Search results for: Components of visual identity

Authors: Erik Vassøy Olsen, Hirpa G. Lemu

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Inspired by the Formula-1 competition, IMechE (Institute of Mechanical Engineers) and Formula SAE (Society of Mechanical Engineers) organize annual competitions for University and College students worldwide to compete with a single-seat racecar they have designed and built. Design of the chassis or the frame is a key component of the competition because the weight and stiffness properties are directly related with the performance of the car and the safety of the driver. In addition, a reduced weight of the chassis has direct influence on the design of other components in the car. Among others, it improves the power to weight ratio and the aerodynamic performance. As the power output of the engine or the battery installed in the car is limited to 80 kW, increasing the power to weight ratio demands reduction of the weight of the chassis, which represents the major part of the weight of the car. In order to reduce the weight of the car, ION Racing team from University of Stavanger, Norway, opted for a monocoque design. To ensure fulfilment of the competition requirements of the chassis, the monocoque design should provide sufficient torsional stiffness and absorb the impact energy in case of possible collision. The study reported in this article is based on the requirements for Formula Student competition. As part of this study, diverse mechanical tests were conducted to determine the mechanical properties and performances of the monocoque design. Upon a comprehensive theoretical study of the mechanical properties of sandwich composite materials and the requirements of monocoque design in the competition rules, diverse tests were conducted including 3-point bending test, perimeter shear test and test for absorbed energy. The test panels were homemade and prepared with equivalent size of the side impact zone of the monocoque, i.e. 275 mm x 500 mm, so that the obtained results from the tests can be representative. Different layups of the test panels with identical core material and the same number of layers of carbon fibre were tested and compared. Influence of the core material thickness was also studied. Furthermore, analytical calculations and numerical analysis were conducted to check compliance to the stated rules for Structural Equivalency with steel grade SAE/AISI 1010. The test results were also compared with calculated results with respect to bending and torsional stiffness, energy absorption, buckling, etc. The obtained results demonstrate that the material composition and strength of the composite material selected for the monocoque design has equivalent structural properties as a welded frame and thus comply with the competition requirements. The developed analytical calculation algorithms and relations will be useful for future monocoque designs with different lay-ups and compositions.

Keywords: Composite material, formula student, ion racing, monocoque design, structural equivalence.

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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: Mustafa M. Donma, Orkide Donma

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Metabolisms of macrominerals, those of calcium, phosphorus and magnesium, are closely associated with the metabolism of vitamin D. Particularly magnesium, the second most abundant intracellular cation, is related to biochemical and metabolic processes in the body, such as those of carbohydrates, proteins and lipids. The status of each mineral was investigated in obesity to some extent. Their products and ratios may possibly give much more detailed information about the matter. The aim of this study is to investigate possible relations between each macromineral and some obesity-related parameters. This study was performed on 235 children, whose ages were between 06-18 years. Aside from anthropometric measurements, hematological analyses were performed. TANITA body composition monitor using bioelectrical impedance analysis technology was used to establish some obesity-related parameters including basal metabolic rate (BMR), total fat, mineral and muscle masses. World Health Organization body mass index (BMI) percentiles for age and sex were used to constitute the groups. The values above 99^th percentile were defined as morbid obesity. Those between 95^th and 99^th percentiles were included into the obese group. The overweight group comprised of children whose percentiles were between 95 and 85. Children between the 85^th and 15^th percentiles were defined as normal. Metabolic syndrome (MetS) components (waist circumference, fasting blood glucose, triacylglycerol, high density lipoprotein cholesterol, systolic pressure, diastolic pressure) were determined. High performance liquid chromatography was used to determine Vitamin D status by measuring 25-hydroxy cholecalciferol (25-hydroxy vitamin D₃, 25(OH)D). Vitamin D values above 30.0 ng/ml were accepted as sufficient. SPSS statistical package program was used for the evaluation of data. The statistical significance degree was accepted as p < 0.05. The important points were the correlations found between vitamin D and magnesium as well as phosphorus (p < 0.05) that existed in the group with normal BMI values. These correlations were lost in the other groups. The ratio of phosphorus to magnesium was even much more highly correlated with vitamin D (p < 0.001). The negative correlation between magnesium and total fat mass (p < 0.01) was confined to the MetS group showing the inverse relationship between magnesium levels and obesity degree. In this group, calcium*magnesium product exhibited the highest correlation with total fat mass (p < 0.001) among all groups. Only in the MetS group was a negative correlation found between BMR and calcium*magnesium product (p < 0.05). In conclusion, magnesium is located at the center of attraction concerning its relationships with vitamin D, fat mass and MetS. The ratios and products derived from macrominerals including magnesium have pointed out stronger associations other than each element alone. Final considerations have shown that unique correlations of magnesium as well as calcium*magnesium product with total fat mass have drawn attention particularly in the MetS group, possibly due to the derangements in some basic elements of carbohydrate as well as lipid metabolism.

