Rectangular Base Research Articles

Дослідження процесів самозаймання у насипі з прямокутним перерізом методами Роте та двобічних наближень

Self-ignition of a stockpile of material (coal, peat, grain) occurs as a result of the accumulation of heat released by an exothermic reaction of oxidation, which makes it possible to consider the stockpile as a body with an internal heat source. The research of self-ignition processes using mathematical modeling methods leads to the need to find a solution to the initial boundary value problem for a two-dimensional semilinear heat conduction equation. This cannot always be done analytically, so it makes sense to use numerical analysis methods. The aim of this article is to apply Rothe’s method in combination with the method of two-sided approximations based on the use of the Green's function to find the solution of the initial boundary value problem for the two-dimensional semilinear heat conduction equation that arises during the mathematical modeling of self-ignition processes of an stockpile of bulk material of cylindrical shape with a rectangular base. To achieve the goal, after the discretization of the heat conduction equation by the time variable, a sequence of boundary value problems was obtained by the Rothe’s method, each of which was reduced to the Hammerstein equation. For this nonlinear operator equation, an iterative process of the two-way method was constructed with its stopping condition obtained through a posteriori error estimation. The power of the internal heat source was approximated using an exponential dependence. As a result of the computational experiment, a sequence of approximate solutions was obtained. The graphs of heat maps constructed for them made it possible to examine over time the course of the self-ignition process in the cross-section of a stockpile of cylindrical shape with a rectangular base and to identify areas of heat accumulation

Characterisation of four species of the genus Acrobeloides Cobb, 1924 (Rhabditida, Cephalobidae) from xeric areas in Spain, with revision of the genus and restoration of Paracephalobus Akhtar, 1962

New material of four Acrobeloides species (Acrobeloides arenicola, Acrobeloides bodenheimeri, Acrobeloides nanus and Acrobeloides tricornis) are redescribed from xeric areas in Spain. This species are morphological (based on light microscopy and scanning electron microscopy study) and morphometrically differentiated in two groups. One of them, including A. arenicola, A. nanus and A. tricornis (belonging to the buetschli-group), are characterised by having smaller body, lip region with labial probolae having rectangular base, pharynx with long isthmus, female genital system scarcely developed with vulva midventral, and usually males absent, these with small spicules. Other species group, including A. bodenheimeri (belonging to the maximus-group), is characterised by having longer body, lip region with triangular base, pharynx with very short isthmus, female genital system well developed with vulva usually located ventrolateral, and males frequent with large and robust spicules. This division is corroborate with molecular analyses based on 18S and 28S rDNA. According to this, the separation of the genus Acrobeloides in two different genera is proposed. As Paracephalobus litoralis is morphologically similar to the species of the maximus-group, the genus Paracephalobus is restored to name the species included in the maximus-group. An updated list of species for the genera Acrobeloides and Paracephalobus is included. In addition, Acrobeloides insignis, A. sexlineatus, A. thornei and A. varius are proposed new junior synonyms of A. tricornis.

Research on Pressure Sensor of Circular Monocrystalline Silicon Chassis

Abstract Traditional sensors, such as pressure, piezoelectric or piezoresistive, mostly use square silicon-based materials as chassis and use Wheatstone bridge circuits to measure pressure and resistance values. Nowadays, reducing the size of sensors is also a problem to be solved in the increasingly wide range of sensor applications. In this paper, a circular monocrystalline silicon base pressure sensor is designed and its performance is studied. We applied COMSOL software to model the circular chassis base pressure sensor, tested the deformation of the circular chassis base pressure sensor under different access volttimes and pressures, analyzed its sensitivity and other performance, and compared the above performance with the rectangular monocrystalline silicon chassis base pressure sensor. The experimental results show that the circular monocrystalline silicon chassis pressure sensor has excellent electrostriction performance, and the variation of the potential and potential difference in the measuring area is more obvious than that of the rectangular monocrystalline silicon chassis pressure sensor. This paper provides a reference for sensor makers.

