As a matter of fact, it is possible to identify a number of characteristic features in the dynamic behavior of symmetric systems that make their use particularly convenient. A dichotomous lattice with different coefficients of similarity between rows is considered. Vibrations of Systems with Geometric Symmetry. This paper provides a tutorial and summary of the theory of circulant matrices and their application to the modeling and analysis of the free and forced vibration of mechanical structures with cyclic symmetry. The physical sense of the introduction of complex variables in rotor systems is justified. The E-mail message field is required. The use of idealized elements with distributed parameters and known analytical solutions for both the local elements and the subsystems.
The second approach deals with statistical method of the increase of solution stability. The article is of interest for specialists in the field of creation of vibration technology machines and equipment. The study of the dynamic processes in such systems can lead to exhaustive results only when the system is treated as a whole entity and the interactions between the all substructures and elements are taken into consideration. The various kinds of bases under machines, cyclically repeated forms of stators, reduction gears, rotors with blades mounted on them, etc. A number of static and dynamic features of lattice under vibration have been found. Methods using lumped parameters models, i.
They have been studied in many areas of science: chemistry, physics, biology, etc. Optimal relationships are established between the balancing accuracy, the precision of measurement instrumentation, and the dynamic model of the system under consideration. The computational models of such systems represent a hierarchical structure and contain hundreds and thousands of parameters. Mechanical Vibratory Systems with Hierarchical Structure. The area stability for a rotating rotor is found analytically.
The two most widely used approaches to the simulation of such systems are as follows: 1. Methods using lumped parameters models, i. They form various kinds of machine platforms, cyclically repeated forms of stators, rotors with blades mounted on them, etc. Is this product missing categories? We will call the system that satisfies the above-mentioned conditions an unidirectional chain system with reflection symmetry elements. Symmetric systems are widely applied also in the civil engineering where their use is convenient due to technological process, type-design, and architectural requirements. Systems with geometric symmetry find wide application in many areas of engineering. Knowledge of an impact of a linked mass on a behavior of machine tools is a useful guide for their designers.
Vibrations of Rotor Systems with Periodic Structure Liudmila Ya. A nonexhaustive survey of the relevant literature is also included, which can be used for further examples and to point the reader to important extensions, applications, and generalizations of the theory. Approaches to build mathematical models that take into account unilateral constraints, the relationships between elements, with the vibrating surface are developed. They have been studied in many areas of science: chemistry, physics, biology, etc. The possibility of control of dynamical condition of the shakers that are designed for vibration treatment of parts interacting with granular media is discussed. The concept of monitoring the dynamic state of the vibration table based on the original measuring devices is proposed.
Does this product have an incorrect or missing image? The difficulties of design determination of the quantitative characteristics of weight, elasticity, damping, critical frequencies of fast-revolving rotors are demonstrated. . Vibrational properties of self-similar structures in which each cell at a certain scale follows the structure of the previous one are studied. The vibrations of the systems with the parameters changing in length with some scale, namely, longitudinal vibrations of a bar with localized masses, a beam with a stepped section, and the two-dimensional self-similar grating, are studied as examples. Systems with Periodic Structure Liudmila Ya. The work is based on original research by the authors.
In turn, these mechanisms consist of various elastic subsystems and components. Mechanical Vibratory Systems with Hierarchical Structure. The computational models of such systems with a hierarchical structure contain hundreds and thousands of parameters. The accuracy of the algorithm developed for identification by static influence coefficients is studied. Small oscillations about the position of static equilibrium are performed. There exists a large body of literature devoted to the study of the statics and dynamics of symmetrical structures. The book includes extended studies of even complicated machinery structures with an emphasis on flight vehicle engines.
The main problems in the analysis of such systems are the dim- sion reduction of model and revealing the dominant parameters that determine its dynamics and form its energy nucleus. The computational models of such systems represent a hierarchical structure and contain hundreds and thousands of parameters. All connections of an element at the input into and the output from it must be symmetric with respect to П-П. Our presentation of the basic theory is distilled from the classic book of Davis 1979, Circulant Matrices, 2nd ed. Contents: Mechanical Vibratory Systems with Hierarchical Structure. Systems with geometric symmetry are used widely in many areas of engineering.
This paper demonstrates a general approach which leads to a set of locally optimal parameters of mass, whose connection to the machine consequently suppresses vibrations during machining. It is suggested to use two approaches in order to obtain accurate and stable solutions of ill-conditioned reverse problems of rotor dynamics. The various kinds of bases under machines, cyclically repeated forms of stators, reduction gears, rotors with blades mounted on them, etc. General Imprint: Springer-Verlag Country of origin: Germany Series: Foundations of Engineering Mechanics Release date: November 2009 First published: 2010 Authors: Dimensions: 235 x 155 x 15mm L x W x T Format: Hardcover Pages: 252 Edition: 2010 ed. Obtained parameters can be structurally interpreted e.