The stability analysis of the market price using Lambert function method

In this article we are going to analyze market price stability with different market intensity coefficient and delay argument values. Market price is described as a scalar differential equation with a delay argument. In order to find solutions for the transcendental equation we will use method based on Lambert function. We will present examples of the applications of the method.

Application of the ultrasound control to evaluation of the crack-resistance of low-carbon martensite steel 07Kh3GNMYuA

The goal of the study is to reveal the impact of change in the structural state of steel 07Kh3GNMYuA after heat treatment on the values of the critical stress intensity coefficient (K1c) obtained at a temperature of 50°C and on the velocity of ultrasound wave propagation, as well as to determine a correlation between them for rapid assessment of the crack resistance using acoustic characteristics. The mechanical characteristics of the material and the critical stress intensity coefficient K1c were obtained on the test machine «Inspekt 100 Table». The tangent method is used for determination of K1c. Three samples per K1c value were used in the experiment for a three-point bending scheme at the operating temperature T = –50°C. Acoustic parameters were measured using the echo-pulse method. The results of ultrasonic scanning of heat-strengthened samples made of steel 07Kh3GNMYuA demonstrated the possibility of non-destructive quantitative evaluation of the critical stress intensity coefficient. New data on the mechanical properties of steel 07Kh3GNMYuA and on the correlation between the velocity of longitudinal elastic waves and the values of the critical stress intensity coefficient of structures were obtained. Deviation of the calculated values of K1c obtained using acoustic measurements from the experimental values does not exceed 10%. The proposed model, which explains change in the acoustic characteristics of steel 07Kh3GNMYuA on the basis of phase changes occurring in the steel structure upon tempering, provides conducting of similar studies for other modes of heat treatment and other steel grades. The method is a low labor- and time-consuming procedure for determination of the mechanical characteristics of the products made of steel 07Kh3GNMYuA, since it does not require the manufacturing of samples and their testing. The developed procedure can be proposed for manufacturing application, as the main or additional method for evaluation of the mechanical parameters of materials after various modes of heat treatment.

Crack Resistance Increase of Bushings while Assembling Joints with Tension

In order to restore worn parts during repair work, it is often used to press the repair bushings. While assembling joints, cracks may form in the spanning part (bushing), as it may have surface and structure defects. Therefore, an urgent task is to increase the crack resistance of joints with tension during its assembly. The paper examines the influence of the geometry of the spanning part on the process of cracking. To assess the effect of defects on the crack formation, the method of modeling defects with a surface crack of a semi elliptical shape was used. The crack resistance is estimated using the force criterion of fracture mechanics – the stress intensity coefficient. As a result, it was found that the ratio between the wall thickness of the enclosing sleeve and its outer diameter has a significant effect on the crack resistance of the joint with tension, which allows reducing the origin probability and crack development during its pressing by varying these parameters. While assembling joints, the following methods are often used: mechanical-using a press and thermal with heating of the covering part. When the method of joint with cooling of the covered part, the greatest strength of the joint is achieved, but the probability of cracking increases. This is because when the temperature of the enclosing sleeve decreases in contact with the cooled shaft, the critical stress intensity coefficient (fracture toughness), which is a mechanical characteristic of crack resistance, decreases. To reduce the effect of cooling the sleeve, you can use a combined method of assembling the joint, in which the covered part is cooled and the covering part is heated. It is shown that to assess the fracture resistance at low temperatures, it is optimal to conduct full-scale tests, where the cooling and heating temperatures of the press joint parts are the experimental factors.