The Impact of Roughness and Partitions in Thermal Convection to Enhance the Heat Transport

Abstract In this investigation, we explore the profound impact of adiabatic partitions on heat transport within a square Rayleigh-Bénard (RB) convection enclosure characterized by surface roughness on the lower hot and upper cold plates. The surface irregularities take the form of a rectangular base and a triangular apex. Our study employs two-dimensional direct numerical simulations spanning the Rayleigh number (Ra) range of 106–108 and a Prandtl number (Pr) of 1. Adiabatic partitions, strategically positioned between successive roughness, serve as the focal point of our exploration. Remarkably, our findings reveal a substantial enhancement in heat transport with the introduction of a partition board between consecutive roughness elements. As we escalate the number of partitions from one to four, the heat flux experiences a notable augmentation, reaching 2.3 times that of the classical square RB configuration. This enhancement is attributed to the breakdown of large-scale rolls into multiple rolls, a phenomenon intensified by the increased partition height. Further intriguing observations unfold as we investigate the interplay of surface roughness and partitions. Configurations featuring roughness with partitions exhibit an impressive 2.7 times heat flux enhancement compared to the classical square RB setup. The complex interplay of heat transport improvement is closely connected to optimizing the distance between the conduction plate and the partition. Through meticulous analysis, we identify that the optimal gap facilitates heightened local velocity, effectively thinning the thermal boundary layer and consequently augmenting the overall heat flux. In essence, our study sheds light on the synergistic effects of adiabatic partitions and surface roughness in the context of RB convection. The observed enhancements in heat transport underscore the potential for tailored design strategies involving partitions and surface modifications to optimize thermal performance in diverse applications.

Experimental validation of automated OMA and mode tracking for structural health monitoring of transmission towers

This article presents a cost-effective method to monitor the structural health of transmission towers, a critical yet aging infrastructure that plays an important role in the overall reliability of the electrical grid. The method is validated experimentally on a real-world transmission tower which was subjected to several (exaggerated) damage scenarios. The proposed monitoring strategy relies on four accelerometers installed on the four faces of the rectangular base of the transmission tower. The collected vibration data is processed using a classic operational modal analysis (OMA)-based structural health monitoring scheme, comprising; automated OMA, tracking, data normalization, and decision-making. The proposed algorithm processes the four faces independently to maximize the likelihood of detecting (local) damage near the sensors in the quasi-symmetric structure. Furthermore, with widespread deployment in mind, the current article introduces a semi-automated tracking algorithm using “Density-based spatial clustering of applications with noise.” Environmental effects were removed using principal component analysis, eliminating the need for additional (environmental) sensors. Finally, Q and T2 statistics were used to assess damage on each face of the structure using all tracked modes. The experimental results of this study demonstrate that this workflow can effectively track a large number of modes; in the current study, 10 modes per face of the structure, and from them detect and to some level localize the majority of structural damage-inducing events, such as the removal of a bolt or a bar.

Development of new lead free ceramic substrate for rectangular patch antenna application in X-band communication

This work introduces the use of Bi0.5Na0.5TiO3 (BNT) ceramic material as substrates for microstrip patch antennas operating within the frequency range of 8-12 GHz. The simulated antenna was constructed using a substrate composed of a synthesized ferroelectric perovskite-based material with a thickness of t=1.02 mm. This study investigated the intricate electromagnetic properties including permittivity, permeability, dielectric loss, magnetic loss, and miniaturization factor. Characterization techniques are used to investigate the crystal structure, local vibrational properties, surface morphology, and elemental composition of the synthesized sample. The reflection loss, return loss, and radiation pattern of the split ring microstrip patch antenna with a rectangular base were calculated using CST Microwave Studio version 2019. The parametric adjustment of the synthesized sample's uniqueness was achieved by modifying its thickness for t=0.7 mm, t=0.9 mm, t=1 mm, t=1.02 mm, and t=1.04 mm.

The effect of orthodontic bracket base shape on shear bond strength to human enamel, an in vitro study.

The purpose of this study was to evaluate the in vitro effect of orthodontic bracket base shape on shear bond strength (SBS) to human enamel and assess the nature of debonding fractures using the Adhesive Remnant Index (ARI). Orthodontic brackets with different-shaped bases (flower, heart, rectangle) were bonded to 120 extracted human third molars. Shear bond strength was measured using a Servohydraulic Test System at 24 h and 2 months after bonding. Adhesive Remnant Index scores were evaluated under 10x magnification to assess the amount of resin left on the tooth. The control bracket (rectangular base shape) had the highest mean SBS (26.8 ± 8.2 megapascals [MPa]), and significantly differed from the flower (17.2 ± 4.4 MPa) and heart (18.9 ± 3.5 MPa) base shapes (p < 0.001). The mean SBS between debonding times at 24 h (21.5 ± 7.4 MPa) and 2 months (20.4 ± 6.7 MPa) were not statistically significant (p > 0.05). Analysis of ARI scores showed a significant difference between flower-24 h versus heart-2 months (p = 0.039), flower-24 h versus heart-24 h (p = 0.004), and control-2 months versus heart-24 h (p = 0.015). Bracket base shape influenced SBS, with the rectangular base shape having a higher mean SBS compared to flower and heart base shapes. Variations in ARI scores occurred based on bracket shape and were of a mixed adhesive-cohesive nature. All bracket shapes had bond strengths above the clinically acceptable range of 6-8 MPa, and may thus provide adequate SBS in a clinical situation.

