APPLICATION OF SINGULAR MATRIX BEAMS IN THE SYMMETRICAL PROBLEM OF DEFINITION OF EIGENVALUES - Semenova, Elena; Ivakin, Yan; Frolova, Elena; Fomina, Alena; Smirnova, Maria (Journal of Applied Engineering Science, 2018)
The generalized problem of eigenvalue and vectors for singular matrix beams is central in the class of problems of rational construction of computed spectral models of complex modular systems. Solving this problem provides an opportunity to solve these problems, what determined the relevance of this work. The design calculations of complex modular-modular systems have a multivariate character for ensuring their optimal characteristics due to variation within the permissible limits of the elastic-inertial parameters. In the general case such calculations acquire the character of structural-parametric synthesis, when the varied space is supplemented by corrective dynamic devices. The purpose of this article was to provide basic methods for carrying out these calculations. The approach based on the singular decomposition of characteristic matrices was taken as the basis of the research in this paper. This allowed the authors to propose a set of methods for solving this problem, adaptively taking into account the specificity of the available input data. The theoretical significance of the work lies in the development of the modern mathematical and algorithmic apparatus of singular matrix beams, and practical in developing a scientific and methodological basis for solving a corresponding class of applied problems of the dynamics of mechanical and electromechanical systems, for equivalent mathematical and simulation modeling of systems of this class.