Periodic Responses of a Rotating Hub-Beam System with a Tip Mass under Gravity Loads by the Incremental Harmonic Balance Method
Dynamic characteristics of a flexible hub-beam system with a tip mass under gravity loads are investigated. The slope angle of the centroid line of the beam is utilized to describe its motion. Hamilton’s principle is used to derive the equations of motion and their boundary conditions. By using Lagr...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2018/8178274 |
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| author | D. W. Zhang J. K. Liu J. L. Huang W. D. Zhu |
| author_facet | D. W. Zhang J. K. Liu J. L. Huang W. D. Zhu |
| author_sort | D. W. Zhang |
| collection | DOAJ |
| description | Dynamic characteristics of a flexible hub-beam system with a tip mass under gravity loads are investigated. The slope angle of the centroid line of the beam is utilized to describe its motion. Hamilton’s principle is used to derive the equations of motion and their boundary conditions. By using Lagrange’s equations, spatially discretized equations based on assumed mode method are derived, and the equations of motion are expressed in nondimensional matrix form. The incremental harmonic balance (IHB) method is used to solve for periodic responses of a high-dimensional model of the rotating hub-beam system with a tip mass for which convergence is reached. A frequency equation is derived giving the relationship between the nondimensional natural frequencies and three nondimensional parameters, that is, the rotating angular velocity, the tip mass, and the hub radius ratio. A comparative study is performed for nonlinear frequency responses of the system with a tip mass under different values of tip masses and damping ratios. |
| format | Article |
| id | doaj-art-4cfba3e7e4584b868dde9ca74b53318c |
| institution | OA Journals |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-4cfba3e7e4584b868dde9ca74b53318c2025-08-20T02:38:38ZengWileyShock and Vibration1070-96221875-92032018-01-01201810.1155/2018/81782748178274Periodic Responses of a Rotating Hub-Beam System with a Tip Mass under Gravity Loads by the Incremental Harmonic Balance MethodD. W. Zhang0J. K. Liu1J. L. Huang2W. D. Zhu3Department of Applied Mechanics and Engineering, Sun Yat-sen University, Guangzhou 510275, ChinaDepartment of Applied Mechanics and Engineering, Sun Yat-sen University, Guangzhou 510275, ChinaDepartment of Applied Mechanics and Engineering, Sun Yat-sen University, Guangzhou 510275, ChinaDepartment of Mechanical Engineering, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USADynamic characteristics of a flexible hub-beam system with a tip mass under gravity loads are investigated. The slope angle of the centroid line of the beam is utilized to describe its motion. Hamilton’s principle is used to derive the equations of motion and their boundary conditions. By using Lagrange’s equations, spatially discretized equations based on assumed mode method are derived, and the equations of motion are expressed in nondimensional matrix form. The incremental harmonic balance (IHB) method is used to solve for periodic responses of a high-dimensional model of the rotating hub-beam system with a tip mass for which convergence is reached. A frequency equation is derived giving the relationship between the nondimensional natural frequencies and three nondimensional parameters, that is, the rotating angular velocity, the tip mass, and the hub radius ratio. A comparative study is performed for nonlinear frequency responses of the system with a tip mass under different values of tip masses and damping ratios.http://dx.doi.org/10.1155/2018/8178274 |
| spellingShingle | D. W. Zhang J. K. Liu J. L. Huang W. D. Zhu Periodic Responses of a Rotating Hub-Beam System with a Tip Mass under Gravity Loads by the Incremental Harmonic Balance Method Shock and Vibration |
| title | Periodic Responses of a Rotating Hub-Beam System with a Tip Mass under Gravity Loads by the Incremental Harmonic Balance Method |
| title_full | Periodic Responses of a Rotating Hub-Beam System with a Tip Mass under Gravity Loads by the Incremental Harmonic Balance Method |
| title_fullStr | Periodic Responses of a Rotating Hub-Beam System with a Tip Mass under Gravity Loads by the Incremental Harmonic Balance Method |
| title_full_unstemmed | Periodic Responses of a Rotating Hub-Beam System with a Tip Mass under Gravity Loads by the Incremental Harmonic Balance Method |
| title_short | Periodic Responses of a Rotating Hub-Beam System with a Tip Mass under Gravity Loads by the Incremental Harmonic Balance Method |
| title_sort | periodic responses of a rotating hub beam system with a tip mass under gravity loads by the incremental harmonic balance method |
| url | http://dx.doi.org/10.1155/2018/8178274 |
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