DOI: https://doi.org/10.32347/2410-2547.2018.101.83-102

Investigation of seismic wave reaction of spatial structure

Olga Lukіanchenko, Olena Kostina, Oleg Gerashchenko

Abstract


The stochastic behavior of the spatial structure under seismic action was studied on the basis of theories and methods of nonlinear mechanics, finite elements, traveling wave and wavelet analysis. The spatial concrete structure in the form of a square plate, which rests on four columns rigidly fixed in the foundation was presented. A probabilistic simulation of acceleration of seismic action with different magnitudes using the statistical method of Ruiz and Penzien was performed. The effect of horizontal seismic displacement in the soil on the design was taken into account with the help of simulation of a transverse bending traveling wave in the form of an initial imperfection of the four columns of the structure. Mathematical models of non-stationary stochastic vibrations structure in the form of a system of second-order differential equations in generalized coordinates were formed on the basis of the Dahlberger-Lagrange method. The influence of the traveling waves and surface pressure on the static characteristics structure was estimated.  The nonlinear static problem by the Newton-Ruffson method and the stability problem by Lanczos method were solved. A modal analysis of the spatial structure without and with traveling waves and surface pressure by the Lanczos method was carried. Realizations of dynamic characteristics of the structure: acceleration, velocity and displacement were obtained by the direct method of numerical integration of Runge-Kutta of the fourth order. The wavelet analysis of the seismic acceleration and structure reactions to the seismic action of different magnitudes was performed using discrete orthogonal (Dobesh4) and continuous nonorthogonal (Morle) one-dimensional complex wavelet functions. Wavelet-spectrograms and Fourier-images of the seismic acceleration and of the structure reactions were presented. The expediency of accounting for the flexural traveling waves in a spatial structure in the study of its seismic behavior was estimated.


Keywords


seismic loads; stochastic behavior; finite element method; nonlinear mechanics; traveling wave theory; wavelet analysis; spatial structure

References


Clough R., Penzien J. Dinamika sooruzheniy (Dynamics of structures). – M.: Stroyizdat, 1979. – 320 p. (rus)

Augusti G., Baratta A., Kashiati F. Veroyatnostnyie metodyi v stroitelnom proektirovanii (Probabilistic methods in building design). – M.: Stroyizdat, 1988. – 584 s. (rus)

DBN V.1.2-2:2006. Derzhavni budivelni normy Ukrayiny. Systema zabezpechennia nadiinosti ta bezpeky budivelnykh ob’iektiv. Navantazhennia i vplyvy. Normy proektuvannia. (National Structural Rules and Regulations. The system of reliability and safety provision of constructional projects. Loads and effects. Design codes). – K.: Minbud Ukrainy, 2007. - 60 p.

DBN V.1.1-12:2014. Derzhavni budivelni normy Ukrayiny. Budivnytstvo u seysmichnykh rayonakh Ukrayiny (National Structural Rules and Regulations. Construction in the seismic regions of Ukraine) – K.: Minrehion Ukrayiny, 2014. − IV. − 110 s. (ukr).

Bazhenov V.A., Dekhtiariuk Ie.S. Imovirnisni metody rozrakhunku konstruktsii. Vypadkovi kolyvannia pruzhnykh system (Probabilistic methods of structure analysis. Random oscillations of elastic systems). – K.: KNUBA, 2005. - 420 p. (ukr)

Kurzanov A.M. Predlozheniya po normativnomu raschetu sooruzheniy na volnovuyu seysmicheskuyu nagruzku (Proposals for the normative analysis of constructions under wave seismic loading) // Promyishlennoe i grazhdanskoe stroitelstvo, 2010. – № 9. – S. 54-55. (rus).

Pashynskyi V.A. Imovirnisni modeli dlia rozrakhunkiv nadiinosti ta normuvannia klimatychnykh navantazhen i vplyviv na budivelni konstruktsii // Stroytelnaia mekhanyka y stroytelnye konstruktsyy: Sbornyk statei posviashchennyi vosmydesiatyletyiu A.V. Perelmutera.[Probabilistic models for the reliability analysis and standardization of environmental loads and impacts on the constructions // Structural mechanics and constructions: A collection of articles dedicated to the A.V. Perelmouter 80 anniversary.] – M.: Yzdatelstvo SKAD SOFT, 2013. – 323-332 p. (ukr).

Nemchynov Yu.I., Khavkin O.K., Mar"yenkov M.H. ta in. Praktychni pytannya dynamiky budivel (Practical issues of buildings dynamics) // Budivnytstvo Ukrayiny, 2013. − #6. – S. 6-21. (ukr)

Daubechies I. Desyat’ lektsiy po veyvletam (Ten Lectures on Wavelets). Izhevsk, NITs «Regulyarnaya i khaoticheskaya dinamika» publ., 2001, 454 p. (rus).

Luk’yanchenko О.О., Vorona Yu.V., Kostina О.V., Kuz’ko O.V Wavelet analysis features to study stochastic behavior of complex casing construction // VIII International Antarctic Conf. Kyiv. 2017. – P. 186 -187.

Lukianchenko О.О., Vorona Yu.V., Kostina О.V., Geraschenko O.V. Zastosuvannya vejvlet-analizu do modelyuvannya stoxasty`chnoyi povedinky` pruzhny`x sy`stem pry` sejsmichnomu vply`vi – К: КNUBA, 2017. – Vyp. 99. – Р. 160 –180.

Shimkovich D.G. Raschet konstruktsiy v MSC/NASTRAN for Windows (Structural analysis in MSC/NASTRAN for Windows) - M.: DMK Press, 2001.- 448 p. (rus)

Kiryanov D.V. Samouchitel Mathcad 13 (Mathcad 13 self-tutorial).– SPb.: BHV-Peterburg, 2006. – 528 s.


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