Search results for: instability modes

Authors: Chengfeng Fang, Mohamed Ali Sadakkathulla, Abdul Sheikh

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Ultra-high-performance fiber reinforced concrete (UHPFRC) is a specially formulated cement-based composite characterized with an ultra-high compressive strength (f_c^’ = 240 MPa) and a low water-cement ratio (W/B= 0.2). With such material characteristics, UHPFRC is favored for the design and constructions of structures required high structural performance and slender geometries. Unlike conventional concrete, the structural performance of members manufactured with UHPFRC has not yet been fully studied, particularly, for UHPFRC columns with high slenderness. In this study, the behaviors of slender UHPFRC columns under concentric or eccentric load will be investigated both experimentally and numerically. Four slender UHPFRC columns were tested under eccentric loads with eccentricities, of 0 mm, 35 mm, 50 mm, and 85 mm, respectively, and one UHPFRC beam was tested under four-point bending. Finite element (FE) analysis was conducted with concrete damage plasticity (CDP) modulus to simulating the load-middle height or middle span deflection relationships and damage patterns of all UHPFRC members. Simulated results were compared against the experimental results and observation to gain the confidence of FE model, and this model was further extended to conduct parametric studies, which aim to investigate the effects of slenderness regarding failure modes and load-moment interaction relationships. Experimental results showed that the load bearing capacities of the slender columns reduced with an increase in eccentricity. Comparisons between load-middle height and middle span deflection relationships as well as damage patterns of all UHPFRC members obtained both experimentally and numerically demonstrated high accuracy of the FE simulations. Based on the available FE model, the following parametric study indicated that a further increase in the slenderness of column resulted in significant decreases in the load-bearing capacities, ductility index, and flexural bending capacities.

Keywords: Eccentric loads, ductility index, RC column, slenderness, UHPFRC.

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Authors: Wann-Ming Wey

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In recent years, in addition to face the external threats such as energy shortages and climate change, traffic congestion and environmental pollution have become anxious problems for many cities. Considering private automobile-oriented urban development had produced many negative environmental and social impacts, the transit-oriented development (TOD) has been considered as a sustainable urban model. TOD encourages public transport combined with friendly walking and cycling environment designs, however, non-motorized modes help improving human health, energy saving, and reducing carbon emissions. Due to environmental changes often affect the planners’ decision-making; this research applies dynamic network process (DNP) which includes the time dependent concept to promoting friendly walking and cycling environmental designs as an advanced planning support system for environment improvements.

This research aims to discuss what kinds of design strategies can improve a friendly walking and cycling environment under TOD. First of all, we collate and analyze environment designing factors by reviewing the relevant literatures as well as divide into three aspects of “safety”, “convenience”, and “amenity” from fifteen environment designing factors. Furthermore, we utilize fuzzy Delphi Technique (FDT) expert questionnaire to filter out the more important designing criteria for the study case. Finally, we utilized DNP expert questionnaire to obtain the weights changes at different time points for each design criterion. Based on the changing trends of each criterion weight, we are able to develop appropriate designing strategies as the reference for planners to allocate resources in a dynamic environment. In order to illustrate the approach we propose in this research, Taipei city as one example has been used as an empirical study, and the results are in depth analyzed to explain the application of our proposed approach.

Keywords: Environment Planning Support Systems, Walking and Cycling, Transit-oriented Development (TOD), Dynamic Network Process (DNP).