HEAT TRANSFER ANALYSIS ON BASE OF HEAT SINK WITH UNIFORM HEAT GENERATION

The present work describes the important results of problem of combined conduction, convection and radiation from a rectangular heat sink base subjected to uniform internal heat generation in its base. The governing equations for temperature distribution within the base are obtained by a relevant energy balance between rate of heat generation, heat conducted, convected and radiated. The derived non-linear partial differential equations are converted into algebraic form using finite difference method with 2nd order accuracy. The obtained algebraic equations have been solved simultaneously by Gauss-siedel iterative method with stringent convergence criteria and a C code has been written for above purpose. The computational domain has been discretized uniformly in all directions. A grid convergence test has been carried out to optimize the size of element. A complete parametric study has been carried out to study the effect of material of heat sink, regime of convection and role of radiation on local temperature distribution and maximum heat sink base temperature. It has been observed that material with high conductivity decreases the local temperature gradient and thus the maximum temperature. The regime of convection has a great influence on maximum temperature of heat sink with 15K of drop in Tmax. for a change in flow regime from free convection to forced convection. A special study on exclusive role of convection on maximum temperature reveals that one should not ignore the role forced convection in heat dissipation. Key Words: Heat generation, Multimode heat transfer, Radiation

Rancang Bangun Alat Bantu Fiksasi Pemeriksaan Radiografi Lumbal Oblik

Background: The oblique lumbar examination has been carried out. The position of object isn't object angle at 45° to the image receptor, but only estimate it. It caused not optimal image of scottie dog sign and spondylolysis (pressure in pars interarticularis). Therefore, an examination aid is needed to make it easier to obtain the position of the oblique lumbar object.Methods: This research design is a RnD study with the ADDIE model which is carried out with five stages, namely analysis, design, development, implementation, and evaluation. The data is carried out by observing, designing, testing, and analyzing whether there are artifacts.Results: An oblique lumbar radiographic examination fixation aid was produced from acrylic material with a thickness of 5 mm. Acrylic is shaped like a right-angled triangular prism building which has a longer base measuring 50 cm, width 42 cm, and height 25 cm. A rectangular base with a length of 50 cm is pressed against the patient's body so that the supporting part of the angled triangle that supports the patient's lumbar region or the patient's body does not shift during an oblique lumbar radiography examination. This tool has a mass dimension of 2.5kg.Conclusion: The design of the oblique lumbar radiographic examination fixation tool resembles a right-angled triangular prism with one side tilted at a 45 degree angle to adjust the position of the object so that it can obtain a good view of the Scottie dog sign to show part of the pars interarticularis.

Experimental and Numerical Analysis of Concrete Columns under Axial Load Based on European Design Norms

This study presents a comparison between numerical and experimental results for reinforced concrete columns subjected to axial compression. Depending on the columns support and their organization within the structure, columns primarily work under either concentric or eccentric compression, respectively, bending in situations where horizontal actions such as wind or/and earthquakes are present in the structure. Different countries have specific design codes, and in this study, the calculation of columns is based on the European design codes, specifically EN 1992-1-1. As a common practice in most cases during research, tests are conducted using computational models, and based on the obtained results through the application of similarity theory, an attempt is made to transition to the actual behavior of structural elements. Therefore, this paper applies a logic of "almost real" testing, where two columns with square cross-sections were produced and tested. The columns had a rectangular base with cross-section dimensions of 20/20 cm and a height (L) of 300 cm, with a concrete strength of fcm,cube=61.80 MPa. They were reinforced with longitudinal reinforcement (4Ø12 mm) and had a tensile strength of ftm=588.10 MPa. Additionally, stirrups of Ø8 mm were placed at every sw=25 cm. Experimental results show a closer alignment with software calculations using SEISMOSOFT with an accuracy of 96%, while results according to EN 1992-1-1, based on simplified methods, show 64% for the Nominal Stiffness Method and 59% for the Curvature Method. Doi: 10.28991/CEJ-2024-010-02-05 Full Text: PDF

