Static accounting of highest modes in problems of structural dynamics

The calculation of building structures for dynamic effects is usually performed according to the method of decomposition by its own forms of vibrations. However, the problem is that such a method gives an exact solution of the dynamic problem with full consideration of the entire spectrum of modes. Moreover, when solving practical problems with the use of software systems, dynamic calculations are performed approximately taking into account a limited number of the first natural modes of oscillation. The contribution to the dynamic response of the structure of unaccounted higher forms of oscillations, as a rule, is not evaluated at all. The results show that the error of such a solution to a dynamic problem can be significant. Consequently, this paper is devoted to the method of static registration of higher forms of oscillations in problems of the dynamics of building structures. The description of the main provisions of the method is given, examples of its implementation in the calculation of spatial structures under the action of an external harmonic load are given. With the help of a computational program complex, the displacements of nodes and internal forces in the elements of the structures under consideration are determined. Various parameters of the dynamic effect and the number of vibration modes taken into account were set. The adopted method of static accounting for higher forms of oscillations requires solving one dynamic problem and two auxiliary static problems. An important circumstance of the approach is that one of the static problems should be solved by the method of decomposition in its own forms of vibrations. The approach proposed in the article allows to significantly reduce the computational costs of dynamic calculation in comparison with the classical approach. This result can be of great importance when solving problems for complex dynamic effects and for structures that are not uniform in hardness.