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Authors: Z. M. Biyasheva, M. Zh. Tleubergenova, Y. A. Zaripova, A. L. Shakirov, V. V. Dyachkov

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In recent years, interest in ecogenetic and biomedical problems related to the effects on the population of radon and its daughter decay products has increased significantly. Of particular interest is the assessment of the consequence of irradiation at hazardous radon areas, which includes the Almaty region due to the large number of tectonic faults that enhance radon emanation. In connection with the foregoing, the purpose of this work was to study the genetic effects of exposure to supernormal radon doses on the alpha-radiation model. Irradiation does not affect the growth of the cell, but rather its ability to differentiate. In addition, irradiation can lead to somatic mutations, morphoses and modifications. These damages most likely occur from changes in the composition of the substances of the cell. Such changes are epigenetic since they affect the regulatory processes of ontogenesis. Variability in the expression of regulatory genes refers to conditional mutations that modify the formation of signs of intraspecific similarity. Characteristic features of these conditional mutations are the dominant type of their manifestation, phenotypic asymmetry and their instability in the generations. Currently, the terms “morphosis” and “modification” are used to describe epigenetic variability, which are maintained in Drosophila melanogaster cultures using linkaged X- chromosomes, and the mutant X-chromosome is transmitted along the paternal line. In this paper, we investigated the epigenetic effects of alpha particles, whose source in nature is mainly radon and its daughter decay products. In the experiment, an isotope of plutonium-238 (Pu²³⁸), generating radiation with an energy of about 5500 eV, was used as a source of alpha particles. In an experiment in the first generation (F₁), deformities or morphoses were found, which can be called "radiation syndromes" or mutations, the manifestation of which is similar to the pleiotropic action of genes. The proportion of morphoses in the experiment was 1.8%, and in control 0.4%. In this experiment, the morphoses in the flies of the first and second generation looked like black spots, or melanomas on different parts of the imago body; "generalized" melanomas; curled, curved wings; shortened wing; bubble on one wing; absence of one wing, deformation of thorax, interruption and violation of tergite patterns, disruption of distribution of ocular facets and bristles; absence of pigmentation of the second and third legs. Statistical analysis by the Chi-square method showed the reliability of the difference in experiment and control at P ≤ 0.01. On the basis of this, it can be considered that alpha particles, which in the environment are mainly generated by radon and its isotopes, have a mutagenic effect that manifests itself, mainly in the formation of morphoses or deformities.

Keywords: Alpha-radiation, genotoxicity, morphoses, radioecology, radon.

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Authors: Albert Albers, Pablo Enrique Leslabay

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The Institute of Product Development is dealing with the development, design and dimensioning of micro components and systems as a member of the Collaborative Research Centre 499 “Design, Production and Quality Assurance of Molded micro components made of Metallic and Ceramic Materials". Because of technological restrictions in the miniaturization of conventional manufacturing techniques, shape and material deviations cannot be scaled down in the same proportion as the micro parts, rendering components with relatively wide tolerance fields. Systems that include such components should be designed with this particularity in mind, often requiring large clearance. On the end, the output of such systems results variable and prone to dynamical instability. To save production time and resources, every study of these effects should happen early in the product development process and base on computer simulation to avoid costly prototypes. A suitable method is proposed here and exemplary applied to a micro technology demonstrator developed by the CRC499. It consists of a one stage planetary gear train in a sun-planet-ring configuration, with input through the sun gear and output through the carrier. The simulation procedure relies on ordinary Multi Body Simulation methods and subsequently adds other techniques to further investigate details of the system-s behavior and to predict its response. The selection of the relevant parameters and output functions followed the engineering standards for regular sized gear trains. The first step is to quantify the variability and to reveal the most critical points of the system, performed through a whole-mechanism Sensitivity Analysis. Due to the lack of previous knowledge about the system-s behavior, different DOE methods involving small and large amount of experiments were selected to perform the SA. In this particular case the parameter space can be divided into two well defined groups, one of them containing the gear-s profile information and the other the components- spatial location. This has been exploited to explore the different DOE techniques more promptly. A reduced set of parameters is derived for further investigation and to feed the final optimization process, whether as optimization parameters or as external perturbation collective. The 10 most relevant perturbation factors and 4 to 6 prospective variable parameters are considered in a new, simplified model. All of the parameters are affected by the mentioned production variability. The objective functions of interest are based on scalar output-s variability measures, so the problem becomes an optimization under robustness and reliability constrains. The study shows an initial step on the development path of a method to design and optimize complex micro mechanisms composed of wide tolerated elements accounting for the robustness and reliability of the systems- output.

