Study of nonlinear vibration of Euler-Bernoulli beams by using analytical approximate techniques

Bagheri S.; Nikkar A.; Ghaffarzadeh H.

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Study of nonlinear vibration of Euler-Bernoulli beams by using analytical approximate techniques

机译：应用解析近似技术研究Euler-Bernoulli梁的非线性振动

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In this paper, nonlinear responses of a clamped-clamped buckled beam are investigated. Two efficient and easy mathematical techniques called He's Variational Approach and Laplace Iteration Method are used to solve the governing differential equation of motion. To assess the accuracy of solutions, we compare the results with the Runge-Kutta 4th order. The results show that both methods can be easily extended to other nonlinear oscillations and it can be predicted that both methods can be found widely applicable in engineering and physics.

机译：在本文中，研究了一种夹固式弯折梁的非线性响应。两种有效且简便的数学技术分别称为He's Variational方法和Laplace迭代方法，用于求解运动的控制微分方程。为了评估解决方案的准确性，我们将结果与Runge-Kutta四阶比较。结果表明，这两种方法都可以很容易地扩展到其他非线性振荡，并且可以预测，这两种方法可以广泛地应用于工程和物理领域。

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《Latin American Journal of Solids and Structures》 |2014年第1期|共12页
作者
Bagheri S.; Nikkar A.; Ghaffarzadeh H.;
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中图分类土力学、地基基础工程;
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1. An Analytical Study of Nonlinear Vibrations of Buckled Euler-Bernoulli Beams [J] . I. Pakar, M. Bayat Acta Physica Polonica . 2013,第1期

机译：屈曲Euler-Bernoulli梁非线性振动的解析研究
2. Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams [J] . Jafari S.S., Rashidi M.M., Johnson S. Latin American Journal of Solids and Structures . 2016,第7期

机译：Euler-Bernoulli梁的非线性振动的解析近似
3. Approximate analytical solutions for the nonlinear free vibrations of composite beams in buckling [J] . Samir A. Emam Composite Structures . 2013,第juna期

机译：屈曲组合梁非线性自由振动的近似解析解。
4. GEOMETRICALLY NONLINEAR FORCED VIBRATIONS OF MULTIPLE-STEPPED EULER-BERNOULLI BEAMS [C] . I. El Hantati, A. Adri, H. Fakhreddine International Conference on Structural Dynamics . 2020

机译：几何非线性强制振动多阶梯式欧拉伯尔努利梁
5. Nonlinear vibration of beam structures: Analytical and explicit dynamics FEA evaluations. [D] . Mei, Kuiyin. 2000

机译：梁结构的非线性振动：分析和显式动力学有限元分析。
6. A new multistage technique for approximate analytical solution of nonlinear differential equations [O] . Saheed Ojo Akindeinde 2020

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7. A semi-analytical method for nonlinear vibration of Euler-Bernoulli beams with general boundary conditions [O] . Jianshe P, Liu Y, Yang J 2010

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8. Hybrid Analytical Technique for Evaluating the Sensitivity of the Nonlinear Vibrational Response of Beams [R] . Noor, A. K., Hadian, M. J., Andersen, C. M. 1993

机译：用于评估梁非线性振动响应灵敏度的混合分析技术

Study of nonlinear vibration of Euler-Bernoulli beams by using analytical approximate techniques

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