Analysis of Complex Modal Characteristics of Fractional Derivative Viscoelastic Rotating Beams
For the transverse vibration problem of a fractional derivative viscoelastic rotating beam, the differential equation of the system is obtained based on the Euler–Bernoulli beam theory and Hamilton principle. Then, introducing dimensionless quantities to differential equations and boundary condition...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2019/5715694 |
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| author | Tianle Lu Zhongmin Wang Dongdong Liu |
| author_facet | Tianle Lu Zhongmin Wang Dongdong Liu |
| author_sort | Tianle Lu |
| collection | DOAJ |
| description | For the transverse vibration problem of a fractional derivative viscoelastic rotating beam, the differential equation of the system is obtained based on the Euler–Bernoulli beam theory and Hamilton principle. Then, introducing dimensionless quantities to differential equations and boundary conditions, the generalized complex eigenvalue equations of the system are obtained by the differential quadrature method. The effects of the slenderness ratio, the viscoelastic ratio, the hub radius-beam length ratio, and dimensionless hub speed and fractional order on the vibration characteristics of fractional derivative viscoelastic rotating beams are discussed by numerical examples. Numerical calculations show that when the dimensionless hub speed is constant, the real part of complex frequency increases with the increase of the fractional order, and the higher-order growth trend is more obvious. Through the study of displacement response at different points on the beam, it can be seen that the closer to the free end, the larger the response amplitude. And, the amplitude of response has been attenuated, which is also consistent with the vibration law of free vibration considering damping. |
| format | Article |
| id | doaj-art-0af09fd2bae44abd88a253d92b66f75d |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-0af09fd2bae44abd88a253d92b66f75d2025-02-03T06:11:26ZengWileyShock and Vibration1070-96221875-92032019-01-01201910.1155/2019/57156945715694Analysis of Complex Modal Characteristics of Fractional Derivative Viscoelastic Rotating BeamsTianle Lu0Zhongmin Wang1Dongdong Liu2School of Civil Engineering and Architecture, Xi’an University of Technology, 710048 Xi’an, ChinaSchool of Civil Engineering and Architecture, Xi’an University of Technology, 710048 Xi’an, ChinaSchool of Civil Engineering and Architecture, Xi’an University of Technology, 710048 Xi’an, ChinaFor the transverse vibration problem of a fractional derivative viscoelastic rotating beam, the differential equation of the system is obtained based on the Euler–Bernoulli beam theory and Hamilton principle. Then, introducing dimensionless quantities to differential equations and boundary conditions, the generalized complex eigenvalue equations of the system are obtained by the differential quadrature method. The effects of the slenderness ratio, the viscoelastic ratio, the hub radius-beam length ratio, and dimensionless hub speed and fractional order on the vibration characteristics of fractional derivative viscoelastic rotating beams are discussed by numerical examples. Numerical calculations show that when the dimensionless hub speed is constant, the real part of complex frequency increases with the increase of the fractional order, and the higher-order growth trend is more obvious. Through the study of displacement response at different points on the beam, it can be seen that the closer to the free end, the larger the response amplitude. And, the amplitude of response has been attenuated, which is also consistent with the vibration law of free vibration considering damping.http://dx.doi.org/10.1155/2019/5715694 |
| spellingShingle | Tianle Lu Zhongmin Wang Dongdong Liu Analysis of Complex Modal Characteristics of Fractional Derivative Viscoelastic Rotating Beams Shock and Vibration |
| title | Analysis of Complex Modal Characteristics of Fractional Derivative Viscoelastic Rotating Beams |
| title_full | Analysis of Complex Modal Characteristics of Fractional Derivative Viscoelastic Rotating Beams |
| title_fullStr | Analysis of Complex Modal Characteristics of Fractional Derivative Viscoelastic Rotating Beams |
| title_full_unstemmed | Analysis of Complex Modal Characteristics of Fractional Derivative Viscoelastic Rotating Beams |
| title_short | Analysis of Complex Modal Characteristics of Fractional Derivative Viscoelastic Rotating Beams |
| title_sort | analysis of complex modal characteristics of fractional derivative viscoelastic rotating beams |
| url | http://dx.doi.org/10.1155/2019/5715694 |
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