Keywords: Micro molded components, Optimization, Robustness und Reliability, Simulation

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Authors: R. Bourziza, A. Hammani, M. Kuper, A. Bouaziz

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In oases, the surface water resources are becoming increasingly scarce and groundwater resources, which generally have a poor quality due to the high levels of salinity, are often overexploited. Water saving have therefore become imperative for better oases sustainability. If drip irrigation is currently recommended in Morocco for saving water and valuing, its use in the sub-desert areas does not keep water safe from high evaporation rates. An alternative to this system would be the use of subsurface drip irrigation. This technique is defined as an application of water under the soil surface through drippers, which deliver water at rates generally similar to surface drip irrigation. As subsurface drip irrigation is a recently introduced in Morocco, a better understanding of the infiltration process around a buried source, in local conditions, and its impact on plant growth is necessarily required. This study aims to contribute to improving the water use efficiency by testing the performance of subsurface irrigation system, especially in areas where water is a limited source. The objectives of this research are performance evaluation in arid conditions of the subsurface drip irrigation system for young date palms compared to the surface drip. In this context, an experimental test is installed at a farmer’s field in the area of Erfoud (Errachidia Province, southeastern Morocco), using the subsurface drip irrigation system in comparison with the classic drip system for young date palms. Flow measurement to calculate the uniformity of the application of water was done through two methods: a flow measurement of drippers above the surface and another one underground. The latter method has also helped us to estimate losses through evaporation for both irrigation techniques. In order to compare the effect of two irrigation modes, plants were identified for each type of irrigation to monitor certain agronomic parameters (cumulative numbers of palms and roots development). Experimentation referred to a distribution uniformity of about 88%; considered acceptable for subsurface drip irrigation while it is around 80% for the surface drip irrigation. The results also show an increase in root development and in the number of palm, as well as a substantial water savings due to lower evaporation losses compared to the classic drip irrigation. The results of this study showed that subsurface drip irrigation is an efficient technique, which allows sustainable irrigation in arid areas.

Keywords: Subsurface drip irrigation, Water conservation, Arid areas, Young date palms.

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Authors: Bhaskar Basu

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Universities and higher education institutes are finding it increasingly difficult to engage students fruitfully through traditional pedagogic tools. Web 2.0 technologies comprising social networking sites (SNSs) offer a platform for students to collaborate and share information, thereby enhancing their learning experience. Despite the potential and reach of SNSs, its use has been limited in academic settings promoting higher education. The purpose of this paper is to assess the perception of social networking sites among business school students in India and analyze its role in enhancing quality of student experiences in a business school leading to the proposal of an agenda for future research. In this study, more than 300 students of a reputed business school were involved in a survey of their preferences of different social networking sites and their perceptions and attitudes towards these sites. A questionnaire with three major sections was designed, validated and distributed among  a sample of students, the research method being descriptive in nature. Crucial questions were addressed to the students concerning time commitment, reasons for usage, nature of interaction on these sites, and the propensity to share information leading to direct and indirect modes of learning. It was further supplemented with focus group discussion to analyze the findings. The paper notes the resistance in the adoption of new technology by a section of business school faculty, who are staunch supporters of the classical “face-to-face” instruction. In conclusion, social networking sites like Facebook and LinkedIn provide new avenues for students to express themselves and to interact with one another. Universities could take advantage of the new ways  in which students are communicating with one another. Although interactive educational options such as Moodle exist, social networking sites are rarely used for academic purposes. Using this medium opens new ways of academically-oriented interactions where faculty could discover more about students' interests, and students, in turn, might express and develop more intellectual facets of their lives. hitherto unknown intellectual facets.  This study also throws up the enormous potential of mobile phones as a tool for “blended learning” in business schools going forward.

Keywords: Business school, India, learning, social media, social networking, university.

