FEATURES OF CALCULATION OF VIBRATIONS OF A PINCHED ROUND PLATE

A method for calculating the vibrations of a circular steel plate, clamped around the circumference and loaded with a short-term load, with the determination of the frequency of the fun damental tone (the lowest type of vibration), is considered. For practical calculations, the influence of the mass of the plate itself, as well as the mass of air or liquid, on the frequency of natural oscillations is taken into account.

CALCULATION OF THE DEFLECTION OF A PINCHED ROUND PLATE

A method for calculating the deflection of a round flat steel plate pinched along the edge, bearing an axisymmetric load, is considered. For practical calculations, dimensionless coeffi cients of deflection in the center and in the area of fixing a round flat plate pinched along the edge are applied, the stress coefficient and the accompanying function, which depends on the deflection of the plate and the pressure force on it, are taken into account

ANALYSIS OF PROPERTIES AND STRUCTURE CHANGE PROCESS SAMPLES MATERIAL UNDER EXPOSURE ULTRASONIC STABILIZATION

The most important task of precision engineering on the modern stage is the development of effective technological processes of manufacturing, providing not only achieving high precision at low costs, but also retaining the original in terms of accuracy throughout the life of the product. (Research purpose) The research purpose is in studying the possible negative effect of ultrasonic mechanical vibration in the process of stabilizing the deformation of circular plates on the subject of appearing of various kinds of micro-cracks, which result will be a sharp decrease in resource products in general, and to make a comparative analysis of changes in the properties and structure of the material. (Materials and methods) Half of the prepared samples were processed using a thermomechanical technology based on the cyclic action of a liquid or gas in different temperature conditions, the other part of the samples was processed using the proposed technology based on the method of ultrasonic mechanical action. The end section of the round plate for both processing options was prepared. (Results and discussion) In the structure of the material of both the samples treated by different methods, there are certain bundles of the micro-cracks type caused by plastic impact. The structure of sample material processed by standard method is more rough, the concentration of microcracks in the material of the sample treated by ultrasonic impact does not exceed the concentration of microcracks of the sample material processed in a standard way. (Conclusions) Changing the structure of the material of the round plate after ultrasonic treatment may not have a negative impact and does not affect the durability of the product during operation. With the correct choice of the ultrasonic treatment mode, a more uniform stress reduction can be achieved during the processing, and the quality and efficiency of the process can be improved. Ultrasonic processing increases the mechanical characteristics of the material, such as tensile strength and proportionality.

ANALYSIS OF PROPERTIES AND STRUCTURE CHANGE PROCESS SAMPLES MATERIAL UNDER EXPOSURE ULTRASONIC STABILIZATION

The most important task of precision engineering on the modern stage is the development of effective technological processes of manufacturing, providing not only achieving high precision at low costs, but also retaining the original in terms of accuracy throughout the life of the product. (Research purpose) The research purpose is in studying the possible negative effect of ultrasonic mechanical vibration in the process of stabilizing the deformation of circular plates on the subject of appearing of various kinds of micro-cracks, which result will be a sharp decrease in resource products in general, and to make a comparative analysis of changes in the properties and structure of the material. (Materials and methods) Half of the prepared samples were processed using a thermomechanical technology based on the cyclic action of a liquid or gas in different temperature conditions, the other part of the samples was processed using the proposed technology based on the method of ultrasonic mechanical action. The end section of the round plate for both processing options was prepared. (Results and discussion) In the structure of the material of both the samples treated by different methods, there are certain bundles of the micro-cracks type caused by plastic impact. The structure of sample material processed by standard method is more rough, the concentration of microcracks in the material of the sample treated by ultrasonic impact does not exceed the concentration of microcracks of the sample material processed in a standard way. (Conclusions) Changing the structure of the material of the round plate after ultrasonic treatment may not have a negative impact and does not affect the durability of the product during operation. With the correct choice of the ultrasonic treatment mode, a more uniform stress reduction can be achieved during the processing, and the quality and efficiency of the process can be improved. Ultrasonic processing increases the mechanical characteristics of the material, such as tensile strength and proportionality.

