Primary resonance of traveling viscoelastic beam under internal resonance

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• 作者：Hu Ding ; Linglu Huang ; Xiaoye Mao ; Liqun Chen
• 关键词：Key wordstraveling beam ; nonlinear vibration ; viscoelasticity ; primary resonance ; internal resonance
• 刊名：Applied Mathematics and Mechanics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：38
• 期：1
• 页码：1-14
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Applications of Mathematics; Classical Mechanics; Mathematical Modeling and Industrial Mathematics;
• 出版者：Shanghai University
• ISSN：1573-2754
• 卷排序：38

文摘

Under the 3:1 internal resonance condition, the steady-state periodic response of the forced vibration of a traveling viscoelastic beam is studied. The viscoelastic behaviors of the traveling beam are described by the standard linear solid model, and the material time derivative is adopted in the viscoelastic constitutive relation. The direct multi-scale method is used to derive the relationships between the excitation frequency and the response amplitudes. For the first time, the real modal functions are employed to analytically investigate the periodic response of the axially traveling beam. The undetermined coefficient method is used to approximately establish the real modal functions. The approximate analytical results are confirmed by the Galerkin truncation. Numerical examples are presented to highlight the effects of the viscoelastic behaviors on the steady-state periodic responses. To illustrate the effect of the internal resonance, the energy transfer between the internal resonance modes and the saturation-like phenomena in the steady-state responses is presented.