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Authors: Indunil Jayatilake, Warna Karunasena, Weena Lokuge

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An Australian manufacturer has fabricated an innovative GFRP sandwich panel made from E-glass fiber skin and a modified phenolic core for structural applications. Debonding, which refers to separation of skin from the core material in composite sandwiches, is one of the most common types of damage in composites. The presence of debonding is of great concern because it not only severely affects the stiffness but also modifies the dynamic behaviour of the structure. Generally it is seen that the majority of research carried out has been concerned about the delamination of laminated structures whereas skin-core debonding has received relatively minor attention. Furthermore it is observed that research done on composite slabs having multiple skin-core debonding is very limited. To address this gap, a comprehensive research investigating dynamic behaviour of composite panels with single and multiple debonding is presented. The study uses finite-element modelling and analyses for investigating the influence of debonding on free vibration behaviour of single and multilayer composite sandwich panels. A broad parametric investigation has been carried out by varying debonding locations, debonding sizes and support conditions of the panels in view of both single and multiple debonding. Numerical models were developed with Strand7 finite element package by innovatively selecting the suitable elements to diligently represent their actual behavior. Three-dimensional finite element models were employed to simulate the physically real situation as close as possible, with the use of an experimentally and numerically validated finite element model. Comparative results and conclusions based on the analyses are presented. For similar extents and locations of debonding, the effect of debonding on natural frequencies appears greatly dependent on the end conditions of the panel, giving greater decrease in natural frequency when the panels are more restrained. Some modes are more sensitive to debonding and this sensitivity seems to be related to their vibration mode shapes. The fundamental mode seems generally the least sensitive mode to debonding with respect to the variation in free vibration characteristics. The results indicate the effectiveness of the developed three dimensional finite element models in assessing debonding damage in composite sandwich panels.

Keywords: Debonding, free vibration behaviour, GFRP sandwich panels, three dimensional finite element modelling.

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Authors: Emiliano Matta

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Passive resonant vibration absorbers are among the most widely used dynamic control systems in civil engineering. They typically consist in a single-degree-of-freedom mechanical appendage of the main structure, tuned to one structural target mode through frequency and damping optimization. One classical scheme is the pendulum absorber, whose mass is constrained to move along a curved trajectory and is damped by viscous dashpots. Even though the principle is well known, the search for improved arrangements is still under way. In recent years this investigation inspired a type of bidirectional pendulum absorber (BPA), consisting of a mass constrained to move along an optimal three-dimensional (3D) concave surface. For such a BPA, the surface principal curvatures are designed to ensure a bidirectional tuning of the absorber to both principal modes of the main structure, while damping is produced either by horizontal viscous dashpots or by vertical friction dashpots, connecting the BPA to the main structure. In this paper, a variant of BPA is proposed, where damping originates from the variable tangential friction force which develops between the pendulum mass and the 3D surface as a result of a spatially-varying friction coefficient pattern. Namely, a friction coefficient is proposed that varies along the pendulum surface in proportion to the modulus of the 3D surface gradient. With such an assumption, the dissipative model of the absorber can be proven to be nonlinear homogeneous in the small displacement domain. The resulting homogeneous BPA (HBPA) has a fundamental advantage over conventional friction-type absorbers, because its equivalent damping ratio results independent on the amplitude of oscillations, and therefore its optimal performance does not depend on the excitation level. On the other hand, the HBPA is more compact than viscously damped BPAs because it does not need the installation of dampers. This paper presents the analytical model of the HBPA and an optimal methodology for its design. Numerical simulations of single- and multi-story building structures under wind and earthquake loads are presented to compare the HBPA with classical viscously damped BPAs. It is shown that the HBPA is a promising alternative to existing BPA types and that homogeneous tangential friction is an effective means to realize systems provided with amplitude-independent damping.

Keywords: Amplitude-independent damping, Homogeneous friction, Pendulum nonlinear dynamics, Structural control, Vibration resonant absorbers.