NUMERICAL ANALYSIS OF CIRCULAR PLATES ON AN ELASTIC BASE WITH VARIABLE BED COEFFICIENT

The paper presents the results of a study of the stress-strain state of a circular plate of constant cylindrical stiffness, which lies on a variable elastic foundation and is under the influence of a continuously distributed transverse load. Twelve variants of calculation are considered ‒ six for a steel round plate and six more ‒ for a concrete round plate under two conditions of fixing and three different laws of variation of the bed coefficient. To solve the problem, the finite element method implemented in the LIRA-SAPR software package is used. It is noted that in the case when the bedding coefficient is a variable value depending on the coordinate in which the foundation settlement is determined, the analytical approach leads to the need to solve the corresponding differential equations with variable coefficients. Therefore, calculations of circular and annular plates lying on a variable elastic foundation by means of analytical solutions of differential equations are extremely rare in scientific periodicals and are of a private nature. An effective method for the analytical solution of differential equations with variable coefficients for a number of problems in mechanics was proposed by one of the authors of the article, however, the application of the method to the calculation of a circular plate on an elastic foundation with a variable bed coefficient requires verification, therefore, here we consider the features of the finite element analysis of such a plate under different boundary conditions and different laws of variation of the bed coefficient. In all versions, the results completely coincide with the known results of bending of slabs that do not have an elastic base and in the case when this base exists and its resistance is constant. The discrepancy here is very insignificant ‒ in the third significant digit after the decimal point for deflection when hinged and in the second for moments. In case of rigid clamping, the deflections and moments also differ from the corresponding values of the known solutions in the second significant digit after the decimal point.

ANALYTICAL AND NUMERICAL STUDIES OF THE STRESS-STRAIN STATE OF ROUND PLATES ON AN ELASTIC BASE WITH A VARIABLE BED COEFFICIENT

The results of the study of the stress-strain state of a circular plate of constant cylindrical stiffness lying on an elastic foundation with a variable coefficient of elastic resistance are presented. Eight calculation options are considered − four each for a concrete round slab and for a steel round plate − under two conditions of fastening (hinged and rigid along the entire contour) and two laws of variation of the bed coefficient (according to the linear law and according to the law of the concave parabola). To solve the problem, the authors applied a general analytical method for solving differential equations with variable coefficients. The finite element method is used to verify the results. Comparison shows that the results coincide very well in deflections, differing in the third or fourth decimal places, and somewhat worse − in moments.

Mathematical analysis of influence of ultrasonic stabilization of residual stresses in round plate details

The most important task of precision engineering at the present stage is the development of more efficient technological processes for manufacturing parts that ensure not only high accuracy at a minimum cost, but also the preservation of the original accuracy indicators throughout the entire service life of the product. (Research purpose) The research purpose is in studying the technological operation of stabilization of residual stresses of a round plate based on the method of relaxation of residual stresses by the influence of oscillatory movements of ultrasonic frequency. (Materials and methods) The article notes that the parts and components of the sensors are connected to each other, mainly by means of screws and other threaded connections; the abundance of springs (of return type), internal backlashes of mobile mechanisms, contributes to the occurrence of residual stresses (shrinkage, lapping), which affects the stability of the readings. Authors proposed a method and performed mathematical modeling of ultrasonic stabilization of the deformation of a round plate (elastic sensing element), having previously provided tension by the influence of an external load on its surface. Authors have found that this technology provides high performance and is not difficult to implement from a technical point of view. (Results and discussion) It was found by mathematical analysis that the processing time depends inversely on the vibration frequency of the plate, so processing the plate with an ultrasonic frequency significantly reduces the required processing time, increases its performance compared to traditional methods of training. (Сonclusions) With a small amplitude of these vibrations, the energy of a single oscillation cycle decreases, and this significantly reduces the amount of accumulated deformation, which improves the quality of processing.