Experimental study and design method of embedded concrete-filled rectangular steel tube column base under cyclic load

Embedded column base has been widely used in concrete-filled steel tube (CFST) structures due to its high rigidity and good seismic performance. However, the strength analysis of the embedded CFST column base was not yet clear since there was little experimental research on it. In this paper, the experimental investigations of six embedded concrete-filled rectangular steel tube (CFRST) column bases under constant axial load and cyclic load were carried out to study the effects of embedded depth, improvement measures and axial compression ratios on the seismic performance of the column bases. The experimental results indicated that setting stiffeners, increasing the embedded depth or axial compression ratios could improve the seismic performance of the column base. In this experiment, the critical embedded depths of the columns with or without stiffeners were 0.7 and 1.5 times the column width B respectively. When the embedded depth was 0.7B, the contribution of anchor bolts to the moment resistance capacity of the column bases could reach up to 14.2%. Based on the analysis of the force transmission mechanism between the column and the concrete foundation in the embedded CFRST column base, a design method considering the contribution of different components to the moment resistance capacity of the CFRST column bases is proposed. The prediction results are in good agreement with the tested results and collected data, within ± 15% error. The parameter analysis based on the design method has revealed the influence patterns of various parameters on the moment resistance capacity of the column bases.

Numerical Investigation of Optimal Hydrodynamic Performance by Changing the Orifice Ratio and Relative Opening of a Land-Fixed Rectangular-based OWC

The energy that can be extracted from the ocean is inexhaustible. An oscillating water column (OWC) is a wave energy converter that extracts this energy. A numerical investigation has been conducted by altering relative opening (α) and orifice ratio (τ) to assess the maximal energy of a land-fixed rectangular-based OWC model in a nonlinear wave field. The power of OWC has also been evaluated by the wave steepness (H/L) alteration. The numeric analysis has been imposed to obtain the optimal power using Fluent software in a three-dimensional tank. Validation of the present numeric model’s result correlates with the printed empirical data. The Finite Volume Method (FVM) solves RANS equations, and the relevant waves are generated at the inlet of the numerical tank by the inlet velocity approach. The efficiency (η) increases with relative openings (α) increase. The efficiency (η) decreases with wave steepness (H/L) increase. The η reaches the optimum shown in the study at H/L = 0.02 and τ = 1.03% for entire values of α. The excellent energy of around 71.3% is attained at α =75% and H/L = 0.02. This study is a highly relevant source of information that finds the optimal efficiency of a land-fixed rectangular base OWC and gives prior knowledge of the performance of OWC before the real-life experiment.

Assessing Seismic Behavior in RC Buildings with Varied Vertical Aspect Ratios: A Comparative Study

Limited space in cities due to urbanization and population growth has given rise to tall and distinctively designed buildings. This study focuses on how a building's vertical aspect ratio (height-to-width ratio) affects the seismic performance of residential concrete buildings. In earthquake-prone Nepal, seismic analysis is crucial for buildings in high-risk areas. We investigated the impact of vertical aspect ratio and the presence of masonry infills and soft stories in reinforced concrete frame buildings. Rectangular base models were analysed at 3, 5, and 7 stories. These models were categorized into bare frames, infill frames, and infill frames with soft stories at the ground level. Linear analysis, non-linear analysis, and design of the building have been performed as per the relevant Indian codes of practice. The effect of infills on dynamic characteristics, yield patterns and capacity has been studied with the help of Non-Linear Analysis. The result of the analysis indicates that the structures have lesser capacity and higher drift with the increase in vertical aspect ratio. It also has been observed that infills contribute to a large increase in the stiffness and strength of the structure, so the deformation capacity of the structure gets reduced.

Perluasan Masalah Isoperimetrik pada Bangun Ruang

In this paper, several extensions of the isoperimetric problem in solid figures are explored, focusing on oblique and right prisms with rectangular, right-angled triangular, and regular hexagonal bases. The objective of this research is to find the prism with the largest volume while keeping the surface area constant. Through manipulations of algebra and simple trigonometry, evidence is obtained that a right prism provides a larger volume than an oblique prism if their surface areas are equal. By utilizing partial derivatives of a two-variable function and the Lagrange multiplier method, conditions for the side lengths are derived to obtain the prism with the maximum volume. The results show that a cube is the solution to the isoperimetric problem, meaning it has the largest volume among prisms with rectangular bases, while for the isoperimetric solution on prisms with right-angled triangular bases, the base of the prism must be an isosceles right-angled triangle. A regular hexagonal prism has a larger volume than prisms with rectangular and right-angled triangular bases if their surface areas are the same.