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Authors: Luminiţa Duţică, Gheorghe Duţică

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Many of the interrogations or dilemmas of the contemporary world found the answer in what was generically called the appeal to matrix. This genuine spiritual exercise of re-connection of the present to origins, to the primary source, revealed the ontological condition of timelessness, ahistorical, immutable (epi)phenomena, of those pure essences concentrated in the archetypal-referential layer of the human existence. The musical creation was no exception to this trend, the impasse generated by the deterministic excesses of the whole serialism or, conversely, by some questionable results of the extreme indeterminism proper to the avant-garde movements, stimulating the orientation of many composers to rediscover a universal grammar, as an emanation of a new ‘collective’ order (reverse of the utopian individualism). In this context, the music of oral tradition and therefore the world of the ancient modes represented a true revelation for the composers of the twentieth century, who were suddenly in front of some unsuspected (re)sources, with a major impact on all levels of edification of the musical work: morphology, syntax, timbrality, semantics etc. For the contemporary Romanian creators, the music of rituals, existing in the local archaic culture, opened unsuspected perspectives for which it meant to be a synthetic, inclusive and recoverer vision, where the primary (archetypal) genuine elements merge with the latest achievements of language of the European composers. Thus, anchored in a strong and genuine modal source, the compositions analysed in this paper evoke, in a manner as modern as possible, the atmosphere of some ancestral rituals such as: the invocation of rain during the drought (Paparudele, Scaloianul), funeral ceremony (Bocetul), traditions specific to the winter holidays and new year (Colinda, Cântecul de stea, Sorcova, Folklore traditional dances) etc. The reactivity of those rituals in the sound context of the twentieth century meant potentiating or resizing the archaic spirit of the primordial symbolic entities, in terms of some complexity levels generated by the technique of harmonies of chordal layers, of complex aggregates (gravitational or non-gravitational, geometric), of the mixture polyphonies and with global effect (group, mass), by the technique of heterophony, of texture and cluster, leading to the implementation of some processes of collective improvisation and instrumental theatre.

Keywords: Archetype, improvisation, instrumental theatre, polyphony, ritual.

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Authors: Roberto Sabatini, Celia Bartel, Anish Kaharkar, Tesheen Shaid, Subramanian Ramasamy

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Two multisensor system architectures for navigation and guidance of small Unmanned Aircraft (UA) are presented and compared. The main objective of our research is to design a compact, light and relatively inexpensive system capable of providing the required navigation performance in all phases of flight of small UA, with a special focus on precision approach and landing, where Vision Based Navigation (VBN) techniques can be fully exploited in a multisensor integrated architecture. Various existing techniques for VBN are compared and the Appearance-Based Navigation (ABN) approach is selected for implementation. Feature extraction and optical flow techniques are employed to estimate flight parameters such as roll angle, pitch angle, deviation from the runway centreline and body rates. Additionally, we address the possible synergies of VBN, Global Navigation Satellite System (GNSS) and MEMS-IMU (Micro-Electromechanical System Inertial Measurement Unit) sensors, and the use of Aircraft Dynamics Model (ADM) to provide additional information suitable to compensate for the shortcomings of VBN and MEMS-IMU sensors in high-dynamics attitude determination tasks. An Extended Kalman Filter (EKF) is developed to fuse the information provided by the different sensors and to provide estimates of position, velocity and attitude of the UA platform in real-time. The key mathematical models describing the two architectures i.e., VBN-IMU-GNSS (VIG) system and VIGADM (VIGA) system are introduced. The first architecture uses VBN and GNSS to augment the MEMS-IMU. The second mode also includes the ADM to provide augmentation of the attitude channel. Simulation of these two modes is carried out and the performances of the two schemes are compared in a small UA integration scheme (i.e., AEROSONDE UA platform) exploring a representative cross-section of this UA operational flight envelope, including high dynamics manoeuvres and CAT-I to CAT-III precision approach tasks. Simulation of the first system architecture (i.e., VIG system) shows that the integrated system can reach position, velocity and attitude accuracies compatible with the Required Navigation Performance (RNP) requirements. Simulation of the VIGA system also shows promising results since the achieved attitude accuracy is higher using the VBN-IMU-ADM than using VBN-IMU only. A comparison of VIG and VIGA system is also performed and it shows that the position and attitude accuracy of the proposed VIG and VIGA systems are both compatible with the RNP specified in the various UA flight phases, including precision approach down to CAT-II.

