Modified Multi-level Residue Harmonic Balance Method for Solving Nonlinear Vibration Problem of Beam Resting on Nonlinear Elastic Foundation
Modified Multi-level Residue Harmonic Balance Method for Solving Nonlinear Vibration Problem of Beam Resting on Nonlinear Elastic Foundation
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DOI：
10.22055/jacm.2018.26729.1352
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发表时间：
2019-06
影响因子：
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通讯作者：
Md. Saifur Rahman;A. S. M. Hasan;I. A. Yeasmin
中科院分区：
文献类型：
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作者：
Md. Saifur Rahman;A. S. M. Hasan;I. A. Yeasmin
梁的非线性振动行为是结构工程的一个重要问题。在本研究中，提出了基于非线性弹性地基的欧拉-伯努利梁受迫非线性振动的数学模型。采用改进的多级剩余谐波平衡法研究了梁的非线性振动行为。该方法的主要优点是在每个解级别仅生成一个非线性代数方程。使用新方法的计算时间比求解经典调和平衡方法中生成的一组非线性代数方程所花费的计算时间要少得多。此外，新方法可以生成以前的多级剩余谐波平衡方法忽略的更高级别的非线性解。将所提方法得到的结果与经典谐波平衡方法得到的结果进行比较，验证了该方法的准确性，表明所提方法与经典谐波平衡方法之间具有良好的一致性。此外，还考察了激励幅度、线性和非线性地基刚度、剪切刚度等各种参数对非线性振动行为的影响
Nonlinear vibration behavior of beam is an important issue of structural engineering. In this study, a mathematical modeling of a forced nonlinear vibration of Euler-Bernoulli beam resting on nonlinear elastic foundation is presented. The nonlinear vibration behavior of the beam is investigated by using a modified multi-level residue harmonic balance method. The main advantage of the method is that only one nonlinear algebraic equation is generated at each solution level. The computational time of using the new method is much less than that spent on solving the set nonlinear algebraic equations generated in the classical harmonic balance method. Besides the new method can generate higher-level nonlinear solutions neglected by previous multi-level residue harmonic balance methods. The results obtained from the proposed method compared with those obtained by a classical harmonic balance method to verify the accuracy of the method which shows good agreement between the proposed and classical harmonic balance method. Besides, the effect of various parameters such as excitation magnitude, linear and nonlinear foundation stiffness, shearing stiffness etc. on the nonlinear vibration behaviors are examined