Free Vibration Analysis of Quintic Nonlinear Beams using Equivalent Linearization Method with a Weighted Averaging
Free Vibration Analysis of Quintic Nonlinear Beams using Equivalent Linearization Method with a Weighted Averaging
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DOI：
10.22055/jacm.2018.24919.1217
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发表时间：
2019
影响因子：
--
通讯作者：
D. Hieu;N. Hai
中科院分区：
文献类型：
--
作者：
D. Hieu;N. Hai
本文采用Anh（2015）提出的加权平均等效线性化方法，分析了五次非线性欧拉-伯努利梁在轴向载荷作用下的横向振动。该方法不需要方程中存在非线性问题难以找到的小参数。近似解为简谐振荡，并与解析解和精确解进行了比较。比较表明了所提解决方案的准确性。研究了非线性项对梁动力特性的影响以及初始振幅对梁频率的影响。此外，还研究了轴向力和梁长对频率的影响。
In this paper, the equivalent linearization method with a weighted averaging proposed by Anh (2015) is applied to analyze the transverse vibration of quintic nonlinear Euler-Bernoulli beams subjected to axial loads. The proposed method does not require small parameter in the equation which is difficult to be found for nonlinear problems. The approximate solutions are harmonic oscillations, which are compared with the previous analytical solutions and the exact solutions. Comparisons show the accuracy of the present solutions. The impact of nonlinear terms on the dynamical behavior of beams and the effect of the initial amplitude on frequencies of beams are investigated. Furthermore, the effect of the axial force and the length of beams on frequencies are studied.