Keywords: Macrominerals, metabolic syndrome, pediatric obesity, vitamin D.

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Authors: Brandy Yee, Dianne Yee

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Through the exploration of the lived experiences, beliefs and values of instructional leaders, teachers and students in Finland, Germany and Canada, we investigated the factors which contribute to developmentally responsive, intellectually engaging middle-level learning environments for early adolescents. Student-centred leadership dimensions, effective instructional practices and student agency were examined through the lens of current policy and research on middle-level learning environments emerging from the Canadian province of Manitoba. Consideration of these three research perspectives in the context of early adolescent learning, placed against an international backdrop, provided a previously undocumented perspective on leading, teaching and learning in the middle years. Aligning with a social constructivist, qualitative research paradigm, the study incorporated collective case study methodology, along with constructivist grounded theory methods of data analysis. Data were collected through semi-structured individual and focus group interviews and document review, as well as direct and participant observation. Three case study narratives were developed to share the rich stories of study participants, who had been selected using maximum variation and intensity sampling techniques. Interview transcript data were coded using processes from constructivist grounded theory. A cross-case analysis yielded a conceptual framework highlighting key factors that were found to be significant in the establishment of developmentally responsive, intellectually engaging middle-level learning environments. Seven core categories emerged from the cross-case analysis as common to all three countries. Within the visual conceptual framework (which depicts the interconnected nature of leading, teaching and learning in middle-level learning environments), these seven core categories were grouped into Essential Factors (student agency, voice and choice), Contextual Factors (instructional practices; school culture; engaging families and the community), Synergistic Factors (instructional leadership) and Cornerstone Factors (education as a fundamental cultural value; preservice, in-service and ongoing teacher development). In addition, sub-factors emerged from recurring codes in the data and identified specific characteristics and actions found in developmentally responsive, intellectually engaging middle-level learning environments. Although this study focused on 12 schools in Finland, Germany and Canada, it informs the practice of educators working with early adolescent learners in middle-level learning environments internationally. The authentic voices of early adolescent learners are the most important resource educators have to gauge if they are creating effective learning environments for their students. Ongoing professional dialogue and learning is essential to ensure teachers are supported in their work and develop the pedagogical practices needed to meet the needs of early adolescent learners. It is critical to balance consistency, coherence and dependability in the school environment with the necessary flexibility in order to support the unique learning needs of early adolescents. Educators must intentionally create a school culture that unites teachers, students and their families in support of a common purpose, as well as nurture positive relationships between the school and its community. A large, urban school district in Canada has implemented a school cohort-based model to begin to bring developmentally responsive, intellectually engaging middle-level learning environments to scale.

Keywords: Developmentally responsive learning environments, early adolescents, middle-level learning, middle years, instructional leadership, instructional practices, intellectually engaging learning environments, leadership dimensions, student agency.

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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: A. Appe, B. Poluparthi, L. Kasivajjula, U. Mv, S. Bagadi, P. Modi, A. Singh, H. Gunupudi, S. Troiano, J. Paul, J. Stovall, J. Yamamoto

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The necessity of data-driven decisions in healthcare strategy formulation is rapidly increasing. A reliable framework which helps identify factors impacting a healthcare provider facility or a hospital (from here on termed as facility) market share is of key importance. This pilot study aims at developing a data-driven machine learning-regression framework which aids strategists in formulating key decisions to improve the facility’s market share which in turn impacts in improving the quality of healthcare services. The US (United States) healthcare business is chosen for the study, and the data spanning 60 key facilities in Washington State and about 3 years of historical data are considered. In the current analysis, market share is termed as the ratio of the facility’s encounters to the total encounters among the group of potential competitor facilities. The current study proposes a two-pronged approach of competitor identification and regression approach to evaluate and predict market share, respectively. Leveraged model agnostic technique, SHAP (SHapley Additive exPlanations), to quantify the relative importance of features impacting the market share. Typical techniques in literature to quantify the degree of competitiveness among facilities use an empirical method to calculate a competitive factor to interpret the severity of competition. The proposed method identifies a pool of competitors, develops Directed Acyclic Graphs (DAGs) and feature level word vectors, and evaluates the key connected components at the facility level. This technique is robust since it is data-driven, which minimizes the bias from empirical techniques. The DAGs factor in partial correlations at various segregations and key demographics of facilities along with a placeholder to factor in various business rules (for e.g., quantifying the patient exchanges, provider references, and sister facilities). Identified are the multiple groups of competitors among facilities. Leveraging the competitors' identified developed and fine-tuned Random Forest Regression model to predict the market share. To identify key drivers of market share at an overall level, permutation feature importance of the attributes was calculated. For relative quantification of features at a facility level, incorporated SHAP, a model agnostic explainer. This helped to identify and rank the attributes at each facility which impacts the market share. This approach proposes an amalgamation of the two popular and efficient modeling practices, viz., machine learning with graphs and tree-based regression techniques to reduce the bias. With these, we helped to drive strategic business decisions.

