Analysis of the Vibration Behaviors of Rotating Composite Nano-Annular Plates Based on Nonlocal Theory and Different Plate Theories

Rotating machinery has significant applications in the fields of micro and nano meters, such as nano-turbines, nano-motors, and biomolecular motors, etc. This paper takes rotating nano-annular plates as the research object to analyze their free vibration behaviors. Firstly, based on Kirchhoff plate theory, Mindlin plate theory, and Reddy plate theory, combined with nonlocal constitutive relations, the differential motion equations of rotating functionally graded nano-annular plates in a thermal environment are derived. Subsequently, the numerical method is used to discretize and solve the motion equations. The effects of nonlocal parameter, temperature change, inner and outer radius ratio, and rotational velocity on the vibration frequencies of the nano-annular plates are analyzed through numerical examples. Finally, the relationship between the fundamental frequencies and the thickness-to-radius ratio of the nano-annular plates of clamped inner and outer rings is discussed, and the differences in the calculation results among the three plate theories are compared.

Estimation of the value of leaks through a through defect of the pipeline when using in-pipe repair elements

The loss of hydrocarbons when using in-pipe repair elements is determined by the nature of the fluid flow in the gap between the pipe and the repair sleeve. An accurate analytical calculation of the flow parameters for a real sleeve, taking into account its length, the asymmetry of the defect and other design features, is very difficult. In this article, the problem of accurate calculation of the radial flow of a viscous incompressible fluid in a thin layer between two annular plates simulating a circular region with a center coincide with a pipeline defect is solved. The area consists of two circles formed by the pipeline wall with a through defect and the surface of the internal repair element. The results obtained will allow us for accurate calculations in the area adjacent to the defect of the pipe and approximate calculations for the whole repair element.

Determination of Prestress in Circular Inhomogeneous Solid and Annular Plates in the Framework of the Timoshenko Hypotheses

Determination of prestress fields in structures is of the utmost importance, since they have a significant impact on operational characteristics, and their level and distribution must be strictly controlled. In this paper, we present modeling of bending vibrations of solid and annular round inhomogeneous prestressed plates within the framework of the Timoshenko hypotheses. New inverse problems of prestress identification in plates are studied on the basis of the acoustic response subjected to some probing load. To solve direct problems on calculating oscillations and amplitude-frequency characteristics, a computational Galerkin-method-based scheme has been developed. In order to treat the inverse problems, we use a special projection approach based on the constructed weak problems statements, which makes it possible to determine the desired characteristics in the given classes of functions. The developed techniques for solving direct problems are implemented in the form of software packages realized via Maple. For both solid and annular plates, we estimate the sensitivity of the amplitude-frequency characteristics the values of which are used as the additional data in the inverse problems to a change in the prestress level; we conclude that the most favorable frequency range should be selected in the resonance vicinity. We have conducted a series of computational tests on reconstructing the plate’s prestresses of various levels and distribution patterns (decreasing, increasing, sign-changing laws). The results of computational tests revealed that the technique developed allows for the determination of the prestresses with a low error for two cases: when the cause of prestress formation and its type are known and when arbitrary prestress changing laws are considered.