scholarly journals Mathematical Models with Buckling and Contact Phenomena for Elastic Plates: A Review

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 566
Author(s):  
Aliki D. Muradova ◽  
Georgios E. Stavroulakis
Keyword(s):  
Mathematical Models ◽  
Initial Conditions ◽  
Nonlinear Partial Differential Equations ◽  
Composite Plates ◽  
Contact Problems ◽  
Elastic Plates ◽  
Advantages And Disadvantages ◽  
Contact Models ◽  
Set Up ◽  
Unilateral Contact Problems

A review of mathematical models for elastic plates with buckling and contact phenomena is provided. The state of the art in this domain is presented. Buckling effects are discussed on an example of a system of nonlinear partial differential equations, describing large deflections of the plate. Unilateral contact problems with buckling, including models for plates, resting on elastic foundations, and contact models for delaminated composite plates, are formulated. Dynamic nonlinear equations for elastic plates, which possess buckling and contact effects are also presented. Most commonly used boundary and initial conditions are set up. The advantages and disadvantages of analytical, semi-analytical, and numerical techniques for the buckling and contact problems are discussed. The corresponding references are given.

Review of classification studies for machine learning in the development of intelligent management decision support systems

2020 ◽  
Vol 89 ◽  
pp. 20-29
Author(s):  
Sh. K. Kadiev ◽  
◽  
R. Sh. Khabibulin ◽  
P. P. Godlevskiy ◽  
V. L. Semikov ◽  
...  
Keyword(s):  
Machine Learning ◽  
Decision Support ◽  
Mathematical Models ◽  
Decision Support Systems ◽  
Support Systems ◽  
Management Decision ◽  
Classification Methods ◽  
Advantages And Disadvantages ◽  
Intelligent Management ◽  
Management Decision Support

Introduction. An overview of research in the field of classification as a method of machine learning is given. Articles containing mathematical models and algorithms for classification were selected. The use of classification in intelligent management decision support systems in various subject areas is also relevant. Goal and objectives. The purpose of the study is to analyze papers on the classification as a machine learning method. To achieve the objective, it is necessary to solve the following tasks: 1) to identify the most used classification methods in machine learning; 2) to highlight the advantages and disadvantages of each of the selected methods; 3) to analyze the possibility of using classification methods in intelligent systems to support management decisions to solve issues of forecasting, prevention and elimination of emergencies. Methods. To obtain the results, general scientific and special methods of scientific knowledge were used - analysis, synthesis, generalization, as well as the classification method. Results and discussion thereof. According to the results of the analysis, studies with a mathematical formulation and the availability of software developments were identified. The issues of classification in the implementation of machine learning in the development of intelligent decision support systems are considered. Conclusion. The analysis revealed that enough algorithms were used to perform the classification while sorting the acquired knowledge within the subject area. The implementation of an accurate classification is one of the fundamental problems in the development of management decision support systems, including for fire and emergency prevention and response. Timely and effective decision by officials of operational shifts for the disaster management is also relevant. Key words: decision support, analysis, classification, machine learning, algorithm, mathematical models.

scholarly journals On Kaufmann's theory of the impact of the pianoforte hammer

1920 ◽  
Vol 97 (682) ◽  
pp. 99-110 ◽  
Keyword(s):  
Initial Conditions ◽  
Practical Importance ◽  
Prima Facie ◽  
Point Of View ◽  
Infinite Length ◽  
Modes Of Vibration ◽  
Rigorous Treatment ◽  
The Subject ◽  
Set Up ◽  
The Impact

The theory of the vibrations of the pianoforte string put forward by Kaufmann in a well-known paper has figured prominently in recent discussions on the acoustics of this instrument. It proceeds on lines radically different from those adopted by Helmholtz in his classical treatment of the subject. While recognising that the elasticity of the pianoforte hammer is not a negligible factor, Kaufmann set out to simplify the mathematical analysis by ignoring its effect altogether, and treating the hammer as a particle possessing only inertia without spring. The motion of the string following the impact of the hammer is found from the initial conditions and from the functional solutions of the equation of wave-propagation on the string. On this basis he gave a rigorous treatment of two cases: (1) a particle impinging on a stretched string of infinite length, and (2) a particle impinging on the centre of a finite string, neither of which cases is of much interest from an acoustical point of view. The case of practical importance treated by him is that in which a particle impinges on the string near one end. For this case, he gave only an approximate theory from which the duration of contact, the motion of the point struck, and the form of the vibration-curves for various points of the string could be found. There can be no doubt of the importance of Kaufmann’s work, and it naturally becomes necessary to extend and revise his theory in various directions. In several respects, the theory awaits fuller development, especially as regards the harmonic analysis of the modes of vibration set up by impact, and the detailed discussion of the influence of the elasticity of the hammer and of varying velocities of impact. Apart from these points, the question arises whether the approximate method used by Kaufmann is sufficiently accurate for practical purposes, and whether it may be regarded as applicable when, as in the pianoforte, the point struck is distant one-eighth or one-ninth of the length of the string from one end. Kaufmann’s treatment is practically based on the assumption that the part of the string between the end and the point struck remains straight as long as the hammer and string remain in contact. Primâ facie , it is clear that this assumption would introduce error when the part of the string under reference is an appreciable fraction of the whole. For the effect of the impact would obviously be to excite the vibrations of this portion of the string, which continue so long as the hammer is in contact, and would also influence the mode of vibration of the string as a whole when the hammer loses contact. A mathematical theory which is not subject to this error, and which is applicable for any position of the striking point, thus seems called for.