Keywords: Global Navigation Satellite System (GNSS), Lowcost Navigation Sensors, MEMS Inertial Measurement Unit (IMU), Unmanned Aerial Vehicle, Vision Based Navigation.

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Authors: C. Amer, M. Sahin

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The design of an optimised horizontal axis 5-meter-long wind turbine rotor blade in according with IEC 61400-2 standard is a research and development project in order to fulfil the requirements of high efficiency of torque from wind production and to optimise the structural components to the lightest and strongest way possible. For this purpose, a research study is presented here by focusing on the structural characteristics of a composite wind turbine blade via finite element modelling and analysis tools. In this work, first, the required data regarding the general geometrical parts are gathered. Then, the airfoil geometries are created at various sections along the span of the blade by using CATIA software to obtain the two surfaces, namely; the suction and the pressure side of the blade in which there is a hat shaped fibre reinforced plastic spar beam, so-called chassis starting at 0.5m from the root of the blade and extends up to 4 m and filled with a foam core. The root part connecting the blade to the main rotor differential metallic hub having twelve hollow threaded studs is then modelled. The materials are assigned as two different types of glass fabrics, polymeric foam core material and the steel-balsa wood combination for the root connection parts. The glass fabrics are applied using hand wet lay-up lamination with epoxy resin as METYX L600E10C-0, is the unidirectional continuous fibres and METYX XL800E10F having a tri-axial architecture with fibres in the 0,+45,-45 degree orientations in a ratio of 2:1:1. Divinycell H45 is used as the polymeric foam. The finite element modelling of the blade is performed via MSC PATRAN software with various meshes created on each structural part considering shell type for all surface geometries, and lumped mass were added to simulate extra adhesive locations. For the static analysis, the boundary conditions are assigned as fixed at the root through aforementioned bolts, where for dynamic analysis both fixed-free and free-free boundary conditions are made. By also taking the mesh independency into account, MSC NASTRAN is used as a solver for both analyses. The static analysis aims the tip deflection of the blade under its own weight and the dynamic analysis comprises normal mode dynamic analysis performed in order to obtain the natural frequencies and corresponding mode shapes focusing the first five in and out-of-plane bending and the torsional modes of the blade. The analyses results of this study are then used as a benchmark prior to modal testing, where the experiments over the produced wind turbine rotor blade has approved the analytical calculations.

Keywords: Dynamic analysis, Fiber Reinforced Composites, Horizontal axis wind turbine blade, Hand-wet layup, Modal Testing.

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Authors: Dinara F. Gaynutdinova, Vladimir Ya Modorsky, Nikolay A. Shevelev

