its robustness in parameter estimation is verified in presence of noisy data and of physiological changes of aortic flow rate induced by mental stress. Results suggest that the proposed method is able to accurately estimate boundary conditions of arbitrary order. Higher order boundary conditions can improve the accuracy of cardiovascular simulations, and Time-Domain Vector Fitting can automatically estimate them.

Predict the fatigue unloading elastic-plastic reduction mechanism of single crystal 3C-SiC Newton layer by reconstructed multi-dimensional dynamic static combination indenter

To explore the elasto-plastic reduction mechanism of single crystal 3C-SiC Newton layer under fatigue unloading. Reconstructed multi-dimensional single crystal 3C-SiC Newton layer unloading dynamic - static combined head. The evolution law of dislocation loop, the trend of load displacement and the direction of strain concentration expansion during fatigue unloading are analyzed. According to the stress characteristics of nanoindentation process and the requirements of real indentation environment, the NVE ensemble matrix and boundary condition parameters are integrated and optimized. The influence of indenter shape on the evolution process of dislocation ring emergence, fracture and connection and the evolution mechanism are analyzed. Through diamond identification method and stress-strain analysis method, the multi-dimensional force analysis of plastic unloading of nano-indentation is realized. It is found that the yield limit of semi-circular indenter first reaches the yield limit from the elastoplastic loading stage to the plastic loading stage than the normal four-cone. Combined with the load displacement curve, the real stress characteristics of the nano-indentation single crystal 3C-SiC Newton layer are analyzed. The results show that elastoplastic reduction existed in fatigue unloading, and the generation and development of micro-dislocation rings in elastoplastic deformation reduction under fatigue unloading of different dimensions indenter are different. The ultimate yield stress of semi-circular indenter is 3.82GPa and the ultimate strain is 1 %，the ultimate yield stress of positive quad conical indenter is 6.60GPa and the ultimate strain is 1.5 %. The elasto-plastic reduction mechanism of fatigue unloading is directly driven by the plastic evolution mechanism of dislocation ring.

Classification models for impact damage of fiber reinforced concrete panels using Tree-based learning algorithms

This study aims to develop the machine learning models for classification of the local damage levels of FRC panels subjected to missile impact load using the tree-based algorithms and ensembles. Six different algorithms, including Decision Tree, Random Forest, Bagging, AdaBoost, XGBoost, and CatBoost were trained and evaluated based on a dataset collected from 176 experiments of FRC panels under missile impact, which consists of 15 input parameters of geometries, materials, and boundary conditions and one output parameter of local damage level of FRC panels. The Bayesian Optimization algorithm and k-fold cross validation were also utilized to achieve higher accuracy in prediction ability of the models. The obtained results showed that the proposed models can predict the local damage of FRC panels subjected to the missile impact load with acceptable accuracy. The models using ensemble methods have better performance than single estimator model in prediction and each model using ensemble method has its own strength and is suitable for different criteria when classifying. For imbalanced dataset, Random Forest can be chosen as the most suitable classification model for the dataset in this study.

Inverse scattering problem for Sturm-Liouville equation with a rational function of spectral parameter in boundary condition

Inverse scattering problem for Sturm-Liouville equation with a rational function of spectral parameter in boundary condition

Boundary conditions determined by experimentally measured surface properties for wave-based time-domain simulations

Boundary conditions are essential and necessary when simulating sound wave propagation inside an enclosed space. In this work, complex-valued surface acoustical properties for the actual materials are obtained from impedance tube measurements. This work applies model-based Bayesian inference to estimate the exact parameters for arbitrary boundary conditions. The Bayesian approach presented in this work demonstrates the capability to predict the complex-valued surface boundary function of frequency in broadband ranges. This approach is equivalently applicable in different boundary models in time domain depending on wave-based numerical methods used for acoustic modelings, such as the spectral element method or finite-difference time-domain method. With the accurately estimated boundary models, the efficacy of the boundary conditions is explored within the time-domain approaches.

Inverse Sturm–Liouville Problem with Spectral Parameter in the Boundary Conditions

In this paper, for the first time, we study the inverse Sturm–Liouville problem with polynomials of the spectral parameter in the first boundary condition and with entire analytic functions in the second one. For the investigation of this new inverse problem, we develop an approach based on the construction of a special vector functional sequence in a suitable Hilbert space. The uniqueness of recovering the potential and the polynomials of the boundary condition from a part of the spectrum is proved. Furthermore, our main results are applied to the Hochstadt–Lieberman-type problems with polynomial dependence on the spectral parameter not only in the boundary conditions but also in discontinuity (transmission) conditions inside the interval. We prove novel uniqueness theorems, which generalize and improve the previous results in this direction. Note that all the spectral problems in this paper are investigated in the general non-self-adjoint form, and our method does not require the simplicity of the spectrum. Moreover, our method is constructive and can be developed in the future for numerical solution and for the study of solvability and stability of inverse spectral problems.