scholarly journals Study on the applications of two analytical methods for the construction of traveling wave solutions of the modified equal width equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1003-1010
Author(s):  
Asıf Yokuş ◽  
Hülya Durur ◽  
Taher A. Nofal ◽  
Hanaa Abu-Zinadah ◽  
Münevver Tuz ◽  
...  
Keyword(s):  
Traveling Wave ◽  
Analytical Methods ◽  
Nonlinear Evolution ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Dark Soliton ◽  
Mathematical Tool ◽  
Symbolic Calculation ◽  
Advantages And Disadvantages ◽  
Wave Solutions

Abstract In this article, the Sinh–Gordon function method and sub-equation method are used to construct traveling wave solutions of modified equal width equation. Thanks to the proposed methods, trigonometric soliton, dark soliton, and complex hyperbolic solutions of the considered equation are obtained. Common aspects, differences, advantages, and disadvantages of both analytical methods are discussed. It has been shown that the traveling wave solutions produced by both analytical methods with different base equations have different properties. 2D, 3D, and contour graphics are offered for solutions obtained by choosing appropriate values of the parameters. To evaluate the feasibility and efficacy of these techniques, a nonlinear evolution equation was investigated, and with the help of symbolic calculation, these methods have been shown to be a powerful, reliable, and effective mathematical tool for the solution of nonlinear partial differential equations.

Perceived Advantages and Disadvantages of Nonsmoking Sections in Restaurants: Topics to Communicate to Restaurateurs

1989 ◽  
Vol 9 (4) ◽  
pp. 299-304 ◽  
Author(s):  
Gerardo Marin ◽  
Raymond J. Gamba
Keyword(s):  
San Francisco ◽  
Advantages And Disadvantages ◽  
Set Up

Results from interviews with 315 restaurateurs in San Francisco are reported on their perceptions of the advantages and disadvantages of having a nonsmoking section in their restaurants. The major advantage of having a nonsmoking section independent of whether one is present is to please customers. The most commonly mentioned disadvantage for those restaurants with nonsmoking sections is the fact that it is inconvenient to clients' seating preferences primarily because it breaks up dining parties. Efforts at convincing restaurateurs to set up nonsmoking sections may be directed at pointing out savings in cleaning, labor, insurance, and the improvement of the health of their employees together with meeting clients' desires.

Vibration of Rectangular Plates by the Ritz Method

1950 ◽  
Vol 17 (4) ◽  
pp. 448-453 ◽  
Author(s):  
Dana Young
Keyword(s):  
Ritz Method ◽  
Normal Modes ◽  
Approximate Solutions ◽  
The Other ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Modes Of Vibration ◽  
Ritz’S Method ◽  
Square Plate ◽  
Set Up

Abstract Ritz’s method is one of several possible procedures for obtaining approximate solutions for the frequencies and modes of vibration of thin elastic plates. The accuracy of the results and the practicability of the computations depend to a great extent upon the set of functions that is chosen to represent the plate deflection. In this investigation, use is made of the functions which define the normal modes of vibration of a uniform beam. Tables of values of these functions have been computed as well as values of different integrals of the functions and their derivatives. With the aid of these data, the necessary equations can be set up and solved with reasonable effort. Solutions are obtained for three specific plate problems, namely, (a) square plate clamped at all four edges, (b) square plate clamped along two adjacent edges and free along the other two edges, and (c) square plate clamped along one edge and free along the other three edges.

The Nonstationary Effects in Asymmetric, Angle-Ply Laminated Composite Plates

1993 ◽  
Author(s):  
Ross M. Evan-Iwanowski ◽  
J. F. Nayfeh ◽  
C. H. Lu
Keyword(s):  
Initial Conditions ◽  
Laminated Composite ◽  
Composite Plates ◽  
Bench Mark ◽  
Laminated Composite Plates ◽  
Composite Columns ◽  
Decisive Effect ◽  
Initial Values ◽  
Excitation Frequencies ◽  
Nonstationary Effects

Abstract The system in the title has been subjected to a parametric, nonstationary (NS) linear v(t) = v0 + βt, and cyclic v(t) = v0 ± γ sin βt excitations. The NS linear responses settle on the initial, constant values for extended values of the excitation frequencies, thus they stabilize the stationary (ST) response. This is true for the initial conditions taken on the stationary curve, and for different ply-angles. For the initial conditions (I.C.) beyond the ST plots, the NS responses stay also near the initial conditions, but they have the wavy forms, which increase slightly for the lower values of the forcing frequencies. For the cyclic parametric excitations, the NS responses are cyclic contained within the ranges of the excitation amplitudes ±β and (finite) response amplitudes above the ST initial values, raising up and down within these limits. It appears that they cover the whole area within the above described constraints. The decisive effect of the cyclic NS inputs, i.e., almost instantaneous cyclic responses replacing the ST responses regardless of the I.C. and ST responses, is a bench mark of the cyclic NS. This behavior is distinctly different from the NS cyclic responses of the composite columns.