Keywords: Competition, DAGs, hospital, healthcare, machine learning, market share, random forest, SHAP.

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Authors: Ioan Rusu

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In the operation of power transformers of 110 kV/MV from substations, these are traveled by fault current resulting from MV line damage. Defect electrical contacts are heated when they are travelled from fault currents. In the case of high temperatures when 135 °C is reached, the electrical insulating oil in the vicinity of the electrical faults comes into contact with these contacts releases gases, and activates the electrical protection. To avoid auto-flammability of electro-insulating oil, we designed a security system thermal of electrical contact defects by pouring fire-resistant polyurethane foam, mastic or mortar fire inside a cardboard electro-insulating cylinder. From practical experience, in the exploitation of power transformers of 110 kV/MT in oil electro-insulating were recorded some passing disconnecting commanded by the gas protection at internal defects. In normal operation and in the optimal load, nominal currents do not require thermal secure contacts inside electrical transformers, contacts are made at the fabrication according to the projects or to repair by solder. In the case of external short circuits close to the substation, the contacts inside electrical transformers, even if they are well made in sizes of Rcontact = 10^‑6 Ω, are subjected to short-circuit currents of the order of 10 kA-20 kA which lead to the dissipation of some significant second-order electric powers, 100 W-400 W, on contact. At some internal or external factors which action on electrical contacts, including electrodynamic efforts at short-circuits, these factors could be degraded over time to values in the range of 10^-4 Ω to 10^-5 Ω and if the action time of protection is great, on the order of seconds, power dissipation on electrical contacts achieve high values of 1,0 kW to 40,0 kW. This power leads to strong local heating, hundreds of degrees Celsius and can initiate self-ignition and burning oil in the vicinity of electro-insulating contacts with action the gas relay. Degradation of electrical contacts inside power transformers may not be limited for the duration of their operation. In order to avoid oil burn with gas release near electrical contacts, at short-circuit currents 10 kA-20 kA, we have outlined the following solutions: covering electrical contacts in fireproof materials that would avoid direct burn oil at short circuit and transmission of heat from electrical contact along the conductors with heat dissipation gradually over time, in a large volume of cooling. Flame retardant materials are: polyurethane foam, mastic, cement (concrete). In the normal condition of operation of transformer, insulating of conductors coils is with paper and insulating oil. Ignition points of its two components respectively are approximated: 135 °C heat for oil and 200 ⁰C for paper. In the case of a faulty electrical contact, about 10^-3 Ω, at short-circuit; the temperature can reach for a short time, a value of 300 °C-400 °C, which ignite the paper and also the oil. By burning oil, there are local gases that disconnect the power transformer. Securing thermal electrical contacts inside the transformer, in cardboard tube with polyurethane foams, mastik or cement, ensures avoiding gas release and also gas protection working.

Keywords: Power transformer, oil insulatation, electric contacts, gases, gas relay.

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Authors: Ana Pauna, Zbigniew Pleszewski