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The problem under research is that of unpredictable modes occurring in two-stage centrifugal hydraulic pump as a result of hydraulic processes caused by vibrations of structural components. Numerical, analytical and experimental approaches are considered. A hypothesis was developed that the problem of unpredictable pressure decrease at the second stage of centrifugal pumps is caused by cavitation effects occurring upon vibration. The problem has been studied experimentally and theoretically as of today. The theoretical study was conducted numerically and analytically. Hydroelastic processes in dynamic “liquid – deformed structure” system were numerically modelled and analysed. Using ANSYS CFX program engineering analysis complex and computing capacity of a supercomputer the cavitation parameters were established to depend on vibration parameters. An influence domain of amplitudes and vibration frequencies on concentration of cavitation bubbles was formulated. The obtained numerical solution was verified using CFM program package developed in PNRPU. The package is based on a differential equation system in hyperbolic and elliptic partial derivatives. The system is solved by using one of finite-difference method options – the particle-in-cell method. The method defines the problem solution algorithm. The obtained numerical solution was verified analytically by model problem calculations with the use of known analytical solutions of in-pipe piston movement and cantilever rod end face impact. An infrastructure consisting of an experimental fast hydro-dynamic processes research installation and a supercomputer connected by a high-speed network, was created to verify the obtained numerical solutions. Physical experiments included measurement, record, processing and analysis of data for fast processes research by using National Instrument signals measurement system and Lab View software. The model chamber end face oscillated during physical experiments and, thus, loaded the hydraulic volume. The loading frequency varied from 0 to 5 kHz. The length of the operating chamber varied from 0.4 to 1.0 m. Additional loads weighed from 2 to 10 kg. The liquid column varied from 0.4 to 1 m high. Liquid pressure history was registered. The experiment showed dependence of forced system oscillation amplitude on loading frequency at various values: operating chamber geometrical dimensions, liquid column height and structure weight. Maximum pressure oscillation (in the basic variant) amplitudes were discovered at loading frequencies of approximately 1,5 kHz. These results match the analytical and numerical solutions in ANSYS and CFM.

Keywords: Computing experiment, hydroelasticity, physical experiment, vibration.

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Authors: Natalia Podkhodova, Olga Sheremeteva, Mariia Soldaeva

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Creating favourable conditions for students’ comprehension of mathematical content is one of the primary problems in teaching mathematics in secondary school. The fact of comprehension includes the ability to build a working situational model and thus becomes an important means of solving mathematical problems. This paper describes a holistic approach to teaching mathematics designed to address the primary challenges of such teaching; specifically, the challenge of students’ comprehension. Essentially, this approach consists of (1) establishing links between the attributes of the notion: the sense, the meaning, and the term; (2) taking into account the components of student’s subjective experience—value-based emotions, contextual, procedural and communicative—during the educational process; (3) linking together different ways to present mathematical information; (4) identifying and leveraging the relationships between real, perceptual and conceptual (scientific) mathematical spaces by applying real-life situational modelling. The article describes approaches to the practical use of these foundational concepts. Identifying how proposed methods and techniques influence understanding of material used in teaching mathematics was the primary goal. The study included an experiment in which 256 secondary school students took part: 142 in the study group and 114 in the control group. All students in these groups had similar levels of achievement in math and studied math under the same curriculum. In the course of the experiment, comprehension of two topics — “Derivative” and “Trigonometric functions”—was evaluated. Control group participants were taught using traditional methods. Students in the study group were taught using the holistic method: under teacher’s guidance, they carried out assignments designed to establish linkages between notion’s characteristics, to convert information from one mode of presentation to another, as well as assignments that required the ability to operate with all modes of presentation. Identification, accounting for and transformation of subjective experience were associated with methods of stimulating the emotional value component of the studied mathematical content (discussions of lesson titles, assignments aimed to create study dominants, performing theme-related physical exercise ...) The use of techniques that forms inter-subject notions based on linkages between, perceptual real and mathematical conceptual spaces proved to be of special interest to the students. Results of the experiment were analysed by presenting students in each of the groups with a final test in each of the studied topics. The test included assignments that required building real situational models. Statistical analysis was used to aggregate test results. Pierson criterion x2 was used to reveal statistics significance of results (pass-fail the modelling test). Significant difference of results was revealed (p < 0.001), which allowed to conclude that students in the study group showed better comprehension of mathematical information than those in the control group. The total number of completed assignments of each student was analysed as well, with average results calculated for each group. Statistical significance of result differences against the quantitative criterion (number of completed assignments) was determined using Student’s t-test, which showed that students in the study group completed significantly more assignments than those in the control group (p = 0.0001). Authors thus come to the conclusion that suggested increase in the level of comprehension of study material took place as a result of applying implemented methods and techniques.

Keywords: Comprehension of mathematical content, holistic approach to teaching mathematics in secondary school, subjective experience, technology of the formation of inter-subject notions.

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