| 轴向受力屈曲梁弱受迫振动的稳态响应 |
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| 引用本文： | 王昊,张艳雷,陈立群.轴向受力屈曲梁弱受迫振动的稳态响应[J].上海大学学报(自然科学版),2014,20(3):348-354. |
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| 作者姓名： | 王昊 张艳雷 陈立群 |
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| 作者单位： | 1. 上海大学上海市应用数学和力学研究所, 上海200072; 2. 上海第二工业大学机电工程学院, 上海201209;
3. 上海大学理学院, 上海200444; 4. 上海市力学在能源工程中的应用重点实验室, 上海200072 |
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| 基金项目： | 国家自然科学基金资助项目(11232009); 上海市重点学科建设资助项目(S30106) |
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| 摘 要： | 研究了均匀各向同性黏弹性梁的横向非线性振动, 该梁在支承两端受到一对轴向压力的作用而发生屈曲, 同时还受到横向简谐激励作用. 通过对屈曲梁的控制方程作坐标变换, 导出了以屈曲平衡位形为坐标轴的扰动方程. 在两端简支边界条件下, 运用Galerkin 方法将其离散化为多自由度非线性振动系统. 在存在内共振的情况下, 应用多尺度法计算得到弱受迫振动时前两阶模态的幅频响应曲线, 并发现了带有平方非线性项的系统所特有的饱和现象.
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| 关 键 词： | 饱和现象 幅频特性 黏弹性梁 屈曲 受迫振动 非线性 |
| 收稿时间： | 2013-03-29 |
Steady-State Response of Weakly Forced Vibration for a Buckling Beam under Axial Press |
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| WANG Hao,ZHANG Yan-lei,CHEN Li-qun.Steady-State Response of Weakly Forced Vibration for a Buckling Beam under Axial Press[J].Journal of Shanghai University(Natural Science),2014,20(3):348-354. |
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| Authors: | WANG Hao ZHANG Yan-lei CHEN Li-qun |
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| Affiliation: | 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
2. College of Mechanical and Electrical Engineering, Shanghai Second Polytechnic University, Shanghai 201209, China;
3. College of Sciences, Shanghai University, Shanghai 200444, China;
4. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai 200072, China |
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| Abstract: | A nonlinear analysis of the response of a simply-supported viscoelastic buckled beam to a couple of constant axial force and harmonic excitation is resented. The disturbance equation of transverse vibration of the buckled beam is derived from the free governing equation via a coordinate transform. The Galerkin method is applied to truncate the systems to a multiple degrees-of-freedom of nonlinear vibration system. In the presence of internal resonances, a method of multiple scales is developed to obtain the steady-state relationship between the amplitudes in the first two resonant modes in weak forced, and reveal a unique saturation phenomenon in nonlinear system with quadratic items. |
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| Keywords: | amplitude-frequency characteristics buckled forced vibration saturation phenomenon viscoelastic beam nonlinear |
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