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The purpose of this study is to revisit the concept of rape as represented by professionals in the literature as well as its perception (beliefs and attitudes) in the population at large and to propose methodological improvements to its measurement tool. Rape is a serious crime threatening its victim-s physical and mental health and integrity; and as such is legally prosecuted in all modern societies. The problem is not in accepting or rejecting rape as a criminal act, but rather in the vagueness of its interpretations and “justifications" maintained in the mentality of modern societies - known in the literature as the phenomenon of "rape-myth". The rapemyth can be studied from different perspectives: criminology, sociology, ethics, medicine and psychology. Its investigation requires rigorous scientific objectivity, free of passion (victims of rape are at risk of emotional bias), free of activism (social activists, even if wellintentioned are also biased), free of any pre-emptive assumptions or prejudices. To apply a rigorous scientific procedure, we need a solid, valid and reliable measurement. Rape is a form of heterosexual or homosexual aggression, violently forcing the victim to give-in in the sexual activity of the aggressor against her/his will. Human beings always try to “understand" or find a reason justifying their acts. Psychological literature provides multiple clinical and experimental examples of it; just to mention the famous studies by Milgram on the level of electroshock delivered by the “teacher" towards the “learner" if “scientifically justifiable" or the studies on the behavior of “prisoners" and the “guards" and many other experiments and field observations. Sigmund Freud presented the phenomenon of unconscious justification and called it rationalization. The multiple justifications, rationalizations and repeated opinions about sexual behavior contribute to a myth maintained in the society. What kind of “rationale" our societies apply to “understand" the non-consensual sexual behavior? There are many, just to mention few: • Sex is a ludistic activity for both participants, therefore – even if not consented – it should bring pleasure to both. • Everybody wants sex, but only men are allowed to manifest it openly while women have to pretend the opposite, thus men have to initiate sexual behavior and women would follow. • A person who strongly needs sex is free to manifest it and struggle to get it; the person who doesn-t want it must not reveal her/his sexual attraction and avoid risky situations; otherwise she/he is perceived as a promiscuous seducer. • A person who doesn-t fight against the sexual initiator unconsciously accepts the rape (does it explain why homosexual rapes are reported less frequently than rapes against women?). • Women who are raped deserve it because their wardrobe is very revealing and seducing and they ''willingly'' go to highly risky places (alleys, dark roads, etc.). • Men need to ventilate their sexual energy and if they are deprived of a partner their urge to have sex is difficult to control. • Men are supposed to initiate and insist even by force to have sex (their testosterone makes them both sexual and aggressive). The paper overviews numerous cultural beliefs about masculine versus feminine behavior and their impact on the “rape myth".

Keywords: Rape Myth components, psycho-social factors, testing, Likert-type scale

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Authors: Sajjad H. Kasanagh, Perviz Ahmedzade, Alexander Fainleib, Taylan Gunay

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Modification of asphalt is a fundamental method around the world mainly on the purpose of providing more durable pavements which lead to diminish repairing cost during the lifetime of highways. Various polymers such as styrene-butadiene-styrene (SBS) and ethylene vinyl acetate (EVA) make up the greater parts of the all-over asphalt modifiers generally providing better physical properties of asphalt by decreasing temperature dependency which eventually diminishes permanent deformation on highways such as rutting. However, some waste and low-cost materials such as recycled plastics and ground rubber tire have been attempted to utilize in asphalt as modifier instead of manufactured polymer modifiers due to decreasing the eventual highway cost. On the other hand, the usage of recycled plastics has become a worldwide requirement and awareness in order to decrease the pollution made by waste plastics. Hence, finding an area in which recycling plastics could be utilized has been targeted by many research teams so as to reduce polymer manufacturing and plastic pollution. To this end, in this paper, thermoplastic dynamic vulcanizate (TDV) obtained from recycled post-consumer polyethylene and ground tire rubber (GTR) were used to provide an efficient modifier for asphalt which decreases the production cost as well and finally might provide an ecological solution by decreasing polymer disposal problems. TDV was synthesized by the chemists in the research group by means of the abovementioned components that are considered as compatible physical characteristic of asphalt materials. TDV modified asphalt samples having different rate of proportions of 3, 4, 5, 6, 7 wt.% TDV modifier were prepared. Conventional tests, such as penetration, softening point and roll thin film oven (RTFO) tests were performed to obtain fundamental physical and aging properties of the base and modified binders. The high temperature performance grade (PG) of binders was determined by Superpave tests conducted on original and aged binders. The multiple stress creep and recovery (MSCR) test which is relatively up-to-date method for classifying asphalts taking account of their elasticity abilities was carried out to evaluate PG plus grades of binders. The results obtained from performance grading, and MSCR tests were also evaluated together so as to make a comparison between the methods both aiming to determine rheological parameters of asphalt. The test results revealed that TDV modification leads to a decrease in penetration, an increase in softening point, which proves an increasing stiffness of asphalt. DSR results indicate an improvement in PG for modified binders compared to base asphalt. On the other hand, MSCR results that are compatible with DSR results also indicate an enhancement on rheological properties of asphalt. However, according to the results, the improvement is not as distinct as observed in DSR results since elastic properties are fundamental in MSCR. At the end of the testing program, it can be concluded that TDV can be used as modifier which provides better rheological properties for asphalt and might diminish plastic waste pollution since the material is 100% recycled.

Keywords: Asphalt, ground tire rubber, recycled polymer, thermoplastic dynamic vulcanized.

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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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Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

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This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: Wind turbines, aeroelasticity, repetitive control, periodic systems.

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