Calculation of building structures for several dynamic effects with a static accounting of higher forms of oscillation

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Relevance. When calculating building structures for dynamic effects, the method of expanding the desired solution in a series according to the forms of natural oscillation is traditionally used. Depending on the complexity of the tasks to be solved, it is required to take into account a different number of forms - from the first few forms to tens or hundreds of forms. The results obtained are all the more accurate the more forms the calculation takes into account. As a rule, the contribution to the required parameters of the stress-strain state of the structure of unaccounted for higher oscillation forms is not evaluated in any way, although in some cases this must be done. In addition, the important question arises of performing the calculation with a reduced number of considered forms so as to obtain a sufficiently accurate result. The aim of the work. This work is devoted to the method of static accounting of higher forms of oscillation in the problems of the dynamics of building structures. The basic principles of the method are described, its use on a spatial rod system loaded with several harmonic forces with different frequencies is considered. Methods. The method of static accounting of higher forms of oscillations studied in this work requires the solution of one dynamic problem with a small number of forms and an auxiliary static problem. An important circumstance of the approach is that the static problem must be solved in two ways: the exact one and the decomposition method according to its own forms of oscillation, after which the static correction to the dynamic solution is calculated. Results . The approach proposed in the article can significantly reduce the computational cost of dynamic calculation in comparison with the classical approach with comparable accuracy of the results. This may be of value in solving problems of complex dynamic effects and for structures with inhomogeneous rigidity.

About the authors

Vladimir V. Lalin

Peter the Great Saint Petersburg Polytechnic University

Author for correspondence.

Dr.Sc., Professor, Institute of Civil Engineering

29 Polytechnicheskaya St, Saint Petersburg, 195251, Russian Federation

Tu Quang Trung Le

Peter the Great Saint Petersburg Polytechnic University


graduate student, Institute of Civil Engineering

29 Polytechnicheskaya St, Saint Petersburg, 195251, Russian Federation


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Copyright (c) 2020 Lalin V.V., Le T.Q.

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