Experimental definition of lateral stiffness of a pneumatic wheel of the MTZ-82 “Belarus” tractor

BACKGROUND: Due to the excessive vertical and angular vibrations of suspensionless vehicles used in agriculture and road construction that occur during movement, the velocity of their motion is limited, which, in the conditions of a constant traffic flow, reduces the road capacity. Therefore, the search for ways to improve the vibration-isolating properties of wheeled suspensionless vehicles is a relevant issue, the solution of which affects not only on traffic safety and driving comfort, but also on average speed and fuel efficiency.&#x0D; AIMS: To determine the lateral stiffness of the pneumatic wheel from the rear axle of the MTZ-82 Belarus tractor at different tire pressures, basing on bench tests.&#x0D; METHODS: On the basis of the hydraulic pulsation test rig of the Automatic Units department of the VolgGTU, a special-purpose movable supporting and measuring device was developed and assembled, the feature of which is that 4 rollers with flanges are installed on top of the hydraulic actuator force sensor, a flat rectangular base plate is supported on these rollers and connected with a vertical frame of the rig through a force-measuring device by means of a screw mechanism. The tested wheel is mounted on the base plate, the wheels axle is fixed on a vertically-moving traverse, on top of which weights creating the necessary vertical force are fixed. The test procedure consisted in measuring the lateral force and lateral displacement of the base plate until the tire slip occurred at the following tire pressures: at the recommended pressure of 0.16 MPa and at reduced pressures of 0.12, 0.08 and 0.04 MPa.&#x0D; RESULTS: Based on the test results, the elastic characteristic curves of the lateral stiffness of the tested wheel were obtained. These characteristic curves have a regressive form, as their slope significantly decreases with a significant reduce in tire pressure. Thus, when the tire pressure is reduced from 0.16 to 0.12 MPa, there is practically no difference in the obtained values of lateral stiffness, which reaches 112.5 kN/m. After a 2-fold tire pressure reduction, the lateral stiffness decreases by 7%, and after a 4-fold reduction, by 28%. At the same time, the static tire deflection increases from 22 to 32 mm, which significantly increases the contact patch of the tire with the ground.&#x0D; CONCLUSIONS: By means of the tests carried out, it is established that tire pressure reduction by 2550% of the recommended value does not have a significant effect on the loss of lateral stiffness of the pneumatic wheel of the rear axle of the MTZ-82 Belarus tractor, which is important to use in order to increase traction and improve ride comfort of wheeled tractors.

Numerical Analysis on Improving the Rectangular Texture Floating Ring Gas-film Seal Characteristics with Different Bottom Shapes

Finding the right texture pattern to effectively improve the sealing performance of the floating ring gas film seal has always been a topic of interest for engineers. Herein, to reveal the effect of the rectangular textured base shape on the sealing characteristic parameters of floating ring gas film seal, four bottom shapes of rectangle, isosceles triangle, left triangle and right triangle were proposed. The governing equations were solved by the finite difference method and the correctness of the theoretical results was verified by the test bench. The effect of operating conditions parameters on the sealing performance were also analyzed. The results reveal that the trends of the experimental results is consistent well with the theoretical results, in which the relative errors are all less than 9%. It indicates that the theoretical model is scientific and valid. As the speed and inlet pressure increase, the texture bottom shape significantly changes the distribution of pressure and temperature field. And the average gas film thickness determines whether the texture produces an effect or not. Under the same operating conditions, a right-angled triangular bottom shape can obtain a good stability and cooling effect for the sealing device. With a bottom shape of the right triangle and a bottom shape of the rectangle, the maximum difference in opening force and gas film temperature rise were calculated to be 234.91 N and 0.61 oC, respectively. The research results provide theoretical support for further study of the textured floating ring gas film seal and a reference for texture optimization.

