Dynamic Stability of the Periodic and Aperiodic Structures of the Bernoulli-Euler Beams
The study analyzed the influence of periodic and aperiodic stiffness distribution for the four-element Bernoulli-Euler beam on the first two eigenfrequencies and the dynamic stability of the system. The influence of increasing the ratio of cross-sections of the analyzed elements was also analyzed. S...
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| Format: | Article |
| Language: | English |
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Polish Academy of Sciences
2024-04-01
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| Series: | Archives of Metallurgy and Materials |
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| Online Access: | https://journals.pan.pl/Content/130947/PDF/AMM-2024-1-45-Garus.pdf |
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| author | J. Garus J. Petrů W. Sochacki S. Garus |
| author_facet | J. Garus J. Petrů W. Sochacki S. Garus |
| author_sort | J. Garus |
| collection | DOAJ |
| description | The study analyzed the influence of periodic and aperiodic stiffness distribution for the four-element Bernoulli-Euler beam on the first two eigenfrequencies and the dynamic stability of the system. The influence of increasing the ratio of cross-sections of the analyzed elements was also analyzed. Significant differences were found in eigenfrequencies and dynamic stability. Using the variational Hamilton principle, the equation of motion was derived, on the basis of which the values of the eigenfrequencies were determined, and the transformation into the form of the Mathieu equation made it possible to determine the dynamic stability for the analyzed structures. |
| format | Article |
| id | doaj-art-18ed9774512f4bacab67daeefac0cc65 |
| institution | DOAJ |
| issn | 2300-1909 |
| language | English |
| publishDate | 2024-04-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Archives of Metallurgy and Materials |
| spelling | doaj-art-18ed9774512f4bacab67daeefac0cc652025-08-20T02:55:39ZengPolish Academy of SciencesArchives of Metallurgy and Materials2300-19092024-04-01vol. 69No 1275279https://doi.org/10.24425/amm.2024.147819Dynamic Stability of the Periodic and Aperiodic Structures of the Bernoulli-Euler BeamsJ. Garus0https://orcid.org/0000-0001-8001-2113J. Petrů1https://orcid.org/0000-0002-2378-5678W. Sochacki2https://orcid.org/0000-0002-2764-6480S. Garus3https://orcid.org/0000-0002-6649-5435Czestochowa University of Technology, Department of Mechanics and Machine Design Fundamentals, Faculty of Mechanical Engineering and Computer Science, 73 Dąbrowskiego Str., 42-201 Częstochowa, PolandVS B-Technical University of Ostrava, Faculty of Mechanical Engineering Department of Machining, Assembly and Engineering Metrology, 70833 Ostrava, Czech RepublicCzestochowa University of Technology, Department of Mechanics and Machine Design Fundamentals, Faculty of Mechanical Engineering and Computer Science, 73 Dąbrowskiego Str., 42-201 Częstochowa, PolandCzestochowa University of Technology, Department of Mechanics and Machine Design Fundamentals, Faculty of Mechanical Engineering and Computer Science, 73 Dąbrowskiego Str., 42-201 Częstochowa, PolandThe study analyzed the influence of periodic and aperiodic stiffness distribution for the four-element Bernoulli-Euler beam on the first two eigenfrequencies and the dynamic stability of the system. The influence of increasing the ratio of cross-sections of the analyzed elements was also analyzed. Significant differences were found in eigenfrequencies and dynamic stability. Using the variational Hamilton principle, the equation of motion was derived, on the basis of which the values of the eigenfrequencies were determined, and the transformation into the form of the Mathieu equation made it possible to determine the dynamic stability for the analyzed structures.https://journals.pan.pl/Content/130947/PDF/AMM-2024-1-45-Garus.pdfbeamdynamic stabilitymathieu equationaperiodic structure |
| spellingShingle | J. Garus J. Petrů W. Sochacki S. Garus Dynamic Stability of the Periodic and Aperiodic Structures of the Bernoulli-Euler Beams Archives of Metallurgy and Materials beam dynamic stability mathieu equation aperiodic structure |
| title | Dynamic Stability of the Periodic and Aperiodic Structures of the Bernoulli-Euler Beams |
| title_full | Dynamic Stability of the Periodic and Aperiodic Structures of the Bernoulli-Euler Beams |
| title_fullStr | Dynamic Stability of the Periodic and Aperiodic Structures of the Bernoulli-Euler Beams |
| title_full_unstemmed | Dynamic Stability of the Periodic and Aperiodic Structures of the Bernoulli-Euler Beams |
| title_short | Dynamic Stability of the Periodic and Aperiodic Structures of the Bernoulli-Euler Beams |
| title_sort | dynamic stability of the periodic and aperiodic structures of the bernoulli euler beams |
| topic | beam dynamic stability mathieu equation aperiodic structure |
| url | https://journals.pan.pl/Content/130947/PDF/AMM-2024-1-45-Garus.pdf |
| work_keys_str_mv | AT jgarus dynamicstabilityoftheperiodicandaperiodicstructuresofthebernoullieulerbeams AT jpetru dynamicstabilityoftheperiodicandaperiodicstructuresofthebernoullieulerbeams AT wsochacki dynamicstabilityoftheperiodicandaperiodicstructuresofthebernoullieulerbeams AT sgarus dynamicstabilityoftheperiodicandaperiodicstructuresofthebernoullieulerbeams |