The problem of flexible vibrations of a rectangular orthotorque plate clamped along the contour is considered. The general solution of the problem, which satisfies the vibartion equation identically, is constructed on the basis of the superposition method in the form of two Fourier series. Clamped boundary conditions lead to a homogeneous infinite system of linear algebraic equations with respect to unknown coefficients in the general solution. The uniqueness of a bounded non-trivial solution of an infinite system for the natural frequency is proved, the asymptotics of the unknowns are found, and an effective solution algorithm is constructed. Examples of the numerical implementation of the developed algorithm for calculating the natural frequencies and natural modes of the plate vibrations are given.

Keywords: plate, vibrations, natural frequencies, planar forces, superposition method, infinite system of linear equations, asymptotics

The paper calculates the probability of failure-free operation of parts of the supporting structure of foreign-made lifting equipment designed to perform loading and unloading operations of stone building material. When performing calculations, computer modeling of the stress-strain state by the finite element method was used. A distinctive feature of the proposed calculation methodology is the minimum required number of computer experiments, given that some of the input data are variable.

Keywords: probability of failure-free operation, lifting equipment, reliability

The article discusses the importance of using computer modeling to analyze the technical and operational characteristics of products, identify possible failures. The paper presents the results of a study of the operational conditions of a threaded connection, and draws conclusions about the effectiveness of using the ANSYS software in the design of mechanical engineering products.

Keywords: threaded connection, modeling, innovative technologies, optimization, safety margin, performance characteristics, thread pitch, mechanical engineering

In article there is considered the application of the finite difference method to plate bending problems. There are done the calculations of simply supported rectangular plate on an elastic foundation by the finite difference method and to verify the results there is done comparison with the results obtained by double trigonometric series. For more accurate results is studied the degree of discretization of the finite difference mesh.

Keywords: finite difference method, plate on an elastic foundation, Winkler model, governing differential equation of the plate, finite difference operator

The points of stress concentration in the sections of structural elements are considered. These include, in particular, crack tips that may appear both during operation and as a result of a violation of their production technology. The values of stress intensity factors in the vicinity of cracks in the considered sections with contour corner points are obtained. In addition, the study of indicators in the asymptotic solution of the elasticity theory problem for bodies made of isotropic materials in the vicinity of the structure rod element corner point of the section, where the sides (or one of them) are supported by a thin coating, was carried out. On the other side of the corner region, various conditions for its reinforcement are assumed, including the presence of a thin elastic coating. Mathematically, the solution of the problem is reduced to the transcendental characteristic equation solution, that is, to the problem of finding the equation roots that is constructed from the condition for the existence of a non-zero solution to a linear homogeneous equations system. The characteristics of the stress components were determined for various combinations of boundary conditions, physical and geometric parameters. Qualitative conclusions are made. In particular, values these parameters are established combinations , at which the behavior of stresses at the section corner point becomes singular.

Keywords: stress intensity factor, isotropic elastic bodies, structural element, section corner point , crack, thin elastic coating, boundary conditions, characteristic equation, stress concentration