Email this article 
Calculation of building structures for several dynamic effects with a static accounting of higher forms of oscillation
- Authors: Lalin V.V.1, Le T.Q.1
-
Affiliations:
- Peter the Great Saint Petersburg Polytechnic University
- Issue: Vol 16, No 3 (2020)
- Pages: 171-178
- Section: Analysis and design of building structures
- URL: https://journals.rudn.ru/structural-mechanics/article/view/23955
- DOI: https://doi.org/10.22363/1815-5235-2020-16-3-171-178
Cite item
Full Text
Abstract
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.
Email: quangtrung1690@gmail.com
Dr.Sc., Professor, Institute of Civil Engineering
29 Polytechnicheskaya St, Saint Petersburg, 195251, Russian FederationTu Quang Trung Le
Peter the Great Saint Petersburg Polytechnic University
Email: quangtrung1690@gmail.com
graduate student, Institute of Civil Engineering
29 Polytechnicheskaya St, Saint Petersburg, 195251, Russian FederationReferences
- Clough R.W., Penzien J. Dynamics of structures. New York: McGraw-Hill Book Company; 1975.
- Chopra A.K. Dynamic of structures. Theory and Applications to Earthquake Engineering. New Jersey: Prentice-Hall; 2006.
- Ignatyeva V.A., Galishnikova V.V. Osnovy stroitelnoy mekhaniki [Fundamentals of structural mechanics]. Moscow: Assotsiatsii stroitelnykh vuzov Publ.; 2009. (In Russ.)
- Zoloev A.B., Akimov P.A., Sidorov V.N., Mozgaleva M.L. Chislennyye i analiticheskiye metody rascheta stroitelnykh konstruktsiy [Numerical and analytical methods for calculating building structures]. Moscow: ASV Publ.; 2009. (In Russ.)
- Rutman Yu.L., Ostrovskaya N.V. Dinamika sooruzhenii: seysmostokost, seysmozashchita, vetrovyye nagruzki [Dynamics of construction: seismic stability, seismic protection, wind loads]: monograph. Saint Petersburg: SPbGASU Publ., 2019. (In Russ.)
- Nurimbetov A.U., Dudchenko A.A. The modern state of the problem of analyzing the natural frequencies and modes of vibration of a composite structure. Structural Mechanics of Engineering Constructions and Buildings. 2018; 14(4):323–336. (In Russ.)
- Mokin N.A., Kustov A.A., Gandzhuntsev M.I. Numerical investigation of natural frequencies and mode shapes of air-supported structures. Structural Mechanics of Engineering Constructions and Buildings. 2018;14(4):337–347. (In Russ.)
- Kolesnikov A.O., Popov V.N. Calculation of the natural oscillation frequency of the submerged basement subject to pulsed loading. Structural Mechanics of Engineering Constructions and Buildings. 2018;14(5):360–368. (In Russ.)
- Newmark N.M., Rosenblueth E. Fundamentals of earthquake engineering. New York: Englewood Cliffs; 1980.
- Birbrayer A.N. Raschet konstruktsiy na seysmostoykost [Calculation of structures for seismic resistance]. Saint Petersburg: Nauka Publ.; 1998. (In Russ.)
- Datta T.K. Seismic Analysis of Structures. John Wiley & Sons (Asia) Pte Ltd; 2010.
- Uzdin A.M., Elizarov S.V., Belash T.A. Seismostoikie konstruktcii transportnykh zdaniy i sooruzheniy [Earthquake resistant design of transport buildings and structures]. Mosow: Uchebno-metodicheskii centr po obrazovaniiu na zheleznodorozhnom transporte Publ.; 2012. (In Russ.)
- Sucuoğlu Halûk, Akkar Sinan. Basic Earthquake Engineering. From Seismology to Analysis and Design. Springer; 2014.
- Tyapin A.G. Sovremennyye normativnyye podkhody k raschetu otvetstvennykh sooruzheniy na seysmicheskiye vozdeystviya [Modern regulatory approaches to the calculation of critical structures for seismic load]. Moscow: ASV Publ.; 2018. (In Russ.)
- Birbraer A.N., Sazonova J.V. Vklad vysshikh mod v dinamicheskiy otklik konstruktsiy na vysokochastotnyye vozdeystviya [Input of high modes in dynamic response of structures subjected to high frequency loads]. Structural Mechanics and Analysis of Constructions. 2009;227(6):22–27. (In Russ.)
- Tyapin A.G. Implementation of the “Residual Term” Concept in Seismic Analysis by Modal and Spectral Methods. Earthquake engineering. Constructions safety. 2014;(4):32–35. (In Russ.)
- Balakirev Yu.G. Osobennosti vydeleniya kvazistaticheskikh sostavlyayushchikh pri analize dinamicheskogo nagruzheniya uprugikh konstruktsiy [Quasistatic components particularities in the analysis of the elastic structures dynamic loading]. Cosmonautics and rocket engineering. 2014; 76(2):34–40. (In Russ.)
- Likhoded A.I., Sidorov V.V. Nekotoryye osobennosti skhodimosti metoda razlozheniya po tonam kolebaniy primenitelno k kontinualnym i konechno-elementnym modelyam [Certain Convergence Features of the Decomposition Method by Tones Vibrations Concerning Continuum and Finite-Element Models]. Cosmonautics and rocket engineering. (2013);71(2):20–27. (In Russ.)
- Batseva O.D., Dmitriyev S.N. Accounting the highest tones of oscillations when calculating the sensitivity of modes of their own to variations in the parameters of a mechanical system. Engineering Journal: science and Innovation. 2018; 79(7):3–23. (In Russ.)
- Rubin S. Improved component-mode representation for structural dynamic analysis. AIAA Journal. 1975;13(8): 995–1006.
- Tseytlin B.V. Postroyeniye matritsy ostatochnykh podatlivostey i yeye ispolzovaniye pri reshenii zadach dinamiki konstruktsiy [Construction of the matrix of residual compliance and using in solving the problems of structural dynamics]. Scientific and technical problems of predicting the reliability and durability of structures and methods for solving them: Proceedings of the 4th International Conference. Sankt Peterburg: Nestor Publ., 200: 325-331.
- Zegzhda S.A. K zadache o soudarenii deformiruyemykh tel [The problem of the impact of deformable bodies]. Prikladnaya mekhanika. 1979;(4):91–108. (In Russ.)
- Vernigor V.N. Opredeleniye sobstvennykh chastoty i ekvivalentnykh mass uprugogo tela po yego dinamicheskoy podatlivosti [Determination of natural frequencies and equivalent masses of an elastic body by its dynamic flexibility]. Bulletin of the Leningrad University. 1990;4(2):35–42. (In Russ.)
- Le T.Q.T., Lalin V.V., Bratashov A.A. Static accounting of highest modes in problems of structural dynamics. Magazine of Civil Engineering. 2019;88(4):3–13.
- Dolgaya A.A. Modelirovaniye seysmicheskogo vozdeystviya korotkim vremennym protsessom [Simulation of seismic action by a short time process]. E-I. VNIINTPI. Series: Seysmostoykoye stroitelstvo. 1994;(5–6):56–63. (In Russ.)
- Rekomendatsii po zadaniyu seysmicheskikh vozdeystviy dlya rascheta zdaniy raznoy stepeni otvetstvennosti [Recommendations for assigning seismic impacts for the calculation of buildings of different degrees of responsibility]. Saint Petersburg – Petropavlovsk-Kamchatskiy: KamTsentr Publ.; 1996. 12 p. (In Russ.)
