Optimization problem of external dynamic influences for the elimination of vibration phenomena in composite elastic building structures

Abstract

Abstract The paper considers the actual task of construction engineering: the elimination of harmful (undesirable) vibration phenomena in composite metal building structures and bridge cable-stayed systems – complete damping and vibration of the bridge cable-stayed system entails the calming of the entire bridge structure. Similar problems arise when designing devices that lead to dynamic rest of network antenna structures. The presentation of the material is based on the main provisions of the modern theory of optimal control of distributed differential systems with network carriers. An extensive literature is devoted to the sanctification of the research of the mentioned problem, however, an exhaustive solution of the problems of controlling elastic structures by external influences of various types (distributed, boundary, starting, and point control) and a comparative analysis of their properties did not find their place in these studies. In addition, the ways of algorithmization of previously obtained results are not always specified. The paper uses a mathematical model describing small oscillations of a spatial string system. It is convenient to use such a system and approaches to the analysis of its mathematical model as a fairly simple fundamental object when considering a more complex object, which is an elastic system of more complex elements. The results of the work are presented in a form that makes it possible to formalize the computational procedure, which is convenient for algorithmizing the process of determining the solution, and therefore for the modern application of computer technology. It remains to add that the work indicates ways to transfer the obtained results to the case of analyzing optimal control problems with carriers on multidimensional network-like domains.