A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives
We conduct a detailed study and comparison for the one-degree-of-freedom steady-state vibrations under harmonic driving with a single fractional-order derivative and a distributed-order derivative. For each of the two vibration systems, we consider the stiffness contribution factor and damping contr...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2017-12-01
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| Series: | Open Physics |
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| Online Access: | https://doi.org/10.1515/phys-2017-0095 |
| _version_ | 1818730294774071296 |
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| author | Duan Jun-Sheng Cheng Cui-Ping Chen Lian |
| author_facet | Duan Jun-Sheng Cheng Cui-Ping Chen Lian |
| author_sort | Duan Jun-Sheng |
| collection | DOAJ |
| description | We conduct a detailed study and comparison for the one-degree-of-freedom steady-state vibrations under harmonic driving with a single fractional-order derivative and a distributed-order derivative. For each of the two vibration systems, we consider the stiffness contribution factor and damping contribution factor of the term of fractional derivatives, the amplitude and the phase difference for the response. The effects of driving frequency on these response quantities are discussed. Also the influences of the order α of the fractional derivative and the parameter γ parameterizing the weight function in the distributed-order derivative are analyzed. Two cases display similar response behaviors, but the stiffness contribution factor and damping contribution factor of the distributed-order derivative are almost monotonic change with the parameter γ, not exactly like the case of single fractional-order derivative for the order α. The case of the distributed-order derivative provides us more options for the weight function and parameters. |
| first_indexed | 2024-12-17T22:59:30Z |
| format | Article |
| id | doaj.art-0594fd4cb26f41cc927ae27fa3119469 |
| institution | Directory Open Access Journal |
| issn | 2391-5471 |
| language | English |
| last_indexed | 2024-12-17T22:59:30Z |
| publishDate | 2017-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Physics |
| spelling | doaj.art-0594fd4cb26f41cc927ae27fa31194692022-12-21T21:29:27ZengDe GruyterOpen Physics2391-54712017-12-0115180981810.1515/phys-2017-0095phys-2017-0095A comparison study of steady-state vibrations with single fractional-order and distributed-order derivativesDuan Jun-Sheng0Cheng Cui-Ping1Chen Lian2School of Sciences, Shanghai Institute of Technology, Shanghai201418, P.R. ChinaSchool of Sciences, Shanghai Institute of Technology, Shanghai201418, P.R. ChinaSchool of Sciences, Shanghai Institute of Technology, Shanghai201418, P.R. ChinaWe conduct a detailed study and comparison for the one-degree-of-freedom steady-state vibrations under harmonic driving with a single fractional-order derivative and a distributed-order derivative. For each of the two vibration systems, we consider the stiffness contribution factor and damping contribution factor of the term of fractional derivatives, the amplitude and the phase difference for the response. The effects of driving frequency on these response quantities are discussed. Also the influences of the order α of the fractional derivative and the parameter γ parameterizing the weight function in the distributed-order derivative are analyzed. Two cases display similar response behaviors, but the stiffness contribution factor and damping contribution factor of the distributed-order derivative are almost monotonic change with the parameter γ, not exactly like the case of single fractional-order derivative for the order α. The case of the distributed-order derivative provides us more options for the weight function and parameters.https://doi.org/10.1515/phys-2017-0095fractional calculusvibrationdistributed-order derivativeexcitationresponse02.30.hq46.40.-f83.60.bc |
| spellingShingle | Duan Jun-Sheng Cheng Cui-Ping Chen Lian A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives Open Physics fractional calculus vibration distributed-order derivative excitation response 02.30.hq 46.40.-f 83.60.bc |
| title | A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives |
| title_full | A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives |
| title_fullStr | A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives |
| title_full_unstemmed | A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives |
| title_short | A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives |
| title_sort | comparison study of steady state vibrations with single fractional order and distributed order derivatives |
| topic | fractional calculus vibration distributed-order derivative excitation response 02.30.hq 46.40.-f 83.60.bc |
| url | https://doi.org/10.1515/phys-2017-0095 |
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