Modeling and prediction for the oxidation efficiency of magnesium sulfite in aeration tank of magnesium-based seawater exhaust gas clean system

2017 ◽  
Vol 233 (1) ◽  
pp. 164-173
Author(s):  
Quan Liu ◽  
Yimin Zhu ◽  
Tie Li ◽  
Xiaojia Tang ◽  
Weifeng Liu ◽  
...  
Keyword(s):  
Flow Field ◽  
Initial Conditions ◽  
Negative Impact ◽  
Fluid Model ◽  
Aeration Tank ◽  
Exhaust Gas ◽  
Clean System ◽  
Physics Modeling ◽  
Set Up ◽  
Oxidation Efficiency

In magnesium-based seawater exhaust gas clean system, the desulfurization by-product, magnesium sulfite (MgSO3), has a negative impact on the ecological environment, which needs to be treated to make harmless. Due to the limited space on board, the aeration oxidation method is used to convert it to magnesium sulfate. Because of the variable size, shape and flow field of aeration tank, it is difficult and expensive to design and verify the oxidation efficiency of the aeration tank by experimental method. In this work, in order to predict the oxidation efficiency accurately, RFlow, a computational fluid dynamics software, was used to analyze the flow field and MgSO3 oxidation reaction in aeration tank. The subdomain technology was adopted for physics modeling and mesh generation of the aeration tank, and the total number of meshes was 285,000. The multi-phase flow field model was set up using the multi-fluid model and dispersive k-ε turbulence model. Under the given initial conditions, the predicted oxidation efficiency was 94.2%. Compared with the results of the actual ship test, the prediction model for MgSO3 oxidation efficiency of the aeration tank is reliable.

scholarly journals World Experience in Creating Mathematical Models of Air Springs: Advantages and Disadvantages

2021 ◽  
pp. 25-42
Author(s):  
A. Y Kuzyshyn ◽  
S. A Kostritsia ◽  
Yu. H Sobolevska ◽  
А. V Batih
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Mathematical Models ◽  
Dynamic Behavior ◽  
High Speed ◽  
Vertical Direction ◽  
Rolling Stock ◽  
Air Spring ◽  
Advantages And Disadvantages ◽  
Mechanical Models

Purpose. Taking into account the production and commissioning of modern high-speed rolling stock, the authors are aimed to analyze the currently created mathematical models describing the dynamic behavior of the air spring, systematize them and consider the advantages and disadvantages of each model type. Methodology. For the analysis, a comparative chronological method was used, which makes it possible to trace the development of several points of view, concepts, theories. In accordance with the adopted decision equations, the existing models of air springs were divided into three groups: mechanical, thermodynamic and finite-elements. When analyzing mathematical models, the influence of a number of parameters on the dynamic behavior of the air spring, such as disturbing force frequency, heat transfer, nonlinear characteristics of materials, the shape of the membrane, etc., was considered. Findings. A feature of mechanical models is the determination of input parameters based on the analysis of experimental results, requires access to complex measuring equipment and must be performed for each new model of an air spring separately. Unlike mechanical models, which allow taking into account the damping effect of an air spring in the horizontal and vertical direction, thermodynamic models are mainly focused on studying the dynamic behavior of an air spring in the vertical direction. The use of the finite element method makes it possible to most accurately reproduce the dynamic behavior of an air spring, however, it requires significant expenditures of time and effort to create a finite element model and perform calculations. Originality. Mathematical models of the dynamic behavior of an air spring are systematized, and the importance of their study in conjunction with a spatial mathematical model of high-speed rolling stock is emphasized. Practical value. The analysis of the mathematical models of the dynamic behavior of the air spring shows the ways of their further improvement, indicates the possibility of their use in the spatial mathematical model of the rolling stock in accordance with the tasks set. It will allow, even at the design stage of high-speed rolling stock, to evaluate its dynamic characteristic and traffic safety indicators when interacting with a railway track.

Math Modeling of Vacuum Conductive Timber Drying

2014 ◽  
Vol 1040 ◽  
pp. 478-483
Author(s):  
M. Goreshnev ◽  
E. Litvishko
Keyword(s):  
Mathematical Modeling ◽  
Mass Transfer ◽  
Mathematical Models ◽  
Heat And Mass Transfer ◽  
Block Diagram ◽  
Calculated Data ◽  
Math Modeling ◽  
Advantages And Disadvantages ◽  
Transfer Problems

The article is devoted to the mathematical modeling of vacuum conductive timber drying. Analysis of known mathematical models allowed revealing their advantages and disadvantages. The modeling block diagram based on the drying periods is proposed. Lykov’s equations have been selected to solve heat and mass transfer problems. The comparison of experimental and calculated data has been conducted.

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