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Nonlinear free vibration of damped and undamped bi-directional functionally graded beams using a cubic-quintic nonlinear model
Composite Structures ( IF 6.3 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.compstruct.2020.112866 Mostafa Mohammadian
Composite Structures ( IF 6.3 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.compstruct.2020.112866 Mostafa Mohammadian
Abstract In this paper, a novel higher order cubic-quintic nonlinear model is proposed for the nonlinear free vibration of damped and undamped bi-directional functionally graded (2D FG) beams. To the best of the researchers’ knowledge, no study has focused on damping characteristics of 2D FG beams. Thus, the present paper extends the previous studies in this field. It is assumed that the material properties of the beam change in the axial and lateral directions simultaneously according to exponential and power-law functions, respectively. A new neutral surface is defined to remove the stretching and bending couplings effect. The variational iteration method (VIM) and the Hamiltonian approach (HA) are applied to obtain closed-form analytical solutions for the nonlinear vibration of damped and undamped 2D FG beams, respectively. Based on the results, an increase in the material grading indices can similarly decrease the damping coefficient for an underdamped 2D FG beam, and more time is required for dying out the oscillations. Further, compared to the homogeneous beams, a significant difference is observed between the cubic and cubic-quintic models indicating the importance of applying higher order nonlinear models for the nonlinear analysis of 2D FG beams.
中文翻译:
使用三次-五次非线性模型的阻尼和无阻尼双向功能梯度梁的非线性自由振动
摘要 本文针对有阻尼和无阻尼双向功能梯度(2D FG)梁的非线性自由振动问题,提出了一种新的高阶三次-五次非线性模型。据研究人员所知,目前还没有研究关注 2D FG 梁的阻尼特性。因此,本文扩展了先前在该领域的研究。假设梁的材料特性分别根据指数函数和幂律函数在轴向和横向同时变化。定义了一个新的中性表面以消除拉伸和弯曲耦合效应。应用变分迭代法 (VIM) 和哈密顿方法 (HA) 分别获得阻尼和无阻尼二维 FG 梁非线性振动的闭式解析解。根据结果,材料分级指数的增加同样可以降低欠阻尼 2D FG 梁的阻尼系数,并且需要更多时间来消除振荡。此外,与均匀梁相比,在三次和三次-五次模型之间观察到显着差异,表明应用高阶非线性模型对 2D FG 梁进行非线性分析的重要性。
更新日期:2021-01-01
中文翻译:
使用三次-五次非线性模型的阻尼和无阻尼双向功能梯度梁的非线性自由振动
摘要 本文针对有阻尼和无阻尼双向功能梯度(2D FG)梁的非线性自由振动问题,提出了一种新的高阶三次-五次非线性模型。据研究人员所知,目前还没有研究关注 2D FG 梁的阻尼特性。因此,本文扩展了先前在该领域的研究。假设梁的材料特性分别根据指数函数和幂律函数在轴向和横向同时变化。定义了一个新的中性表面以消除拉伸和弯曲耦合效应。应用变分迭代法 (VIM) 和哈密顿方法 (HA) 分别获得阻尼和无阻尼二维 FG 梁非线性振动的闭式解析解。根据结果,材料分级指数的增加同样可以降低欠阻尼 2D FG 梁的阻尼系数,并且需要更多时间来消除振荡。此外,与均匀梁相比,在三次和三次-五次模型之间观察到显着差异,表明应用高阶非线性模型对 2D FG 梁进行非线性分析的重要性。