A ghost-point smoothing strategy for geometric multigrid on curved boundaries

We present a Boundary Local Fourier Analysis (BLFA) to optimize the relaxation parameters of boundary conditions in a multigrid framework. The method is implemented to solve elliptic equations on curved domains embedded in a uniform Cartesian mesh, although it is designed to be extended for general PDEs in curved domains, wherever a multigrid technique can be implemented. The boundary is implicitly defined by a level-set function and a ghost-point technique is employed to treat the boundary conditions. Existing strategies in literature adopt a constant relaxation parameter on the whole boundary. In this paper, the relaxation parameters are optimized in terms of the distance between ghost points and boundary, with the goal of smoothing the residual along the tangential direction. Theoretical results are confirmed by several numerical tests in 1D, 2D and 3D, showing that the convergence factor associated with the smoothing on internal equations is not degraded by boundary effects.

Acoustic insulation characteristics improvement of a thick CNT-reinforced doubly-curved shell by using GPLRC and MEE composite layers

Noise reduction in structures and human living environments is one of the most important issues in engineering that is always given special attention. Sound insulation has always been improved using different methods, one of which is to use the properties of materials. Herewith, the aim of this paper is to take advantage of graphene-platelet reinforced composites and magneto-electro-elastic (MEE) material properties for sound attenuation. The present paper deals with the analysis of sound transmission loss (STL) through a three-layer sandwich doubly-curved shell where an MEE sheet is integrated with two nanocomposite sheets. In addition, these two nanocomposite sheets are reinforced by functionally graded (FG) distributions of CNT and graphene platelet (GPL)-reinforced composites, respectively. Firstly, the three-dimensional elasticity theory is employed to derive the governing equations of motion. Then, the vibroacoustic analysis for the resultant equations is completed according to the state space and transfer matrix method. Comparing the obtained results with the available literature discloses that the offered procedure has a high precision for structural acoustic problems. In the next step, in addition to inspecting two kinds of MEE composites, the effective parameters, such as layup configuration, FG distribution, volume fraction, weight fraction, radii of curvature, electromagnetic boundary conditions, and interphase thickness, are assessed on the STL. This assessment shows that the parameters involved in this paper are highly interdependent. Accordingly, the analysis of these parameters is done simultaneously with the aid of three- and four-dimensional plots in order that the optimal value for each parameter can be realized. As seen clearly in the outcomes, the electromagnetic boundary conditions parameters, compared to the other parameters, can much more alter the STL trend, so that a slight change in electric potential results in great change in the STL.

ESTIMATING THE QUALITY FUNCTIONAL IN OPTIMAL CONTROL VARIATIONAL CALCULUS TASKS UNDER THE CHANGES OF THE LEFT-HAND ARGUMENT OF BOUNDARY CONDITION

Estimating the quality functional in optimal control variational calculus tasks under the changes of boundary condition is considered. In control systems, there is a certain permissible change of the controlled parameter based on which the control system is designed. Unlike ordinary control systems, in optimal control systems, there is another indicator - the quality functional (optimality criteria), which also depends on the controlled parameters. Therefore, the permissible range of changes of controlled parameters in optimal control systems should be determined based on the quality functional value’s tolerances. Therefore, estimating the quality functional under the changes of boundary conditions has theoretical and practical importance. It is particularly important for problems solved by numerical methods because it is quite simple for problems solved analytically. In this article, the estimation methods of the quality functional under the changes of left-hand argument of boundary condition in the form of Taylor series with an accuracy of the second member in optimal control variational calculus tasks solved by the indirect nu-merical method are developed. According to the developed method, both the optimization function and the quality functional are functions of the left-hand argument of boundary condition. In other words, the boundary condition parameter is an argument of the optimi-zation function. The mathematical apparatus for determining the specified series coeffi-cients has been developed. These coefficients depend on the partial derivatives of the op-timization function by boundary parameter. The boundary conditions for partial deriva-tive functions of the optimal function by boundary parameters, and the determination methods for these functions using the known optimal function are studied. The truth of the Taylor series coefficients, and the algorithm for their determination are shown experimen-tally.