MODAL ANALYSIS OF A HORIZONTAL SHALL STRUCTURE UNDER BLAST LOADING
This article addresses the problem of modal analysis of a horizontal steel tank with a capacity of 50 m³ on concrete saddle supports. The structure is modeled as a cylindrical shell of length 8.15 m, radius 1.4 m, and wall thickness 5 mm. The geometric model of the tank is presented in...
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| Date: | 2026 |
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2026
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| author | KUCHERENKO, O. Ye. BLAZHKO, V. A. |
| author_facet | KUCHERENKO, O. Ye. BLAZHKO, V. A. |
| author_sort | KUCHERENKO, O. Ye. |
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| description | This article addresses the problem of modal analysis of a horizontal steel tank with a capacity of 50 m³ on concrete saddle supports. The structure is modeled as a cylindrical shell of length 8.15 m, radius 1.4 m, and wall thickness 5 mm. The geometric model of the tank is presented in a three-dimensional form. To model the horizontal shell, eight-node shell finite elements (SHELL281) are employed. The saddle supports are modeled using three-dimensional twenty-node second-order finite elements (SOLID186). The horizontal shell is reinforced with stiffening beams and a diaphragm. The bottom surfaces of the supports are fixed. Contact interaction between the shell and supports is modeled as well. We use a refined mesh in the contact zones. To model the stiffening beams, nonlinear three-node beam elements based on Timoshenko’s beam theory are utilized. The natural frequencies and mode shapes are computed using the finite-element method. The boundary conditions considered in the modal analysis include the assumption of no contact loss. The calculated modal participation factors show that the first mode plays a dominant role in evaluating dynamic behavior of the structure in the Y-axis direction. This mode is also a torsional one about the vertical Z-axis, thus indicating the possibility of resonance effects under seismic loading. From an energy standpoint, beam elements of the diaphragm exhibit an excessive concentration of specific strain energy; such elements require some reinforcement to prevent resonance-induced excitations. Under blast loading, the extent of structural damage depends on the response rate of the structure to the blast wave. Small, stiff structures respond significantly faster than large ones. When the duration of the blast wave exceeds the natural vibration period of the structure, the critical factor is the overpressure. Conversely, if the blast wave duration is short compared to the natural period, the impulse becomes the dominant factor. A dynamic analysis of the impact of a 100 kg TNT charge on the horizontal shell structure with account for the first natural frequency showed that at distances less than 52.6 m, the blast loading can be considered short and substituted with an instantaneous impulse.  At larger distances, however, both the impulse action and the overpressure must be taken into account.
REFERENCES
1. Dong X., Lian J., Wang H., Yu T., Zhao Y. Structural vibration monitoring and operational modal analysis of offshore wind turbine structure. Ocean Engineering. 2018. V. 150. Pp. 280-297.https://doi.org/10.1016/j.oceaneng.2017.12.052
2. Balageas D., Fritzen C.-P., Güemes A. Structural Health Monitoring. John Wiley & Sons. 2010. 496 pp.
3. Jana K., Pal S., Haldar S. Modal analysis of power law functionally graded material plates with rectangular cutouts. Mechanics Based Design of Structures and Machines. 2023. V. 52. No. 5. Pp. 2411-2439. https://doi.org/10.1080/15397734.2023.2180033
4. Ramu I., Mohanty S. C. Modal analysis of functionally graded material plates using finite element method. Procedia Materials Science. 2014. V. 6. Pp. 460-467.https://doi.org/10.1016/j.mspro.2014.07.059
5. Inaudi J. A. Rayleigh quotient algorithm for modal analysis of structural models. Mecánica Computacional. 2016. Vl. 34. Pp. 1459-1477.
6. Si X. H., Lu W. X., Chu F. L. Modal analysis of circular plates with radial side cracks and in contact with water on one side based on the Rayleigh-Ritz method. Journal of Sound and Vibration. 2012. V. 331. No. 1. Pp. 231-251. https://doi.org/10.1016/j.jsv.2011.08.026
7. Chapelle D., Bathe K. The Finite Element Analysis of Shells - Fundamentals. Heidelberg: Springer-Verlag, 2011. 410 pp. https://doi.org/10.1007/978-3-642-16408-8
8. Krivenko O. P., Vorona Yu. V., Kozak A. A. Finite element analysis of nonlinear deformation, stability and vibrations of elastic thin-walled structures. Strength of Materials and Theory of Structures. 2021. Iss. 107. Pp. 20-34. https://doi.org/10.32347/2410-2547.2021.107.20-34
9. Kucherenko O. Ye., Blazhko V. A. Verification of a finite-element model of a horizontal shell structure - support contact. Teh. Meh. 2025. No. 2. Pp. 63-71. (In Ukrainian).https://doi.org/10.15407/itm2025.02.063
10. Rabbat B. G., Russell H. G. Friction coefficient of steel on concrete or grout. Journal of Structural Engineering. 1985. V. 111. Iss. 3. P. 505-515.https://doi.org/10.1061/(ASCE)0733-9445(1985)111:3(505)
11. Hauck B., Szekrenyes A. Enhanced beam and plate finite elements with shear stress continuity for compressible sandwich structures. Mathematics and Mechanics of Solids. 2024. V. 29. No. 7. Pp. 1325-1363. https://doi.org/10.1177/10812865231221992