RELIABILITY ANALYSIS OF REINFORCED CONCRETE FLEXURAL ELEMENT ON CRACKING BASED ON FRACTURE MECHANICS

The article describes a probabilistic approach to the reliability analysis of a flexural reinforced concrete element by the cracking criterion using the provisions of fracture mechanics. Two mathematical models of limit state are proposed for reliability analysis: with the evaluation of the critical stress intensity coefficient directly and through the design concrete compressive strength. On the basis of regression analysis, the relationship between the critical stress intensity coefficient and the design concrete compressive strength is established which can be used in the inspection of reinforced concrete structural elements. The influence of the design concrete compressive strength on the failure (cracking) probability of the flexural reinforced concrete element is analyzed. The numerical example of reliability analysis is given for the reinforced concrete beam by the criterion of cracking. It is noted that the required level of reliability should be set for each structural object individually based on the acceptable risk value using economic and non-economic losses.

A PROBABLISTIC APPROACH TO EVALUATION OF THE ULTIMATE LOAD ON FLEXURAL RC ELEMENT ON CRACK LENGTH

The fracture mechanics of concrete and reinforced concrete is a promising direction in the development of methods for reinforced concrete structural elements design and inspection. At the same time, probabilistic methods of design and behavior analysis of structural elements are of particular interest. The article describes a probabilistic approach to load-bearing capacity and reliability analysis of flexural reinforced concrete elements based on the crack length criterion. The functional relationship between the critical stress intensity coefficient of concrete and the design compressive strength of concrete is given. The article presents a method for the reliability analysis of flexural reinforced concrete elements at the operational stage with limited statistical data about the critical stress intensity coefficient of concrete. The ultimate value of the failure probability (or reliability index) should be set for each object individually based on the value of the acceptable risk.

Cardiac Microstructural Abnormalities Identify Women at Risk of Incident Heart Failure

ABSTRACTBackgroundIncidence of congestive heart failure is difficult to predict by standard methods. We have developed a method called the signal intensity coefficient that uses echocardiographic texture analysis to quantify microstructural changes which may occur in at-risk patients prior to development of a clinical heart failure syndrome.MethodsParticipants from the Framingham Offspring Cohort study who attended the 8th visit and received screening echocardiography were included. Participants were followed for a mean of 7.4 years for incident congestive heart failure. Cox proportional hazards modeling was used to assess the hazard ratio of signal intensity coefficient in the top quartile of values versus other quartiles in the total and sex-stratified population.Results2511 participants with interpretable echocardiography and no history of congestive heart failure, stroke, or myocardial infarction were included in this study. The top quartile signal intensity coefficient had a hazard ratio of 1.83 (p=0.0048) for incident heart failure. When additional clinical risk factors were added to the model, this became non-significant. Within women, an elevated hazard ratio was significant in multiple models including age and hypertensive medication use. Models were not significant in men.ConclusionsElevated signal intensity coefficient is associated with an increased risk of incident congestive heart failure. This trend remains significant in women after inclusion of age and hypertensive medication use. The signal intensity coefficient may be able to identify patients at risk of developing congestive heart failure using echocardiographic texture analysis.

Increase of energy efficiency and competitiveness of mechanical systems on the basis of anisotropy of nonlinear frictional bonds

Interaction dynamics of contacting micro- and macroroughnesses of friction surfaces defines the main tribocharacteristics: friction factor, a wear-out type, its intensity, coefficient of energy efficiency of all the system. Reliability and energy efficiency of mechanical systems substantially depend on reliability and energy efficiency of their friction units. In their turn, reliability and energy efficiency of friction units are defined by interaction of the dynamic processes happening in frictional and mechanical subsystems.

Sensitivity of the Hawt noise level predicted based on Amiet’s theory on the value of a turbulence intensity coefficient determined numerically

In the paper the authors presented and compared two methods of the HAWT noise predicting. The priority, however, was to test the possibility of using Amiet's theory to determine the noise value in the far field. In this theory it is necessary to know the value of the turbulence intensity coefficient. The value of this coefficient was determined based on numerical modeling. The NACA 0012 profile was used for the airfoil shape. The ANSYS/Fluent program was used for numerical calculations, where the k-ω SST turbulence model was used to simulate the flow, and Ffocs- Williams and Hawkings model was used to determine the noise level. The turbulence intensity coefficient estimated in this way was then used to determine the noise value from the wind turbine airfoils using Amiet's theory.