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This article examines the responses of a structure to both single-component and
multi-component seismic impacts if they are generally described by three linear displacements and
three rotations of the foundation relative to three orthogonal axes.
A mathematical apparatus has been created that allows developing statistical theories of
seismic resistance for studying hereditarily deformable structures under random seismic impacts.
Using impulse transition functions, having established the explicit form of the reaction of hereditarily
deformable structures to an arbitrary form of random disturbance, it is possible to determine: the
mathematical expectation and moments of the outgoing process; correlation functions; spectral
densities, i.e. it is possible to establish all the probabilistic-statistical characteristics of the dynamic
processes being studied.
 

  • Web Address
  • DOI https://doi.org/10.59048/2181-1180.1729
  • Date of creation in the UzSCI system 22-09-2025
  • Read count 17
  • Date of publication 19-09-2025
  • Main LanguageIngliz
  • Pages69-73
English

This article examines the responses of a structure to both single-component and
multi-component seismic impacts if they are generally described by three linear displacements and
three rotations of the foundation relative to three orthogonal axes.
A mathematical apparatus has been created that allows developing statistical theories of
seismic resistance for studying hereditarily deformable structures under random seismic impacts.
Using impulse transition functions, having established the explicit form of the reaction of hereditarily
deformable structures to an arbitrary form of random disturbance, it is possible to determine: the
mathematical expectation and moments of the outgoing process; correlation functions; spectral
densities, i.e. it is possible to establish all the probabilistic-statistical characteristics of the dynamic
processes being studied.
 

Ўзбек

Ushbu maqolada bitta komponentli va ko‘p komponentli seysmik ta’sirlarga
strukturaning reyaktsiyalari ko‘rib chiqiladi, agar ular odatda uchta chiziqli siljish va uchta
ortogonal o‘qga nisbatan asosning uchta aylanishi bilan tavsiflangan bo‘lsa. Tasodifiy seysmik
ta'sirlar ostida irsiy deformatsiyalanadigan tuzilmalarni o‘rganish uchun seysmik qarshilikning
statistik nazariyalarini ishlab chiqish imkonini beruvchi matematik apparat yaratildi. Impulsli o‘tish
funktsiyalaridan foydalanib, irsiy deformatsiyalanadigan tuzilmalarning tasodifiy buzilishning
ixtiyoriy shakliga reaktsiyasining aniq shaklini o‘rnatgan holda, quyidagilarni aniqlash mumkin:
matematik kutish va chiquvchi jarayonning momentlari; korrelyatsiya funktsiyalari; spektral
zichliklar, ya’ni o‘rganilayotgan dinamik jarayonlarning barcha ehtimollik va statistik xususiyatlarini
o‘rnatish mumkin.
 

Русский

В данной статье рассмотрены реакции сооружения на действие как
однокомпонентного, так и многокомпонентного сейсмических воздействий, если они
описываются в общем случае тремя линейными смещениями и тремя вращениями основания
по отношению к трем ортогональным осям.
Создан математический аппарат позволяющий развивать статистические теории
сейсмостойкости для исследования наследственно-деформируемых сооружений при
случайных сейсмических воздействиях. С помощью импульсных переходных функций,
установив явный вид реакции наследственно-деформируемых сооружений на произвольную
форму случайного возмущения, можно определить: математическое ожидание и моменты
выходящего процесса; корреляционные функции; спектральные плотности, т.е. можно
установить все вероятностно-статистические характеристики исследуемых динамических
процессов.
 

№ Name of reference
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3 14. Badalov F. B., Abdukarimov A., Response of hereditarily deformable systems to random effects. FAN. 2011.202 p. 15. Abdukarimov A., Shodmanov G. Non-stationary response of a hereditarily deformed structure to seismic impacts. Bulletin of Tashkent State Technical University No. 3 2013. Tashkent 2013. pp. 7-12. 16. Abdukarimov A. Solution of the problem of random oscillations of hereditarily deformable systems with a finite number of degrees of freedom. Problems of Mechanics. No. 1, 2009, pp. 6-9. 17. Abdukarimov A. Numerical solutions of the problem of random oscillations of hereditarily deformable systems. Problems of Mechanics. No. 1, 2009, pp. 59–63. 18. Rashidov T.R. Dynamic theory of seismic resistance of complex systems of underground structures. Tashkent: FAN. 1973. 179 p.
4 14. Badalov F. B., Abdukarimov A., Response of hereditarily deformable systems to random effects. FAN. 2011.202 p. 15. Abdukarimov A., Shodmanov G. Non-stationary response of a hereditarily deformed structure to seismic impacts. Bulletin of Tashkent State Technical University No. 3 2013. Tashkent 2013. pp. 7-12. 16. Abdukarimov A. Solution of the problem of random oscillations of hereditarily deformable systems with a finite number of degrees of freedom. Problems of Mechanics. No. 1, 2009, pp. 6-9. 17. Abdukarimov A. Numerical solutions of the problem of random oscillations of hereditarily deformable systems. Problems of Mechanics. No. 1, 2009, pp. 59–63. 18. Rashidov T.R. Dynamic theory of seismic resistance of complex systems of underground structures. Tashkent: FAN. 1973. 179 p.
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