12. Birbraer A. N. Seismic Analysis of Structures. St. Petersburg: Nauka, 1998. 255 pp.
13. Crowl D.A. Understanding Explosions. New-York: American Institute of Chemical Engineers, 2003. 214 pp. https://doi.org/10.1002/9780470925287
14. Kobiiev V. H. Deformation features and determining the specificity of the effect of external factors on shell systems under high-power impulse loads. Opir Materialiv i Teoria Sporud. 2006. No. 78. Pp. 82-89. (In Ukrainian).
15. Clough R. W., Penzien J. Dynamics of Structures. New-York: McGrow-Hill Book Company, 1975. 320 pp.
16. Vorob'ev Yu. S., Kolodyazhny A. B., Sevryukov V. I., Yatyunin E. G. High-Rate Straining of Structural Elements. Kiev: Naukova Dumka, 1989. 192 pp. (In Russian).
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| first_indexed | 2026-04-05T01:00:17Z |
| format | Article |
| id | oai:ojs2.journal-itm.dp.ua:article-172 |
| institution | Technical Mechanics |
| keywords_txt_mv | keywords |
| last_indexed | 2026-04-05T01:00:17Z |
| publishDate | 2026 |
| publisher | текст 3 |
| record_format | ojs |
| spelling | oai:ojs2.journal-itm.dp.ua:article-1722026-04-04T20:10:29Z MODAL ANALYSIS OF A HORIZONTAL SHALL STRUCTURE UNDER BLAST LOADING KUCHERENKO, O. Ye. BLAZHKO, V. A. shell, natural frequency, finite element, specific strain energy density, impulse, blast loading. This article addresses the problem of modal analysis of a horizontal steel tank with a capacity of 50 m³ on concrete saddle supports. The structure is modeled as a cylindrical shell of length 8.15 m, radius 1.4 m, and wall thickness 5 mm. The geometric model of the tank is presented in a three-dimensional form. To model the horizontal shell, eight-node shell finite elements (SHELL281) are employed. The saddle supports are modeled using three-dimensional twenty-node second-order finite elements (SOLID186). The horizontal shell is reinforced with stiffening beams and a diaphragm. The bottom surfaces of the supports are fixed. Contact interaction between the shell and supports is modeled as well. We use a refined mesh in the contact zones. To model the stiffening beams, nonlinear three-node beam elements based on Timoshenko’s beam theory are utilized. The natural frequencies and mode shapes are computed using the finite-element method. The boundary conditions considered in the modal analysis include the assumption of no contact loss. The calculated modal participation factors show that the first mode plays a dominant role in evaluating dynamic behavior of the structure in the Y-axis direction. This mode is also a torsional one about the vertical Z-axis, thus indicating the possibility of resonance effects under seismic loading. From an energy standpoint, beam elements of the diaphragm exhibit an excessive concentration of specific strain energy; such elements require some reinforcement to prevent resonance-induced excitations. Under blast loading, the extent of structural damage depends on the response rate of the structure to the blast wave. Small, stiff structures respond significantly faster than large ones. When the duration of the blast wave exceeds the natural vibration period of the structure, the critical factor is the overpressure. Conversely, if the blast wave duration is short compared to the natural period, the impulse becomes the dominant factor. A dynamic analysis of the impact of a 100 kg TNT charge on the horizontal shell structure with account for the first natural frequency showed that at distances less than 52.6 m, the blast loading can be considered short and substituted with an instantaneous impulse.  At larger distances, however, both the impulse action and the overpressure must be taken into account. REFERENCES 1. Dong X., Lian J., Wang H., Yu T., Zhao Y. Structural vibration monitoring and operational modal analysis of offshore wind turbine structure. Ocean Engineering. 2018. V. 150. Pp. 280-297.https://doi.org/10.1016/j.oceaneng.2017.12.052 2. Balageas D., Fritzen C.-P., Güemes A. Structural Health Monitoring. John Wiley & Sons. 2010. 