Aizanoi’dan Yeni Onurlandırma Yazıtları

In this paper, four new honorific inscriptions from Aizanoi are presented. All of the inscriptions have been found in Çavdarhisar during the excavation seasons of 2021 and 2022 and excluding n. 2, the stones are rectangular bomos-type statue bases. Inscriptions are dated to the Roman Imperial Period. N.1 is the honorary inscription of Lucius Claudius Lepidus who was the life-long high priest of the emperor in the reign of Commodus. He was the chief priest of Asia and the neokoros of the temples in Smyrna. The inscription was erected by the phyle Asklepias, the name of which first came into light due to the excavations in the theater in 2020. N. 2 is a honorific inscription of a chreophylakes whose name is unfortunately missing. Chreophylakia was a prominent public office in Aizanoi, as seen in the honorific inscriptions of the city’s elite citizens. N. 3 and n. 4 are rectangular bomos-type statue bases. Both of them are honours of the “πατρίς”. Although ἡ πατρὶς occurs frequently in the inscriptions of Aizanoi, it was in the nominative case in only two published examples. N. 3 belongs to Philiskos, son of Philiskos, the ephebos. Finally, n. 4 is the statue base of Neikostratos, son of Dionysios, the stephanephoros, honoured by his fatherland.

КОНТАКТНАЯ ЗАДАЧА ДЛЯ ПРЯМОУГОЛЬНОЙ ПЛАСТИНКИ НА УПРУГОМ ОСНОВАНИИ В ПОЛЯРНЫХ КООРДИНАТАХ

In this paper, the problem of calculating a rectangular plate on an elastic base in polar coordinates by the Zhemochkin method is considered for the first time. Such problems arise, for example, when metal columns of circular cross-section are supported on rectangular bases lying on a concrete base. When solving this problem, several types of Zhemochkin plots in polar form were used. The Saint-Venant principle was widely used to determine the displacements of the elastic base from a single force distributed over a complex-shaped Zhemochkin section. Two examples are considered: a square plate on an elastic base and a rectangular plate also on an elastic base. In the last example, along with the Zhemochkin sections, rectangular sections were used in polar coordinates. Numerical results are obtained showing the phenomenon of decreasing contact stresses in places near the corners of the plate.

Study of the Materials and Techniques of a Rare Papier-Mâché Mushroom Model Crafted in H. Arnoldi Factory.

The Natural History and Science Museum of the University of Porto houses a collection of 45 models of fungi in papier-mâché from the 19th-century, which were used at the university until 2015 as didactic models. For the first time, the materials and techniques used in the production of a Boletus edulis model were studied (vernacular name: cep, porcini). These sculptures, made to life-size scale, are painted in colors similar to those of the represented species (white, brown, and light brown). They are fixed to a rectangular base, which is painted black, and to which moss has been pasted. To fully characterize each color, at the molecular level, a multi-analytical approach was used, combining energy-dispersive x-ray fluorescence spectroscopy (micro-XRF) with fingerprinting techniques of Raman microscopy (microRaman and handheld Raman) spectroscopy and microFourier transform infrared spectroscopy (microFTIR). The papier-mâché was prepared with a groundwood paper to which kaolin and a quartz-based material have been added to reinforce the structure. Raman microscopy also identified carbon black in it, which is possibly responsible for its grey color. The white color was unequivocally identified as lithopone by microRaman. This white paint was prepared in a proteinaceous tempera, with calcium carbonate having been identified as filler (by microFTIR). In the brown color, iron was identified by microXRF, pointing to the use of ocher, which was not possible to identify by microRaman and microFTIR. Regarding the black rectangular base, the moss was fixed using a collagen-based glue. The binding medium in this black is possibly a mixture of drying oil and protein. Again, XRF detected iron as the main element, but it was not possible to acquire a Raman spectrum due to the high fluorescence of the binder/varnish. Others, such as the writing inks, will also be discussed. The colors identified are in line with the best materials available for use by artists of that time. This new knowledge is fundamental to informing the choice of the best conservation strategies for the preservation of these extraordinary models.

ПЛОСКА ЗАДАЧА ПРО КОЛИВАННЯ БАЛКОВОЇ ПЛИТИ НА ПРЯМОКУТНІЙ ОСНОВІ

he plane contact problem of a beam’s oscillations on a rectangular elastic base is considered. The vertical edges of the rectangular base are in conditions of the nonfriction contact, the lower edge is fixed, and a beam (beam plate) with free ends is attached to the upper edge. The normal loading is applied to the beam and harmonically changes in time. To solve the boundary valued problem for the elastic base the integral transform method is applied. The apparatus of the Green’s function is used to construct the solution for the boundary valued problem for a beam. The displacements of the rectangular base and the deflection of the beam were found. The interface condition between the base and the plate is used to derive the integral singular equation relatively the dynamical contact stress. The orthogonal polynomial method was used to solve the integral equation. The investigation of the oscillations’ frequency influence on the deflection of beam and elastic rectangular base’s displacements and stress was conducted.