| Complex-mode Galerkin approach in transverse vibration of an axially accelerating viscoelastic string |
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| 作者姓名： | 张能辉 王建军 程昌钧 |
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| 作者单位： | Department of Mechanics Shanghai University Shanghai 200444 P. R. China，Shanghai Institute of Applied Mathematics and Mechanics，Shanghai University Shanghai 200072 P. R. China，Department of Mechanics Shanghai University Shanghai 200444 P. R. China，Department of Mechanics Shanghai University Shanghai 200444 P. R. China Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 P. R. China |
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| 基金项目： | 国家自然科学基金;上海市重点学科建设项目;上海市自然科学基金;上海市教委杰出青年基金 |
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| 摘 要： | Under the consideration of harmonic fluctuations of initial tension and axially velocity, a nonlinear governing equation for transverse vibration of an axially accelerating string is set up by using the equation of motion for a 3-dimensional deformable body with initial stresses. The Kelvin model is used to describe viscoelastic behaviors of the material. The basis function of the complex-mode Galerkin method for axially accelerating nonlinear strings is constructed by using the modal function of linear moving strings with constant axially transport velocity. By the constructed basis functions, the application of the complex-mode Galerkin method in nonlinear vibration analysis of an axially accelerating viscoelastic string is investigated. Numerical results show that the convergence velocity of the complex-mode Galerkin method is higher than that of the real-mode Galerkin method for a variable coefficient gyroscopic system.
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| 关 键 词： | 轴向加速弦线 粘弹性 横向振动 几何非线性特性 复合模Galerkin法 |
| 收稿时间： | 2005-10-21 |
| 修稿时间： | 2006-09-14 |
Complex-mode Galerkin approach in transverse vibration of an axially accelerating viscoelastic string |
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| Zhang?Neng-hui,Wang?Jian-jun,Cheng?Chang-jun.Complex-mode Galerkin approach in transverse vibration of an axially accelerating viscoelastic string[J].Applied Mathematics and Mechanics(English Edition),2007,28(1):1-9. |
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| Authors: | Zhang Neng-hui Wang Jian-jun Cheng Chang-jun |
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| Institution: | 1. Department of Mechanics, Shanghai University, Shanghai 200444, P. R. China;Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University, Shanghai 200072, P. R. China
2. Department of Mechanics, Shanghai University, Shanghai 200444, P. R. China |
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| Abstract: | Under the consideration of harmonic fluctuations of initial tension and axially velocity, a nonlinear governing equation for transverse vibration of an axially accelerating string is set up by using the equation of motion for a 3-dimensional deformable body with initial stresses. The Kelvin model is used to describe viscoelastic behaviors of the material. The basis function of the complex-mode Galerkin method for axially accelerating nonlinear strings is constructed by using the modal function of linear moving strings with constant axially transport velocity. By the constructed basis functions, the application of the complex-mode Galerkin method in nonlinear vibration analysis of an axially accelerating viscoelastic string is investigated. Numerical results show that the convergence velocity of the complex-mode Galerkin method is higher than that of the real-mode Galerkin method for a variable coefficient gyroscopic system. |
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| Keywords: | axially accelerating string viscoelasticity transverse nonlinear vibration complex-mode Galerkin method geometry nonlinearity |
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