496 pp. 3. Jana K., Pal S., Haldar S. Modal analysis of power law functionally graded material plates with rectangular cutouts. Mechanics Based Design of Structures and Machines. 2023. V. 52. No. 5. Pp. 2411-2439. https://doi.org/10.1080/15397734.2023.2180033 4. Ramu I., Mohanty S. C. Modal analysis of functionally graded material plates using finite element method. Procedia Materials Science. 2014. V. 6. Pp. 460-467.https://doi.org/10.1016/j.mspro.2014.07.059 5. Inaudi J. A. Rayleigh quotient algorithm for modal analysis of structural models. Mecánica Computacional. 2016. Vl. 34. Pp. 1459-1477. 6. Si X. H., Lu W. X., Chu F. L. Modal analysis of circular plates with radial side cracks and in contact with water on one side based on the Rayleigh-Ritz method. Journal of Sound and Vibration. 2012. V. 331. No. 1. Pp. 231-251. https://doi.org/10.1016/j.jsv.2011.08.026 7. Chapelle D., Bathe K. The Finite Element Analysis of Shells - Fundamentals. Heidelberg: Springer-Verlag, 2011. 410 pp. https://doi.org/10.1007/978-3-642-16408-8 8. Krivenko O. P., Vorona Yu. V., Kozak A. A. Finite element analysis of nonlinear deformation, stability and vibrations of elastic thin-walled structures. Strength of Materials and Theory of Structures. 2021. Iss. 107. Pp. 20-34. https://doi.org/10.32347/2410-2547.2021.107.20-34 9. Kucherenko O. Ye., Blazhko V. A. Verification of a finite-element model of a horizontal shell structure - support contact. Teh. Meh. 2025. No. 2. Pp. 63-71. (In Ukrainian).https://doi.org/10.15407/itm2025.02.063 10. Rabbat B. G., Russell H. G. Friction coefficient of steel on concrete or grout. Journal of Structural Engineering. 1985. V. 111. Iss. 3. P. 505-515.https://doi.org/10.1061/(ASCE)0733-9445(1985)111:3(505) 11. Hauck B., Szekrenyes A. Enhanced beam and plate finite elements with shear stress continuity for compressible sandwich structures. Mathematics and Mechanics of Solids. 2024. V. 29. No. 7. Pp. 1325-1363. https://doi.org/10.1177/10812865231221992 12. Birbraer A. N. Seismic Analysis of Structures. St. Petersburg: Nauka, 1998. 255 pp. 13. Crowl D.A. Understanding Explosions. New-York: American Institute of Chemical Engineers, 2003. 214 pp. https://doi.org/10.1002/9780470925287 14. Kobiiev V. H. Deformation features and determining the specificity of the effect of external factors on shell systems under high-power impulse loads. Opir Materialiv i Teoria Sporud. 2006. No. 78. Pp. 82-89. (In Ukrainian). 15. Clough R. W., Penzien J. Dynamics of Structures. New-York: McGrow-Hill Book Company, 1975. 320 pp. 16. Vorob'ev Yu. S., Kolodyazhny A. B., Sevryukov V. I., Yatyunin E. G. High-Rate Straining of Structural Elements. Kiev: Naukova Dumka, 1989. 192 pp. (In Russian).   текст 3 2026-03-31 Article Article https://journal-itm.dp.ua/ojs/index.php/ITM_j1/article/view/172 Technical Mechanics; No. 1 (2026): Technical Mechanics; 54-61 Институт технической механики Национальной академии наук Украины и Государственного космического агентства Украины; № 1 (2026): Technical Mechanics; 54-61 ТЕХНІЧНА МЕХАНІКА; № 1 (2026): ТЕХНІЧНА МЕХАНІКА; 54-61 Copyright (c) 2026 Technical Mechanics |
| spellingShingle | KUCHERENKO, O. Ye. BLAZHKO, V. A. MODAL ANALYSIS OF A HORIZONTAL SHALL STRUCTURE UNDER BLAST LOADING |
| title | MODAL ANALYSIS OF A HORIZONTAL SHALL STRUCTURE UNDER BLAST LOADING |
| title_full | MODAL ANALYSIS OF A HORIZONTAL SHALL STRUCTURE UNDER BLAST LOADING |
| title_fullStr | MODAL ANALYSIS OF A HORIZONTAL SHALL STRUCTURE UNDER BLAST LOADING |
| title_full_unstemmed | MODAL ANALYSIS OF A HORIZONTAL SHALL STRUCTURE UNDER BLAST LOADING |
| title_short | MODAL ANALYSIS OF A HORIZONTAL SHALL STRUCTURE UNDER BLAST LOADING |
| title_sort | modal analysis of a horizontal shall structure under blast loading |
| topic_facet | shell natural frequency finite element specific strain energy density impulse blast loading. |
| url | https://journal-itm.dp.ua/ojs/index.php/ITM_j1/article/view/172 |
| work_keys_str_mv | AT kucherenkooye modalanalysisofahorizontalshallstructureunderblastloading AT blazhkova modalanalysisofahorizontalshallstructureunderblastloading |