Abstract
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.
First Page
69
Last Page
73
References
- Bolotin B.B. Static methods in structural mechanics. Moscow: Gosstroizdat. 1965. Page 278
- Lomakin V.V. Static problems of mechanics of solid deformable bodies. Moscow: Nauka. 1979. Page 136.
- Bolotin V.V. Application of static methods for assessing the strength of a structure under seismic impacts. // Engineering collection. Vol. 27 Publ. USSR Academy of Sciences 1959. Pages 150-160.
- Bolotin V.V. Statistical theory of seismic resistance of structures.// Bulletin of the USSR Academy of Sciences. OTN. Mechanics and Mechanical Engineering. 1959. No. 4. P. 123-129.
- Sveshnikov A.A. Applied methods of the theory of random functions. Moscow: Nauka. 1968.460 p.
- Khudoyarov B.A. Algorithmization of the problem of flutter of viscoelastic plates streamlined by a supersonic gas flow. // Computational technologies. SB RAS. Novosibirsk. 2003. v. 8.-No. 6 P. 100-103
- Akhundov M.B., Rabotnov Yu.N., Suvorova Yu.V. Model of a deformable body with reaction and its application to problems of biomechanics. // MDTT. 1985. No. 6. P. 90-100.
- Badalov F.B. Dynamic dampers of oscillations of hereditarily deformable systems. Tashkent.: TashGAI. 2003. 81 p.
- Collatz L. Eigenvalue problems Moscow: Science 1968. 503 p.
- Urazbaev M. T. Seismic resistance of elastic and hydroelastic systems. Tashkent.: 1966. 256 p.
- Goldenblat I. I., Nikolaenko N. A. Calculation of a structure for the action of seismic and impulse forces. Moscow: Gosstroyizdat, 1961, 320 p.
- Badalov F. B. Methods for solving integral and integro-differential equations of the hereditary theory of viscoelasticity. Tashkent, 1987. 269 p.
- Badalov F. B., Abdukarimov A. Fractional order sine and cosine functions and their application to solving dynamic problems of hereditarily deformable systems. Tashkent: FAN. 2004. 155 p.
- Badalov F. B., Abdukarimov A., Response of hereditarily deformable systems to random effects. FAN. 2011.202 p.
- 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.
- 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.
- Abdukarimov A. Numerical solutions of the problem of random oscillations of hereditarily deformable systems. Problems of Mechanics. No. 1, 2009, pp. 59–63.
- Rashidov T.R. Dynamic theory of seismic resistance of complex systems of underground structures. Tashkent: FAN. 1973. 179 p.
- Romanov Yu.I. On the possibility of representing seismic impacts in the form of a stationary random process. // Structural mechanics and calculation of structures. 1963 No. 5. p. 44-48
- Khusanov B. E. Dynamic deformation of structurally unstable media and non-stationary interaction of solids with soil. // Abstract of dissertation for the degree of Doctor of Physical and Mathematical Sciences. Tashkent. 2004. 41 p.
Recommended Citation
Abdukarimov, Abdali and Nuratdinov, Kazbek
(2025)
"RESEARCH OF HEREDITARILY DEFORMABLE STRUCTURES UNDER SEISMIC IMPACTS,"
Technical science and innovation: Vol. 2025:
Iss.
2, Article 13.
DOI: https://doi.org/10.59048/2181-1180.1729
Available at:
https://btstu.researchcommons.org/journal/vol2025/iss2/13